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  • Ric Crossman

5.1.9 The Pleasure Principle

Updated: May 7, 2022

Prime Factors

Janeway takes great interest in Gath's low-cut top.
"My eyes are up here."

Shh, don’t worry. No need to be scared. It was bound to happen sometime, with a franchise that flirts with science as often as this one. We’ve finally reached an episode in which mathematics is so important, it features in the actual title.

It’s time for me to ply my trade.

Secrets Unlocked

I realise the threat of another maths-heavy installment of IDFC might have more than a few of you heading for the white cross on the red background. I’m talking about closing your browser window, obviously, rather than moving to Switzerland. I guess it depends how much you hate sums, though – if you want to hide in the Alps to avoid a little light mathematics, that’s your own business. But none of this is my fault, you know. Aside from the obvious pun regarding this episode’s link to the Prime Directive (a link which is actually much weaker than I’d remembered), this episode’s title is most obviously a reference to a fundamental mathematical theorem. It’s known as the Unique-Prime-Factorisation theorem (or, less humbly, the Fundamental Theorem of Arithmetic), and at heart it’s pretty simple. Honest.

The sum total of the FTA – as we cool mathmos call it – is that every whole number greater than 1 is either a prime number, or is equal to a unique list of prime numbers multiplied together. So 2 and 3 are prime numbers, as is 5. 4 isn’t a prime number, but you can make 4 by multiplying prime numbers together in exactly one way: 2 x 2.

All of which makes intuitive sense, I think. If a number isn’t a prime, there must be some other number bigger than 1 that divides it. If that’s the case, you can break the number up into two smaller numbers that multiply together to give the original number. But then each of those numbers is either prime, or they can be divided by some number bigger than one. So you break up those numbers in the same way, if you can. Then you check whether those numbers can be broken up into two, and so on, until eventually you’re left with no more numbers you can break up into two. At that point, what you’re left with is the prime factorisation of the original number.

A quick example might be helpful. Let’s find the prime factorisation of 100. We know we can divide 100 by 2, leaving 50. That’s equivalent to saying 2 x 50 = 100. Now, 2 is prime, as I’ve noted. 50 isn’t, though, there are numbers other than 1 and 50 that divide it. Let’s go with 5, for the sake of argument. 50 divided by 5 is 10, and so 5 x 10 = 50. 5 is prime, but 10 isn’t. But 10 is equal to 2 x 5, and at that point, we can’t break up any more numbers. We have our prime factorisation. In brief, 100 = 2 x 50 = 2 x 5 x 10 = 2 x 5 x 2 x 5.

Note we can use different divisors and get to the same result. 100 = 10 x 10 = 2 x 5 x 2 x 5, for instance.

(All this, by the way, is one reason to not consider 1 a prime number. It shares the property with all prime numbers that it can only be divided by itself and 1. But we exclude it from the definition because if we didn’t, the Fundamental Theorem of Arithmetic wouldn’t work anymore. You could find 4 not just with 2 x 2, but with 2 x 2 x 1, and 2 x 2 x 1 x 1, and so on. Huge swathes of tremendously important mathematical work would collapse instantly. This is something we’re keen to avoid, in general.)

But so, as the saying goes, what? Well, this theorem can be pretty useful in a lot of surprising areas. Take encryption. If you have two very large prime numbers (and at time of writing the largest prime number we’ve found so far has almost twenty-five million digits), the number you get by multiplying them together is unimaginably vast. If you know the two original numbers, though, you can calculate that number really fast, thanks to microchips and suchlike. On the other hand, say all you have is the final number. In that case, working out the two values you multiplied together to get it is actually massively difficult, even for a decent computer. You can therefore use the larger number as part of an encryption system. That number functions as the lock, and the primes multiplied to get that lock provide the key. Delightful.

(The film Cube relied on this idea for one of its late-stage twists, though it did so in a profoundly stupid way that made me sad.)

OK sure, you say, but still. So. What? How does this factor (no apologies!) into the actual episode? Trust me, there is a link. What is important here is that a number’s prime factors are its fundamental building blocks. You can’t break them down any further, and between them they tell you everything about the number itself. “Prime Factors” seems to want to borrow this idea, and apply it to rather less arithmetical identities. After all, every culture – and every person within them – exists as a unique set of individual characteristics. Sometimes a culture – or a person – will meet others that share some, many, or even most of the same idiosyncrasies. They will never be the exact same properties in the exact same amounts, though. They can’t be. Especially since these fundamental properties are as infinite in number as are the primes themselves.

“A Spoonful Of Sugar”

At its core, this story explores the prime factors of the Federation by comparing them with those of the Sikarians. Which is a smart move. As I’ve discussed before, much of the interstellar interactions Star Trek features involve either far less or far more technologically advanced cultures. Actual parity comes along comparatively rarely, and when it does, it’s often framed as threatening (which is both interesting and concerning, but a topic for another time). The unique circumstances of USS Voyager allow for something else; searches for common ground that stem from something other than immediate danger. “Prime Factors” gets to explore how the Sikarians differ from the Federation without having to threaten that those differences will lead to a body count. In doing so, it offers commentary on the Federation itself in a way any other Trek show would struggle to. By identifying the areas of difference between this new society and one we’re familiar with, we see the latter in an entirely new way.

So where do those differences exist? Which are the prime factors Starfleet doesn’t share with the Sikarians?

It’s easiest to tackle those questions by starting with those factors which are common to both. Given both their impressive technological level and their (apparent) largess, it seems likely that, like the Federation, the Sikarians are a post-scarcity society. Additionally, they seem to share Starfleet’s habit of flying the space-lanes looking for aliens to be nice to. The most obvious difference seems to be in how those voyages have impacted upon the surrounding space. Despite their ability to visit an entire quarter of the galaxy, the Sikarians have clearly left far less of an interstellar footprint than that of the Federation. Hell, it’s likely less than the Kazon have managed, and they had to be designed as slightly rubbish just to make the show work.

Where does this difference stem from, though? How is it the Federation expanded so successfully across ten percent of the galaxy or so, while the Sikarians seem to have folded in on themselves? It doesn’t seem to be a dislike of exploration in itself. Even if the Sikarians get their travel tips (one more form of story, of course) from others, rather than mounting expeditions themselves, it would be difficult to square away Eudana’s love of casting herself across a third of the galaxy with a distaste for new locations. Plus, for all that Gath frames his ship’s rendezvous with Voyager as a mission of mercy, it’s also clearly a voyage of discovery. They certainly aren’t an insular people, either, as Gath’s scheme to integrate Janeway and her crew into Sikarian society makes clear.

It’s not an aversion to either new locations or new species that has prevented the Sikarians from forging an expansive interstellar society, then. The limiting factor, as Janeway herself points out, seems to be an aversion to permanence. Gath’s people aren’t settlers, they’re tourists.

This is symptom, though, not cause. The Sikarians are a species obsessed with pleasure, and this focus seems to prevent them grasping the concept of deferred gratification. This indeed is essentially the only way to avoid the conclusion the episode is suggesting long-term relationships aren’t any fun. It isn’t the destination Gath has a problem with, so much as the likelihood of speed-bumps along the way. Of course the Sikarians found a way to transport themselves 40 000 light-years. It was the only way to get the fun of arrival without the drudgery of travel.

Perhaps the most important insight we get into this culture is Eudana’s atmospheric sensor. Designing such a device to mimic a musical instrument is a triumph both of technology and imagination, sure. It also suggests though that the Sikarians can’t even perform a basic task like checking the weather without needing to be entertained throughout. This is the Mary Poppins approach to tolerating otherwise boring tasks. It doesn’t matter how necessary the medicine is, it’s not going down unsweetened.

And hey, fair enough. Prophets know, if there’s anything you can do to make your job more fun you should absolutely go for it. This world is bleak enough. That said, there’s a difference between striving to make a task entertaining, and requiring entertainment as a condition for doing it. Presumably the reason Voyager never encounters a Sikarian colony from this point on is that they don’t exist, because they just wouldn’t be fun enough to set one up. A new world to explore and enjoy is a fine thing, once you’ve got a nice comfy city sporting all mod cons to head home to at the end of the day. Actually building such a settlement would be damn hard graft, though, and offer minimal opportunities for whimsy. The only spoonfuls of sugar would be those going in the builder’s tea.

This, then, is where the Federation and the Sikarians differ in their prime factors. The UFP, as a general rule, understands that sometimes someone is going to have to roll their sleeves up and do something they won’t enjoy, because of what it will lead to. The central focus of Federation society is on self-improvement and maximising one’s potential. That can’t be strawberries and cream every minute of every day, right?

“Have A Good Time ALL The Time”

If this were the sum total of the episode’s insights, that might be enough. But there’s more. This isn’t just about how these two cultures differ, but what their similarities reveal. Let’s talk about the running of Sikarian society. It’s not hard to guess how they managed to reach their current level of development – presumably all the sweat of getting there happened before they switched to their current philosophy. Even given that, though, there have to be some tasks on Sikaria that simply can’t be made pleasurable. Clearing debris out of the city sewers is going to be a lousy job no matter how many flat-screen televisions you put along the walls. You can try and deal with this by waving your hands and muttering about technology handling the rubbish jobs, but that doesn’t completely solve the problem. Even for those jobs that are easier to imagine people enjoying, like Gath’s tailors, there will be days when it starts to feel a bit like drudgery, especially if every Sikarian gets jaded as quickly as he does. Sooner or later, you’ll at least temporarily stop having fun in your job of providing others with enjoyment. At that point, whose pleasure wins out?

Historically speaking, the answer is clear. Sikarian society will almost certainly have some kind of underclass, whose opportunity for pleasure will be ignored in favour of keeping the Gaths of this world happy. This won’t be achieved by anything so direct as insisting such people don’t deserve pleasure. The standard lie will be that some people gain the most pleasure by helping their betters avoid the fingers of ennui brushing against their shoulder. That might very well be what Gath is doing when he offers Janeway a new wardrobe, actually. The “us” he refers to as gaining pleasure from the activity might not actually exist outside of his own assumptions. The actual feelings of the actual workers go conspicuously unrecorded.

This is interesting on its own terms (or at least it’s interesting to me), but the real value of the idea lies in how it ties in to the workings of the Federation. There’s couple of links I could make here. In terms of domestic policy, I always find it difficult to believe everyone in the Federation actually gets to pursue the goal of bettering themselves. Not to equal extents, at least; someone has to be in charge of cleaning up when the space-toilets malfunction. The invisible class structure of the Federation is something else that can wait for another time, though. Right now, let’s focus on another way this episode criticises the Federation through comparison with the Sikarians – via the Prime Directive. As Janeway herself puts it:

How many times have we been in the position of refusing to interfere when some kind of disaster threatened an alien culture. It’s all very well to say we do it on the basis of an enlightened principle, but how does that feel to the aliens?

The observation in itself isn't particularly impressive - indeed it's closer to being banal. What’s interesting is the fact that despite the banality, Janeway has apparently only just considered the idea. It seems to strike her out of the blue that Starfleet’s most fundamental rule might be more about making themselves feel good than it is being of actual service to the galaxy at large. The Sikarians tell themselves they’re helping people by showering them with gifts and hospitality, when in fact they just want their new playthings to hang around until they become boring. What if the Prime Directive is just as firmly rooted in self-gratification? Is it maybe just a little too convenient to conclude the pinnacle of ethical enlightenment is realising you shouldn’t have to a damn thing to help your neighbours? That it’s better to focus on the pleasure you get from self-improvement and leaving the rest of the galaxy to sort itself out?

It may be that the Sikarians and Starfleet share more factors than Janeway is prepared to admit. Both tell themselves a tale about how they help others in the process of helping themselves – the Sikarians through giving gifts, and Starfleet through not expending time or resources. Little wonder then that the use of stories as something to be bartered comes up here, or that Eudana has a particular love for tales that display nobility. A fantasy about doing the right thing would appear to be what her entire society is based on. And maybe not just hers.

“No Way! I Have Scruples”

It’s in this context that we need to consider Janeway’s decision not to make a deal with Otel, and Tuvok’s choice to do it himself instead. I know Tim Russ has expressed disappointment in this episode, believing it doesn’t make Tuvok’s motivations clear enough. For my money, though, the ambiguity actually works in the story’s favour. Let’s start with Russ’ own reading of his character’s actions here. His argument Tuvok is attempting to save Janeway from a ship-wide mutiny certainly makes sense. This is not only the second time in nine episodes that the captain is refusing to make use of alien tech to get the ship (much closer to) home, but her reasoning in rejecting this travel device comes dangerously close to contradicting her justification for blowing up the Caretaker array. Tuvok himself argued that destroying the array was plausibly a breach of the Prime Directive, but Janeway waved the suggestion away. Without seeing the text of the Prime Directive itself I can’t speak to how persuasive either character’s position is, but the point is it was a judgement call, not a slam dunk. Janeway could have gone the other way on the matter, and presumably chose not to because she valued the lives of the Ocampa above getting her own ship home.

It’s hard to quibble with that as a moral stance, but it also plausibly sets a precedent. There are clearly honest readings of the Prime Directive that would lead a person to conclude Janeway violated it when she believes it necessary, and presumably will do so again (her and every other Starfleet captain, of course). So, when the ship gets to Sikaria and Janeway won’t even engage in barter with a more advanced civilisation because the person she’d be dealing with would be committing a criminal act, it could start to look an awful lot like she doesn’t actually care all that much about going home. Again, the absence of an actual text for the ol’ Papa Delta proves an issue, but Janeway’s objections to dealing with Otel don’t appear to stem from it. The Sikarians are both far too advanced and far too hospitable for cultural contamination to be an issue, and Janeway has no intention of using the device in a way that would alter the situation of anyone but her own crew.

Whatever regulation she is following in her dealings with the Sikarians, then, it is by definition one less important than the Prime Directive. From what little we see, said rule would also need to be fairly flexible – it’s hard to insist on only dealing with recognised governments when those governments are, say, transparently oppressive and/or fighting a civil war and/or are in power despite the clear wishes of the population. The proper response to Otel’s offer would seem be to just asking under what authority he claims to negotiate with a foreign power (and it’s clear the Voyager crew haven’t figured out the political landscape of Sikaria, otherwise Gath’s delaying tactics wouldn’t have been as successful as they were). Instead, Janeway dismisses him as a lawbreaker and thus not someone she can deal with. Apparently the Prime Directive is open to interpretation, but necessarily loose rules on diplomatic engagement must be doggedly clung to.

And all that is assuming there is a specific regulation Janeway is following here. The fact she frames this as a matter of her principles, rather than a refusal to break Starfleet rules, brings that into question as well. An uncharitable observer could easily see Janeway as putting her own narrow conception of morality ahead of the very real needs of her crew. Add in Seska’s toxic assumption about the captain favouring Gath because she wants to wind his hair-wires through her fingers, and it’s not remotely difficult to understand why Tuvok fears a mutiny. Especially since he lived among the Maquis crew for months. He understands far better than Janeway can just how badly they need to get home. The Starfleet officers on Voyager miss their families. The Maquis are terrified their families are about to be murdered by space-fascists. If nothing else, once a captain essentially press-gangs you as the only alternative to being stranded forever, the idea they then won’t take a shortcut home because crime is immoral must read an awful lot like high-level trolling.

Arguing Over The Map All of the above gives plenty of weight to Tim Russ’ understanding of his character’s actions here. It’s worth noting though that the episode works just as well if you read Tuvok as trying to save Janeway not from a mutinous crew, but from herself. It’s actually a fairly sound application of lateral thinking Tuvok employs here. Janeway is desperate to return home, but her principles prevent her from acquiring the necessary technology. So he takes her out of the equation. He does the deal himself so the ship can travel 40 000 light years without Janeway’s principles being compromised in the slightest. It’s a perfectly sensible solution, too, so long as he can live with his captain’s reaction.

Unfortunately, Tuvok either underestimates how hard Janeway would take him ignoring her decision, or underestimates how much he would regret upsetting her. At least, that’s the most obvious reading of Tuvok’s insistence that “My logic was not in error; but I was”. His reasoning on how to bypass Janeway’s dilemma was sound, but prioritising doing so over allowing her to maintain trust in him was a mistake. Once again, we’re seeing the problems inherent in the Vulcan approach. Janeway herself gets part of the way there when she says a person “Can use use logic to justify almost anything”. I wouldn’t want to sign off fully on so expansive a conclusion, but it’s certainly true that you can reach any number of different and even contradictory conclusions through the application of the same logical process, simply by changing the underlying axioms. I explained above that 1 can’t be a prime number, otherwise the FTA of algebra completely collapses, and mathematics becomes unrecognisable. But it isn’t mathematically logical to say 1 isn’t prime. If we changed the definition of prime numbers to include 1, logic wouldn’t stop working. It would just lead us to a conception of mathematics utterly at odds with the one we use today. This “new maths” would be of far, far less use to humanity, but that wouldn’t be because it stopped making sense. There are still theorems a mathematician could prove if she decided 1 is now prime. Her logic would not be in error. It just wouldn’t actually be of any use. Tuvok it seems has made a similar mistake by defining Janeway’s love and trust as something he can live without.

This is probably the best use of Tuvok the show has managed to date, and it also provides at least some pushback to my suggestion there are hard limits on what can be done with him. The idea that one’s logic must give way to the feelings of another under certain circumstances is a new one in the IDFC episode ordering, and it complicates things nicely. I’ve argued before that logic divorced from empathy creates results that are at best hollow and at worst monstrous, and this is the first time a Vulcan seems to approach the same conclusion. Tuvok’s seemingly genuine contrition makes it clear he realises he’s screwed up, and that makes his decision not to blame his logic important. It would have been easier, and would require less self-reflection, to pin the blame on uncharacteristically sloppy thinking. Recognising that even perfect logic isn’t sufficient when making decisions is the harder path. A Vulcan willing to interrogate Surakism? I am totally here for that.

In fact, this is probably the first episode of Voyager in which the majority of show’s potential is on display. As well as Tuvok’s struggle to respect and save his captain simultaneously, the Maquis are used well here too. They’re not treated as indistinguishable from their Starfleet crewmates, and their very different perspective on the urgency of heading home is used to good effect (there’s also something quite delightfully ironic about how Carey’s decision to bury the hatchet with Torres allows him to help her disobey the captain who promoted her over him). Everyone’s motivations finally make perfect sense (boy, I hope there’s not an episode later on where some Maquis get treated like truculent teenagers for not loving Janeway, and Tuvok has to give speeches about how she’s never wrong!).

Even Janeway’s position is an understandable one. Arguing there’s no problem with an illegal deal if it’s the other guy doing the lawbreaking isn’t actually all that sympathetic a position to take. It’s also worth considering that even gaining access to the space-folding tech might still leave Voyager with another three decades of travel time. That’s a long time to try and keep control of a starship after you’ve set the precedent that established power structures should be ignored the moment they become inconvenient. Related to this is the fact it’s hard to blame Janeway for concluding that, even if the slow and irreversible degradation of her principles is ultimately inevitable, it would be better to postpone kicking the process off until at least her third month in the captain’s chair.

In short, every character’s position here is defensible to at least some extent, and the resulting conflict makes total sense, even though everybody is ultimately desperate for the exact same result. This is everything Voyager promised it could be – a group of exhausted travellers with a single prime factor in common, who keep trying to tear each other apart over all the other ones they don’t share.

If the show can keep this heading, it could genuinely travel somewhere fascinating.


1. Prime Factors

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