What's the map on Sheldon & Leonard's refrigerator of?

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In the Big Bang Theory, there's a map on Sheldon & Leonard's refrigerator throughout the entire show It has false-color shadings of various kinds, with prominent craters, and so is presumably of some non-terrestrial body, perhaps Mars, the moon, or an asteroid. Can anyone identify it?

It's the Beethoven basin region on Mercury. The MESSENGER image gallery says:

A digital terrain model (DTM) derived from Mercury Dual Imaging System (MDIS) stereo images. The lateral spacing is 330 m and the map is in stereographic (conformal) projection. The image is taken from abstract number 1913 submitted to the 2012 Lunar and Planetary Science Conference, by Frank Preusker and colleagues.

NASA / JHU APL / Carnegie Institution of Washington

A collage of MESSENGER photos from 2011 debuted on the Apt. 4A freezer door around the same time. A statement released 2012-04-05 quotes PI Sean Solomon:

The MESSENGER team is thrilled by the decision of the producers and writers of 'The Big Bang Theory' to weave some of the spacecraft's latest images of Mercury into this week's episode… We look forward to seeing how the images figure in the story line and camera shots, and we hope that interest in the MESSENGER mission is broadened by this exposure on one of the most popular series now on television.

Fundamental solution of a differential operator

I'm trying to solve this question, but I don't know how to deal with it:

If we have $b=(b_1,,dots,b_n)inmathbb^n$ and $etainmathbb$, prove that the differential operator $b_1frac+dots b_nfrac-eta$ has the following distribution $T$ as fundamental solution: $left<T,varphi ight>=int_<0>^varphi(tb)e^<eta t>dt$

Thanks in advance for any help.

On the wall in the living room of Leonard and Sheldon's apartment is an antique fuse holder with fuses.

This odd item was the subject of much discussion by fans who couldn't work out what it was. Eventually, someone identified it on Twitter.

Look closely, each row has a fuse connected from the left to right. Each fuse is bolted to it's connection on the terminal block with two bolt. Each fuse has two eilets (one on each side) where it is bolted onto the terminal block (or strip).

370 Big Bang Theory Trivia Questions & Answers : Television A-C

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Disappointingly, this is a group of fully-dressed men posing under a false name. They had hit songs in the '90s like "One Week" and "Old Apartment".

Sometimes they have performed variations of the theme song with different lyrics, such as lyrics mentioning the characters and lyrics mentioning the days of the week the show is on.

Professor Proton, played by Bob Newhart, first appeared in the episode "The Proton Resurgence". He was a children's TV performer who had a show when Sheldon and Leonard were kids and they both loved him. They found out he could be hired to do private parties, and Sheldon hired him to come over to the apartment.

He did a few experiments with Sheldon, Leonard and Penny Sheldon and Leonard were of course both familiar with all the 'tricks' Professor Proton could perform and the science behind them, but Penny learned many new things. When Sheldon asked Professor Proton to "do potato clock", they explained to Penny that Professor Proton could power a clock with a potato. Penny couldn't believe it. A bit later, the Professor experienced a problem with his pacemaker, and Penny asked if the potato might be of use.

Bob Newhart reprised his role as Professor Proton, a.k.a. Arthur Jeffries, in a few more episodes the character died in season 7, but reappeared in season 9 as an apparition to Sheldon.

Having met at the end of the third season, Sheldon and Amy were getting along famously, to the annoyance of his friends who didn't really care for her. In "The Zazzy Substitution", when Amy said that she didn't think Sheldon's work was as important as her work as a neurobiologist, Sheldon proposed that they "terminate their relationship immediately" and Amy agreed.

The guys were relieved at first, but it soon became clear that Sheldon was distraught over the break up (though according to him, it was not a break up because that would mean she had been his girlfriend and she was not). He got a cat that he named Dr. Robert Oppenheimer. A bit later, he had more cats and introduced them as Enrico Fermi, Richard Feynman, Edward Teller, Otto Frisch - and Zazzles. Sheldon explained that he was going to call Zazzles Herman von Helmholtz, but "he's just so zazzy". Eventually Sheldon had 25 cats and Leonard called his mother to come fix the problem. In the end, Sheldon and Amy resumed their friendship and got rid of the cats.

Answer: Raj and Howard filled out an internet dating application for Sheldon.

The One Thing You Never Noticed About Penny's Apartment From "Big Bang Theory"

When you watch your favorite shows, oftentimes you don't realize all the tiny set details that the decorators work so hard to think of, so it feels like a real person's home. But, whenever hidden easter eggs are shown, it completely blows your mind.

As CBS revealed on their website, The Big Bang Theory, one of the network's big hits, is packed with clever easter eggs tying the show to reality, including a hidden detail about Penny's (Kaley Cuoco) former apartment.

Since "Penny is very girlie," set decorator Ann Shea told CBS, she wanted to bring bright colors into the walls and furnishings. Since she couldn't paint the walls, she went with colorful furniture and accessories to create a "fresh-looking palette," focusing on hues of turquoise, orange, purple, and lime. But that's not all she did to make it personal.

Here's what the kitchen looked like when Penny lived there:

Let's zero in on her refrigerator. If you look closely at the photos tacked up on the fridge, you'll see that they are all real photos of Kaley Cuoco with The Big Bang Theory cast and crew.

Some of the people you can spot in the pictures are Amy (Mayim Bialik), Bernadette (Melissa Rauch), and of course, Leonard (Johnny Galecki).

Now that Sheldon (Jim Parsons) and Amy live there, things have clearly changed.

Which fellow scientist has an on/off relationship with Leonard?

According to IMDb, one of the series creators of The Big Bang Theory, Chuck Lorre, was one of the writers of the show Roseanne. So, when he came to create his own TV show, he created roles that would pair up Johnny Galecki and Sara Gilbert, who were co-stars on Roseanne. Hence, the fellow scientist that Leonard has an on/off relationship with. The character isn't featured too much anymore, but she was in the beginning. Which fellow scientist has an on/off relationship with Leonard?

Critics

• Caroline Preece at Den of Geek! - The simplest thing to say about The Change Constant and The Stockholm Syndrome (which function well as a single episode) is that they do what they need to. No more, no less. That's not to say there isn't plenty to get annoyed about in this finale alone. Penny being pregnant is a massive insult to her character, and doesn't play at all well considering the current news cycle. On the flip-side, I’ve actually come full circle on my feelings regarding a single Raj. Kripke and Bert get their victory laps, Leonard reveals that he's been chilly for twelve years because he still hasn't dared change the thermostat, and the elevator finally gets fixed. That final zoom-out was perfection. [3]
• IMDb user review [4]

The Reference Frame

In the latest episode of The Big Bang Theory, Leonard Hofstadter had an interesting idea while he was talking to Penny: the spacetime is a surface of the superfluid. The surface tension could even explain the negative pressure of the positive cosmological constant which is a constant positive contribution to the vacuum energy density (they incorrectly talk about the negative energy). Sheldon completed the maths and wrote their joint paper quickly. It was a source of pride for much of the episode.

The Troll Manifestation: an excerpt

The sitcom referred to the Quantum Diaries blog – probably because the bloggers were drinking some wine with the filmmakers (Ken Bloom actually contributed the plot of the episode) – and Leonard quoted a flattering comment on that blog written by your humble correspondent.

The Cooper-Hofstadter paper is a variation of the superfluid vacuum theory that has been around for quite some time. While the "surface of superfluid" and "surface tension" could be interesting twists, it seems a bit hard to understand what it could mean quantitatively – probably because it means nothing. Much of these theories seem to be all about words that can't be elaborated upon. Wikipedia correctly introduces the superfluid vacuum theory as one that may be a "fringe theory".

The broader theory began almost a century ago as a revival of the luminiferous aether. Of course, the aether has been ruled out by Albert Einstein's discovery of the special theory of relativity. The spacetime can't be filled with any "stuff composed of any particles or anything that may be localized" because that would pick a preferred reference frame.

However, in quantum field theory, the vacuum isn't quite empty. It has all the violent quantum fluctuations. Doesn't it revive the concept of the aether? Well, yes and no. The quantum fluctuations are in no way composed of "individual particles". By definition, "particles according to quantum field theory" mean excitations by creation operators raising the vacuum. The vacuum itself doesn't have any!

On the other hand, there is "something" in the vacuum and this "something" may be said to be vaguely analogous to the "aether". If you want the analogy to be more specific, it's better to compare this "something" to a Bose-Einstein condensation – a superconductor or a superfluid – because these are the real-world types of materials that eliminate the friction and dissipation. If you move in other materials, you are slowed down by friction and electrical resistance and similar effects. Those may go away in superconductors and superfluids, so these super- substances are better models for the vacuum which, as we know, is friction-free and allows objects to keep their inertia.

