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## Journalist moratorium

For over a decade, one of the main ways I’ve tried to advance the cause of Enlightenment has been talking to journalists writing popular articles on quantum computing (or P vs. NP, or the universe as a computer simulation, or whatever).  Because of my blog, journalists knew how to reach me, and because I’m a ham, I always agreed to be interviewed.  Well, I told myself I was doing it as my way of giving back to the field, so that my smarter colleagues would have more time for research.

Unfortunately, this task has sort of taken over my life.  It used to be once a month, then it became once a week, and by now it’s pretty much every day.  Comment on this claim by IBM, that press release by Rigetti, this embargoed Nature paper by a group in Australia.  And when you do, it would be great if you could address this itemized list of 12 questions, with more questions coming later depending on what the editor needs.

On Friday we were on a family outing, with Dana driving and me in the front passenger seat, typing out another reply to a journalist on my phone.  Because of my engrossment in my Enlightenment duties, I neglected to tell Dana where the exit was, which then made us a half hour late for a scheduled museum tour and nearly ruined the day.

So then and there, I swore an oath to my family: that from now until January 1, 2019, I will be on vacation from talking to journalists.  This is my New Years resolution, except that it starts slightly before New Years.  Exceptions can be made when and if there’s a serious claim to have achieved quantum computational supremacy, or in other special cases.  By and large, though, I’ll simply be pointing journalists to this post, as a public commitment device to help me keep my oath.

I should add that I really like almost all of the journalists I talk to, I genuinely want to help them, and I appreciate the extreme difficulty that they’re up against: of writing a quantum computing article that avoids the Exponential Parallelism Fallacy and the “n qubits = 2n bits” fallacy and passes the Minus Sign Test, yet also satisfies an editor for whom even the so-dumbed-down-you-rip-your-hair-out version was already too technical.  And things have gotten both more exciting and more confusing in the last few years, with even the experts disagreeing about what should count as a “real quantum speedup,” or how much we should expect quantum computers to help with optimization or machine learning problems.  And of course, if journalists are trying to sort this out, then they should talk to someone who knows a bit about it, and I lack the strategic false modesty to deny being such a person.  Like, someone who calls me to fact-check a quantum computing piece should be rewarded for having done something right!  Alas, these considerations are how I let talking to journalists take over my life, so I can no longer treat them as dispositive.

For journalists looking for what to do, my suggestion is to talk to literally anyone else in the field.  E.g., look at the speakers from the past 20 years of QIP conferences—pretty much any of them could answer quantum computing questions as well as I can!  I’m tempted to name one or two specific colleagues to whom everyone should direct all their inquiries for the next year, but I can’t think of anyone I hate enough.

Unrelated Update: There’s at least one striking respect in which a human baby is like a dog, cat, or other domesticated animal. Namely, these are entities for which you can look into their eyes, and wonder whether they have any awareness whatsoever of the most basic facts of their situation. E.g., do they “know” which individual person is looking at them? Whether it’s morning or night? Which room they’re currently in? And yet, as soon as it comes to the entity’s food sources, all these doubts vanish. Yes, the baby / dog / cat clearly does understand exactly which person is supposed to feed it, and at what time of day, and often even where the food is stored. Implications for the mind/body problem (mind/stomach problem?) are left as exercises for the reader.

Unrelated Update #2: As many of you have probably seen, the cruel and monstrous tax bill awaits only Twitler’s signature, but at least the PhD student tuition tax was taken out, so American higher education lives another day. So, does this mean academics’ apoplectic fears were overblown? No, because public opposition, based on widely disseminated information about what the new tax would do to higher education, probably played an important role in causing the provision to be removed. Keep up the fight.

### 84 Responses to “Journalist moratorium”

1. Aviti Says:

Wow, at least you do not stop writing here, because the world would be a much dumber place if you do not write.

2. Scott Says:

Aviti #1: Thanks. Between journalists and the blog, I pretty much only have time for one, so this year I’ll be doing the blog. Then I’ll look back on the experiment at the end of the year and see how it went.

3. Bunsen Burner Says:

Why not create a FAQ for all of those questions and direct them there?

4. Shecky R Says:

Obviously the solution is to have yourself cloned Scott. Now just a few questions about how cloning and quantum computing will mesh together in the future….

5. Scott Says:

Bunsen Burner #3: I’ve made various FAQs in the past, and I’m sure I’ll make more in the future, but in practice, I’be found they do nothing to decrease the number of inquiries. And also, the questions do change over time, not much, but just enough to make any FAQ outdated. Hence the need for a public commitment device like this post.

6. Jim Hefferon Says:

Anyway, thank your for the work you have done. No one can do it all.

7. Alan Hardy Says:

This post will also serve as a “be careful what you wish for” to all those scientists who *think* they’d like to have a higher public profile.

8. Mark Kim Says:

I’ve very much enjoyed working with you as a journalist. Thank you for your service, and I hope you are as productive as you wish to be in 2018.

Now, I’m thinking about actually buckling down and learning some quantum information theory and quantum complexity theory, so here’s hoping that you’d be willing to answer some technical questions. 🙂

9. Sean Carroll Says:

Talking to journalists is important, but so is one’s life and sanity. One good strategy is to not take questions by email, only by phone. Slight reduction in fidelity, but a substantial speedup.

You are on your way to some (long-deserved) academic freedom, but when are you going to complement/replace your past “nose-look” with a “real” look on your Web site (by which I mean the photo I end up getting to see, irritatingly, if I forget to add the “/blog” on your domain name)?

Anyway, nice precedent to set. I will think seriously about having a NYR to reduce the frequency of my blog updates in 2018. … It was important that I did it some or the other time….

What? Is it already (almost) here? whooooo! Wow!! … Who would’ve thought it would come so near, so fast?

Anyway, best, and bye,

–Ajit

11. Mateus Araújo Says:

How about directing journalist’s inquiries to some younger researcher who has more free time and whose career would benefit from the media attention? (not me of course)

12. Scott Says:

Mateus #11: Indeed, that’s exactly what I’ve been doing more and more of lately, and what I plan to do over the next year, when journalists inevitably email me despite this post. And—thanks for planting the idea in my head—I’ll put you on the list on possible contacts … of course! It will be up to you, naturally, whether to field the inquiries or, e.g., farm them out to a still more junior person. 🙂

13. Uncle Craig Says:

Scott, Just so you know, and perhaps to ease your conscience for almost screwing up a museum appointment by failing to say, “turn off here”, you do have other family living in other parts of the world who read, follow, and look forward to your blogging! You deserve to choose who and when to provide commentary, but please, don’t stop commenting in general on topics you desire! We look forward to this means of keeping in touch!

14. Daniel Seita Says:

Does putting that FAQ on your website about students not emailing to ask to work with you for a PhD (before they’re admitted to MIT and now UT Austin) actually work?

15. Raoul Ohio Says:

An assistant to do the grunt work of dealing with interview requests, sending the correct FAQ, etc., might help a lot. The UT might consider funding such a person, using the rational that every mention of UT in a publication has some monetary value that can be estimated.

16. amy Says:

Entirely understandable to call a moratorium. Could we please, though, also have a moratorium on the phrase “dumbed down”. The audiences are not (in general) stupid. They’re often people with significant achievements in other fields. They just don’t speak your language and haven’t spent 15 years acquiring your particular set of mental furniture. You’re translating, as best you can, for people without that set, and usually you’re doing it in ignorance of whatever it is they might know that’d be helpful for analogymaking.

Translating, not dumbing down.

17. Scott Says:

amy #16: I completely agree with you that the best science popularization doesn’t dumb things down at all. Rather, it explains things the way I’d explain my work to (say) a curious biologist or civil engineer, or the way I’d want the biologist or civil engineer to explain their work to me. In the context where I used it, though, I really did mean “dumbed down.”

18. amy Says:

Thanks, Scott. I agree with Raoul Ohio #15, too, though I’ve yet to see a university fund comms people for individual faculty, even faculty with very large research programs — usually those salary lines come out of grants and are half-time. It can be good value, though, esp. since your half-timer would also be the point person for the university news writer(s) assigned to your dept, whose background is probably not in QC. And there’s a strong enough sci-comm community in Austin that you’d probably be able to hire someone decent. Alternately you could advertise it as half-time very flexible with room to maintain a freelance career, esp if half-time comes with benefits at UT.

19. Scott Says:

Craig #13: Thanks! (And nice to have you here; give my regards to the rest of the family.)

As I said, no plans to discontinue blogging.

The museum was in northern Israel, and was about the history of kibbutzim. As it happens, we were almost the only ones there that day, so the tour guide just waited for us. Even having arrived late, we were able to finish the museum (and reach the limits of Lily’s attention span…) before lunchtime.

But me always being on my phone answering QC journalists has been a pet peeve of Dana’s for a long time; this was simply the breaking point where I finally admitted she was right about it.

20. Jacob Aron Says:

Journalists don’t say this enough, so: thanks for putting up with all of my questions over the years. You’ve have helped to make countless stories better, not to mention prevent a fair few duds from being published. Hope you enjoy your media vacation, though I must admit I’m looking forward to your blogged thoughts when (if?) supremacy is achieved in 2018!

21. Scott Says:

Thanks so much, Jacob! I appreciate your efforts as well.

As I said in the post, if and when quantum supremacy is achieved, I probably will give interviews. 🙂

22. Scott Says:

Daniel #14: As far as I can tell, no. Not even a tiny amount.

23. venky Says:

As with students, why not have preset office hours for journalists?

24. Pat Knight Says:

Your update about animals knowing where the food is stored reminds me of an occasion I began to wonder if our cats have a theory of mind. My wife usually feeds them, and they hang by the food bowls waiting for it. When I feed them due to her unavailability, they run to the store cupboard and look at me to make sure I know where the food is kept. So, they have some idea of what another person might know which is distinct from what they know.

25. The problem with gatekeepers Says:

Prediction: the moratorium won’t last in any meaningful way. You yourself seem to hint at that when you say “exceptions can be made when and if there’s a serious claim to have achieved quantum supremacy, or in other special cases”.

That “special case” provision is so vague that it can encompass almost anything.

The spotlight is addictive. Instead of denying your love affair with the popularization of computer science ideas, you should embrace it wholeheartedly. You could be the Carl Sagan of computer science in this age, if you wanted to.

Finally, I take issue with your characterization of your work as “Enlightenment duties”. To begin with, the “Enlightenment” was not a clearly defined ideology, rather an umbrella term for a group of thinkers who sought to bring reason as counter point to superstition at a time when the European elite though that astrology was scientific https://en.wikipedia.org/wiki/Astrology#Renaissance_and_Early_Modern -as an aside, things like these make me be skeptic of beliefs that the elite accepts blindly as facts without much argument. