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The Expedition Approximation

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"The Expedition Approximation" is the sixth episode of the eighth season of the American sitcom The Big Bang Theory. The episode aired Monday, October 20, 2014.


Raj and Sheldon test themselves to see if they can handle an underground scientific expedition; and Leonard and Penny worry about money in their marriage.

Extended Plot

During takeout dinner in apartment 4A, Penny is wearing her new business suit while Howard comments how good she looks while going out on sales calls and fliting with doctor. Leonard stays at home just looking nerdy. Penny disagrees that she is flirting to make sales, though she does agree with Amy that is good that she is showing her cleavage when she leans over. Bernadette asks Sheldon how his work in dark matter is going and he remarks that it is the most exciting time to work in it since HE is now working in it. Raj mentions that the government is funding the dark matter field by sending teams down into a salt mine to conduct experiments. Raj suggests that he and Sheldon apply since they could be on the ground floor of something big. Penny tells Sheldon that he shouldn't go down into a mine since he had a panic attack while going through a car wash. They others start making fun of them going down into a mine, while Sheldon complains that he liked it better when he didn't know they were making fun of him.


Penny sold the car Leonard got her after she gets a company car.

At dinner, Leonard tries to tell Penny about a new version of an old video game he was playing; however, Penny is thinking about her new job as a sales rep for a pharmaceutical company. She says she has some good news and hands Leonard an envelope full of money. She tells him she was given a company car, so she sold the car Leonard gave her. He agrees that she didn’t need two cars, but seems hurt that she sold the first one without telling him. Penny says, "What should I have done? Taken a picture of it and put it in a frame with little hearts and puffy letters that say 'Best Fiancée Ever'?" "Well, that doesn't sound so bad," Leonard pouts. "Good," Penny says, "because that's what I did!!"—and indeed, she pulls out a framed photo of the car just as she described it. Leonard says it's so sweet and Penny says it's not that sweet since she paid for the frame with Leonard's money and then got a massage. They then spend a while passing the envelope of money back and forth, trying to get the other to accept it.

Raj enters Sheldon's office and asks if he is busy. Sheldon's mind is always multi-tasking. He is working on a complex problem, composing his Nobel Prize acceptance speech for solving that problem and trying to figure out how mermaids have offspring. Raj says that they just lay eggs on rocks which means that Sheldon's mind can now work on another problem. Raj wonders if their friends were right that the conditions would be too harsh for the two of them down in the mine. It would be hot, humid, live explosions, since it is a working mine, twelve hour shifts underground and the toilet facilities would be a bucket. Sheldon was fine with everything except the last condition. Raj still wants to test themselves under simulated conditions to see if they can do it since it is such a great opportunity. Sheldon wants to try it and goes to his computer to check for hot, dark moist places and finding a bunch of sex video sites.

Leonard comes into Penny's apartment with the money to work something out. Last night Penny felt that it was really weird for Leonard to leave a large envelope of money on her dresser after they had sex. Leonard wants them to put it in a joint savings account to use for their wedding expenses which Penny thinks is a great idea. Leonard realizes that Penny feels great about being financially independent and he is nothing but proud of her. Penny tells Leonard that her making money means that she is not as dependent on Leonard, while he thinks that she has a problem with her control issues. They finally agree not to fight and that the money belong to both of them..

Down in the mine.

Raj and Sheldon dressed in mining gear and carrying a bucket arrive with Amy at a basement access door to the university steam locomotive pipe tunnels. Amy had stayed in one for three days to pledge a sorority, but they forgot she was down there. The conditions there are more consistent than in the steam bath and there are no naked men. Amy is very proud of Sheldon for facing up to all his fears, about a dozen of them. In case of an emergency, she has to rescue him first and then come back for Raj. Down in the tunnel, Sheldon starts his mine simulation log and quickly finds Raj's stating of the obvious very tedious.

Penny and Leonard are visiting Howard and Bernadette to discuss how they handle finances in their marriage. Howard thought that they wanted to swing together and change partners as couples. Howard and Bernadette sometimes do fight about money. She makes a lot more than him, though Howard claims to have brought assets into the marriage. Like his incomplete set of Star Trek collectible plates? Howard replies that he just got the last one on eBay without telling Bernadette. Then Howard brings up all the late fees from not paying the credit card bills on time. Bernadette retorts that she would if she wasn't spending all her time cleaning the apartment. Howard grabs his chore chart and shows her all the stars he has though Bernadette berates the quality of his work. Howard runs into the bedroom after she mentions his allowance. Bernadette apologizes and tells them that the pressure to be the provider is tough on Howard. Penny worries about them; however, he grew up in a home where his mother earned more and also emasculated his father in every way. Penny and Leonard decide to work things out before they are married and to use the Wolowitzes as an example of what not to do.


Eleven minutes. Longer than I thought.

Back in the tunnel, Sheldon is feeling a bit claustrophobic and starts singing a miners song which described all the bad conditions. Raj switches over to Miley Cyrus, though Sheldon doesn't know who he is. Raj starts to describe her "Hannah Montana" TV show, Sheldon wonders how just a wig could hide her alter ego. But then what about Superman and his eyeglass disguise? Amy asks if they need anything since she's going to the vending machine. Sheldon gives her a long list. Sheldon's claustrophobia gets worst as does his need to use the bucket which he refuses to do. He is also struggling with his work. He is now in his thirties and starting over with studying dark matter where he used to be at the top of his field. This scares him. When Raj is scared he thinks of Voyager. Not the Star Star Trek series which Sheldon found terrible. The space probe mission was all ready over after he was born, but the probe just keeps going still sending back data from outside our solar solar system. Sheldon then sees some rats behind Raj and heads up the ladder. As Amy is returning as Sheldon yells that everything is falling apart and it's too late for Raj. Amy shrugs, looks at her watch thinking that it had been eleven minutes which was longer than she thought it would last. Raj is shouting from inside the tunnel as the rats crawl into his shirt.

Leonard and Penny decide to spread the money all over the bed and make love on it. Penny thinks that that is the most fun someone can have with money, but won't say if it's only the first time she's done it. Bernadette apologizes to Howard after sex and tells him that she wants them to handle their money as equal adult partners. Then they change the subject to Howard's birthday party and he wants to have laser tags. Amy is busy transcribing Sheldon's mine simulation log for future generations who obviously want to hear about his melted Kit Kat bar. Raj comes charging to yell at him that Sheldon left him there to fend off a family of rats. Friends don't do that.



  • Title Reference: Since there is an opportunity to study dark matter in a salt mine, Raj and Sheldon decide to test themselves under the conditions found in a mine.
  • Taping date: September 30, 2014.
  • This episode was watched by 16.02 million people with a rating of 4.6 (adults 18-49).
  • Total viewers including DVR users 21.39 million.
  • The Big Bang Theory was ranked #3 for the week ending 28 October 2014.
  • This episode aired in Canada on October 20, 2014 with 3.14 million viewers with a weekly ranking of #1.
  • In Australia, it aired on February 2, 2015 with 0.98 million viewers.
  • Episode transcript [1]   


  • Jesse Schedeen for IGN - "The Expedition Approximation" started off on fairly weak ground as it focused on the latest bit of Leonard/Penny drama. The good news is that things picked up quickly as the couple paired up with Howard and Bernadette. Meanwhile, Raj and Sheldon's latest wacky escapade was consistently amusing. Running beneath both story lines was a sense that these characters really are evolving and maturing in various ways, however slowly. The older this show gets, the more important that quality becomes. [2]
  • Dhruv Rao of The DR Club stated that the episode "brought the show's game back" and gave the episode an A-
  • IMDb user reviews[3]


  • The car that Penny sells is the one Leonard bought her in "The Friendship Turbulence" (S7E17).
  • Howard's money allowances were first mentioned in "The Cooper/Kripke Inversion" (S6E14), when he and Raj bought a 3D printer. Howard is clearly insecure and embarrassed about being supported by his wife, but will nonetheless still take the money (though he prefers the term stipend to allowance), even though he should be perfectly able to support himself financially (all the other guys do with roughly equivalent jobs, plus Howard had been living, presumably rent-free, in his mother's house for years, suggesting he may have decent savings).
  • Sheldon attempts to prove the Penrose Conjecture, an open mathematical problem in general relativity related to the asymptotically defined mass of an astrophysical system, and envisions giving a Nobel Prize acceptance speech for solving the Penrose Conjecture problem in this episode.
  • The second time that Howard and Bernadette are seen naked in bed together. It first happened in two scenes of "The Cohabitation Formulation" (S4E16)
  • The Penrose Conjecture is a highly advanced statement in spacetime geometry which has to do with the minimum area of space that can contain a mass (why area and not volume is considered is rather involved; the answer can be found in the work of Stephen Hawking). The Penrose Conjecture has been proven for 3 dimensions in 1999 (Bray); however, proof for arbitrary number of dimensions is still pending. Proving that the conjecture holds would be an important step towards a quantum mechanical theory of gravity, and given the problem's notoriety and importance, it is quite possible that a general solution would be awarded the Nobel Prize.[1]
  • Sheldon and Raj want to collaborate on dark matter research again, last arguing about the topic in "The Hot Troll Deviation" (S4E4). Their initial foray into this field was in "The Pirate Solution" (S3E4).
  • The group previously survived a field scientific expedition's hardships in "The Monopolar Expedition" (S2E23). It is in fact mildly puzzling that Sheldon and Raj would avoid the mines when they -- Sheldon in particular -- held up quite well on a prolonged trip to the equally hostile conditions of the Arctic.
  • "Lenny" can handle their marriage financial issues better than "Howardette". Howardette's issues stem mainly from Bernadette making "a lot more" than Howard, which tends to be hard for men to take due to psychological and social archetypes, and Howard likely being somewhat insecure about his maturity, having lived with his mother until recently and probably being worried that he may be viewed by his peers as a "mama's boy". On the other hand, Penny probably does not make more than Leonard even with her new sales job, even though Leonard would probably enjoy being in a position of perceived inferiority no more than Howard, given the former's high-achieving family and distant, overly demanding mother.
  • This marks the second time Sheldon unknowingly performed an innocent web search with potentially compromising keywords ("hot, dark, and moist... let's see what comes up"). The first was "The Contractual Obligation Implementation" (S6E18).


Bernadette: (admiring Penny) I like your suit.
Penny: Oh, thanks. Got a couple new outfits for work.
Howard: How does it feel knowing your fiancée’s job is to go out and flirt with doctors, looking like that, while you sit here, you know, looking like this?
Leonard: She doesn’t flirt with doctors.
Penny: Yeah. It’s all very professional.
Amy: You know when you bend over, I can see down your shirt?
Penny: Okay, good.
Bernadette: Speaking of new careers, how are things going with dark matter, Sheldon?
Sheldon: Oh, yeah, I’d have to say it’s the most exiting time in the history of the field.
Bernadette: (being curious to Sheldon) Oh. What’s going on?
Sheldon: (shouts) I started doing it.
(Bernadette has a reacting smile to Sheldon's shout)
Raj: You know, the government funded the biggest experiment yet to detect dark matter.
Leonard: Yeah, I’ve read about that, they’re sending research teams down into abandoned salt mines.
Raj: You know, Sheldon, if we apply to be one of those teams, we could be on the ground floor of something big, not just for theoretical physics but for astrophysics as well.
Penny: (surprised with unhappiness) Wait, hang on, you guys are gonna work in a mine?
Sheldon: Why not?
Penny: You had a panic attack when we went through the car wash.
Sheldon: Perhaps the emotion you’re referring to was shock at you having something cleaned.
(Penny gets shocked by this)
Leonard: I think what Penny meant is, the thought of you two in a mine is kind of funny, it’s like a cat riding a Roomba.
Howard: If they get scared, they’ll have those hats with the lights on them, ’cause down there it’s night-night all the time.
Bernadette: (joyfully) Maybe they could ride around in one of those mine carts that go ee-oo-ee-oo-ee-oo.
Leonard: Yeah, it’ll help them get away when they see a g-g-ghost.
Sheldon: Are they making fun of us?
Raj: Yup.
Sheldon: I miss the old days when I couldn’t tell.
(Penny just smiles madly at what Sheldon has said and the opening theme begins).

Amy: Sheldon, I'm really impressed you're willing to try this.
Sheldon: Admittedly, this brushes up against my well-known aversions to heat, small places, going below floor level, dampness, hatches, ladders, darkness, echoes, and eliminating in Home Depot buckets. That last one is quite new, but I have a feeling that's going to rocket to the top of the list.

Penny: If I do well in sales, I could end up making a lot more money than you.
Leonard: Not a problem. I grew up with a mother who emasculated my father financially and in every other aspect of his life, so really it's what I think love looks like.

Raj: So I did a little research on what the conditions are like in the mines, and the guys might be right. It sounds pretty rough down there. For starters, it's very humid and about a hundred degrees.
Sheldon: I'm from Texas and you're from India. We're no strangers to the fragrant arm pit. Next.
Raj: It's also a live mine, so there'll be dynamite explosions going off in the distance.
Sheldon: I have a lactose-intolerant roommate with a taste for ice cream. Next.
Raj: You have to be down there for twelve hours at a time.
Sheldon: Have to be somewhere.
Raj: There's no toilet, so we'll have to do our business in a bucket.
Sheldon: So it's settled? We're not doing it.

Leonard: Hear me out. I know things got a little weird last night.
Penny: Well, leaving an envelope of cash on my night-stand after sex would count as weird.

Penny: Or maybe, now that I'm no longer an out-of-work actress who can't pay for her own dinner, that makes you a little insecure.
Leonard: I can't believe you would say that. You know how insecure I am about my insecurities.

Raj: All this time, I never knew there were steam tunnels down here.
Amy: Most universities have them. When I was an undergrad, I spent three days in one pledging a sorority.
Raj: Did you get in?
Amy: No, they forgot I was there. But it really opened up my pores.

Leonard: Thanks again for having us.
Howard: Oh, of course. What did you guys want to talk about?
Penny: Well, you know, now that we’re engaged, we had some questions about how you handle money as a couple.
Bernadette: (with a smile of anger) I told you they weren’t gonna ask us to swing with them.
Howard: I didn’t think they were going to. I just wanted to have a way to say no without hurting Leonard’s feelings.
(Bernadette remains silent whilst smiling crossly)
Leonard: Well, nailed it.
Howard: So what did you want to know?
Penny: Well, do you guys ever fight over money?
Bernadette: Sure, sometimes. I mean, it can be a little awkward since I make so much more money than Howie.
Howard: You didn’t have to say so much more.
Bernadette: Well, I didn’t have to, but for the sake of accuracy I felt that I should.
Howard: I brought a lot of significant assets into the relationship, too.
Bernadette: (1st time: she's asking Howard in surprise) Like what? Your incomplete set of Star Trek collector plates?
(Penny thinks for a second)
Howard: (he speaks nervously) For your information, I just bought the last one I needed on eBay.
Bernadette: (2nd time: she's asking Howard in surprise) Without asking me?
Howard: (he grunts with anger) There were only three minutes left in the auction and it was a mint condition Scotty from a smoke-free home.
(Leonard and Penny look face-to-face over Howard and Bernadette's argument)
Bernadette: (she's asking Howard crossly) How much, Howie?
Howard: Not a lot.
Bernadette: (she's asking Howard in slow anger) How much?
Howard: Let’s not talk about this in front of our friends.
Bernadette: (she's asking Howard with loud anger) Was it more or less than falconry school?
Howard: For the tenth time, that was a Groupon.
(Bernadette is now very cross by this point)
Leonard: Like I would swing with him.

Sheldon: Miners often sang mining songs to keep their spirits up.
Raj: You know any mining songs?
Sheldon: Just the hits.

Raj: Okay. How about a little Miley Cyrus next?
Sheldon: Who's he?

Howard: Talk about wasted money. What about the late fees on our credit card because somebody didn’t pay the bill on time?
Bernadette: (she's so completely angry) Well, maybe I would have paid it if I wasn’t also doing everything else around here.
Howard: (he yells with quiet anger) Oh, you’re saying I don’t do anything around here.
(Bernadette nods sadly for a second whilst Howard lifts himself off the couch in anger and he tears the chore chat off the fridge door)
Howard: (he's shouting with big loud anger) Look at my chore chart!
(Bernadette storms up to it with enormous anger)
Leonard: She made him a chore chart.
Penny: I see it.
Howard: Do the dishes. There’s a star right there.
Bernadette: (she's so gigantically cross by this) That was a pity star. Putting water in the roasting pan and leaving it in the sink is not doing the dishes.
Howard: (he's still angry, but is getting frightened) That pan had to soak and you know it.
Bernadette: (she snaps at him with more complete anger) Well, don’t come crying to me when you don’t get your allowance.
(Penny and Leonard exchange glances over Howard and Bernadette's shouting)
Howard: (he's angry with complete sadness) It’s not an allowance. It’s a stipend, and we said we weren’t gonna call it an allowance in front of my friends.
(Howard now runs off to his bedroom and slams the door to which the loud slamming sound is played to Bernadette's smile of embarrassing fury).
Leonard: (nervously) I usually don’t like lemon bars, but these, these are really good.
(Bernadette just ignores Leonard and tries to hide her embarrassment from him).

Sheldon: We'll take some Funions.
Amy: Anything else?
Sheldon: Some York Peppermint Patties, a couple of Dr. Peppers, and run to Best Buy and see if they have a portable DVD player and Season 1 of a show called Hannah Montana.
Raj: Have her get Season 2. In Season 1 it was still finding itself.

Bernadette: (she's quite embarrassed and very sad) Sorry you guys had to see that.
Penny: Oh, don’t apologize.
Leonard: Yeah. It just makes it a lot harder to pretend it never happened.
Bernadette: (she is so mega-fully upset) Money’s a sensitive subject for Howie because of the difference in our income.
Penny: (worried) It really bothers him?
Bernadette: (she's extremely concerned and upset) Well, sure. There’s still a lot of pressure on guys to be providers. So even though he’s happy for me, it’s just a little tough on him.
Penny: Uh-oh.
Leonard: What?
Penny: Well, if I do well in sales, I could end up making a lot more money than you.
Leonard: Not a problem. I grew up with a mother who emasculated my father financially and in every other aspect of his life, so really, it’s what I think love looks like.
Bernadette: (she speaks with a concerned smile) I’ll be right back. I’m gonna go check on him.
Penny: Maybe it’s a good thing we came here. It’s like a lesson in what not to do.
Leonard: Yeah I don’t want something dumb like money to come between us.
Penny: It won’t. Let’s just promise to figure this kind of stuff out before we get married.
Howard (out of vision, yelling at her with loud anger): Why are you being so bossy?
Bernadette (out of vision, yelling at him with loud anger): Why are you being a baby?
Howard: (out of vision with loud grouchiness) I’m not a baby. I’m a grown man, and I made the bed. Now where’s my star?
Leonard: (he suggests nervously) Should we go?
Penny: (she informs Leonard with some firm quietness) Hang on. I want to see if he gets the star.

Raj: Sheldon, you busy?
Sheldon: I'm always busy. This mind is capable of advanced multitasking. Currently, I'm attempting to solve the Primrose Conjecture, I'm composing my Nobel acceptance speech for when I've solved the Primrose Conjecture, and I'm wondering how mermaids have babies.

[The first ending scene in Penny's bedroom]
Penny: (stripping her shirt off) Okay, this is definitely the most fun thing we can do with the money.
[Leonard is organizing a big pile of dollar notes on the sheet]
Leonard: I’ve never done it on a big old pile of cash before.
[Penny now puts on a strange smile of embarrassment]
Leonard: (imitates Penny) Me neither, Leonard. It’s my first time, too.
[Penny and Leonard now exchange glances and we now go to the second ending scene of Howard and Bernadette (without her glasses on) naked in their bed with candles all around them in the bedroom of their apartment and they are making up for their row about the money]
Bernadette: (quiet and embarrassed) I’m so sorry I made you feel bad about the money stuff.
Howard: It’s okay.
Bernadette: (with sad embarrassment) No, it’s not okay. I want us to be partners, equals. Adults in a mature relationship.
Howard: (with quiet happiness) I want that, too.
[the kiss each other]
Bernadette: Now, let’s talk about your birthday party.
[Howard jumps with complete excitement and Bernadette shrieks "Oh" and grabs the duvet with rage]
Howard: (he's yelling with loud excitement) Ooh, laser tag, laser tag.
[Howard now sorts out the angry Bernadette saying "Oh" in quiet anger (which could mean 'oh, no. not this thing about the money again') and the duvet just as we now go to the last ending scene at Apartment 4A with Amy sorting her Dictaphone out on her desk with Sheldon standing up above her]
Amy: (she asks Sheldon firmly) Do you really need me to transcribe this?
Sheldon: You’re not doing it for me. You’re doing it for future generations who will benefit from my struggle.
[Amy just slams the Dictaphone down]
Sheldon's Voice on Recorder: Sheldon’s Mine Simulation Log, entry four. My Kit Kat has melted. All is lost.
[An angry Raj immediately bursts in the apartment]
Raj: (he's gigantically angry at Sheldon) You call yourself a friend?! I was trying to help you, and at the first sign of trouble you ran away, leaving me to fend off a family of rats!
[Amy and Sheldon are rather surprised by Raj's yell of anger]
Raj: (he is still furious) You’re a completely selfish human being and a physical and a moral coward!
Sheldon: (he speaks firmly to Amy) His statements of the obvious continue to annoy.
[Sheldon and Raj look at each other for one second].



  • Taping Report [4] Taping Report by MichyGeary

(a lecture on the Penrose Conjecture, from the University of Salamanca, Spain)

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