In fact, in the electroweak theory, this analogy goes much further. The Higgs field is a kind of a "superconductor" and even the phases of the Higgs field may be interpreted as the phases we know from superconductors. In other words, superconductors in condensed matter physics may be described as a field theory with a spontaneously broken electromagnetic (U(1)) gauge group. It's broken by a condensate of composite charged (Q=-2e) particles, the Cooper pairs (of electrons).

(To be honest, these Cooper pairs are *not* named after Sheldon Cooper but rather after Leon Cooper. Similarly, the Nobel prize laureate Hofstadter who got it with Mössbauer for the electron-nuclear scattering wasn't Leonard Hofstadter but Leonard could have been named after Robert Hofstadter – who was born 100 years and 1 day ago.)

If you look at this analogy from the other direction, you may understand why some people refer to the spontaneous breaking of the electroweak (SU(2)_W imes U(1)_Y) gauge group as the "electroweak superconductivity". As far as I can say, this is just a matter of an "unusual diplomatic language", one that tries to mask that condensed matter physics is just squalid state physics, as Murray Gell-Mann discovered decades ago.

But more seriously, is there something else that condensed matter physics may teach us? I am a bit skeptical. While it's true that the Higgs field is a kind of a Bose-Einstein condensate or even a superconductor, many other analogies with the condensed matter counterparts simply fail. In condensed matter, the superconductors are ultimately composed of atoms – nuclei and electrons – but this seems impossible for the vacuum because that would almost certainly break the Lorentz symmetry and violate special relativity. The superfluids and superconductors may eliminate some anti-inertial effects such as friction or resistance – which is why they are better models of the vacuum than generic materials – but they cannot (naturally) eliminate all Lorentz-violating effects and terms.

So the "vacuum as a superconductor or superfluid" is just a matter of terminology. It's jargon that may be taken seriously up to some point but not quite literally.

Years ago, I talked to a crackpot named Friedwardt Winterberg, a guy who used to be a student of Werner Heisenberg, if you believe him. You shouldn't be surprised that I was the only guy at the Santa Barbara conference who would talk to him. However, as he learned quickly, it wasn't necessarily because I was more enthusiastic about his crazy theories. It's probably more accurate to say that I have always been more enthusiastic about debunking garbage. For years, I would be getting snail mail from him etc.

What Sheldon and Leonard want to add to this picture is to say that we live on the "surface of a superfluid". That's surely a new addition but what does it exactly mean, what explanatory power or evidence can it add to the picture, how can it be translated to mathematics, and is that better than the old models? I am not sure. The "surface of a superfluid" surely makes this model analogous to a braneworld scenario where the Standard Model lives at the end-of-the-world brane. So it may be either a variation of the Hořava-Witten (HW) heterotic M-theory or the Randall-Sundrum (RS) models.

If that's so, it should be possible to formulate the "general properties" of this Cooper-Hofstadter model in terms o the usual HW or RS formalisms. How do the Cooper-Hofstadter models differ from the HW and RS models we know from literature? And is there anything good about this difference? It is not clear to me. So at the end, I probably tend to agree with the sentiments expressed by the anonymous trolls according to the sitcom (the most important anonymous troll turned out to be Stephen Hawking, he told us, who just wanted to have some fun: once you sit on the chair for 40 years, you may get a bit bored).

If there's some wisdom or evidence in the Cooper-Hofstadter paper or related research that I am overlooking, I surely hope that we will be clearly told what it is. -)

One of the Zermelo-Frankel axioms is the axiom of regularity.

The Axiom of Regularity. For every nonempty set $A$ there exists an $ain A$ such that $acap A=varnothing$.

One may use this axiom to answer your question in the negative.

Proposition. Let $A$ and $B$ be sets. Then $A otin B$ or $B otin A$.

Proof. Seeking a contradiction, suppose $Ain B$ and $Bin A$. Then $Bin Acap$ and $Ain Bcap$. It follows that $Acap eqvarnothing$ and $Bcap eqvarnothing$.

Now, the axiom of regularity ensures an $Xin$ such that $Xcap=varnothing$. But this implies $Acap=varnothing$ or $Bcap=varnothing$, a contradiction. Hence $A otin B$ or $B otin A$. $Box$

Isn't the answer rather boringly "No according to some set theories, yes according to others"?

If we conceive of the universe of sets "bottom up" -- we start with some urelements (or nothing at all if you are feeling really mean), form sets of those, then form sets of what we've got, then form sets of everything so far, keep on going . -- then natural theories of this cumulative hierarchy will take the membership relation to be well-founded (so, in particular, there are no chains like $A in B in A$).

If we conceive of the universe of sets "top down" -- a set (as it were) has arrows out pointing to its members (if any), which have arrows out pointing to their members, and so on -- then we might countenance looping chains of arrows.

Character Information

Stephen Hawking is a hero of Sheldon, Leonard, Rajesh, and Howard. Howard and Raj were overjoyed to show Sheldon and Leonard a Stephen Hawking lecture from MIT in 1974, before "he became a creepy computer voice," according to Howard, who reveals as much with his characteristic hand-to-mouth impression. (1x01: "Pilot") Meanwhile, Leonard anxiously shared with the guys that David Underhill did this hysterical impersonation of Stephen Hawking having phone sex with a robotic monotone: "What are you wearing?" (2x11: "The Bath Item Gift Hypothesis") Also, Raj has stated the guys left that fake message from Stephen Hawking on Sheldon's voice mail, with Howard's impression: "I wish to discuss your theories of black holes. Meet me at the Randy’s Donut by the airport at 2:00 a.m." (4x21: "The Agreement Dissection") Sheldon particularly worships Stephen Hawking. In fact, Sheldon dressed up as him for Halloween when he was six years old, thinks he is perhaps his only intellectual equal, and was willing to undergo a series of grueling tasks beyond comparison to the Twelve Labors of Hercules in order to meet him. ("The Hawking Excitation")

Hawking appeared in "The Hawking Excitation", following the guest appearance of Leonard Nimoy. Hawking was coming to the university for a couple weeks to lecture, and he was looking for an engineer to help maintain the equipment on his wheelchair. Hence, Howard got an e-mail from the office of Stephen Hawking. Amazed, Leonard compared Howard to Hawking's pit crew, and as a word of caution, he said Howard should not do his Stephen Hawking impression in front of him. Right then, Howard did the impression: "You're right. I suppose that could be considered offensive." On his first day with Hawking, Howard talked about movies, showed him some card tricks, and even read a couple pages from his new book. Later, he made an adjustment on the motor drive to Hawking's wheelchair, and when he was putting it back together, he could not for the life of himself figure out where some gears and springs went. Howard gave them to Leonard and Raj who appreciated them as "Hawking souvenirs," keeping one for himself. In the interim, Sheldon proffered to Howard, "Well, how about this? Just give him my paper on the Higgs boson. If he sees the incredible breakthrough I've made, he'll reach out to me." After Howard gave Sheldon's paper to him, Professor Hawking was really impressed and wanted to meet Sheldon, causing Sheldon to excitedly shout. Eagerly standing before him, Sheldon politely told Stephen Hawking it was a pleasure and honor to meet him, to which Hawking simply asserted he knew. Professor Hawking expressed his joy in reading Sheldon's paper, and moreover, told Sheldon that he clearly has a brilliant mind. Similarly, Sheldon stated, "I know." Fascinated by Dr. Cooper's thesis that the Higgs boson is a black hole accelerating backwards through time, Hawking told him. Sheldon thanked him, and gave the anecdote that it just came to him one morning in the shower. Next, Hawking divulged that it was wrong, unfortunately, with an arithmetic mistake on page two. A dumbfounded Sheldon proclaimed he doesn't make arithmetic mistakes, so Hawking then posed the query of whether he was saying that Hawking did. Sheldon quickly recovered with a series of "no"'s. He fainted, uttering he made a "boo-boo" and gave it to Stephen Hawking, whom was dismayed with this recent turn of events. ("The Hawking Excitation")

While Sheldon spent hours combing through his childhood journals and research papers, thinking perhaps he already hit upon the idea that would win him his Nobel Prize, Sheldon's assistant Alex Jensen informed Amy, "He’s asked me to hold all calls unless you’re Stephen Hawking, his mother or himself from the future." ("The Higgs Boson Observation")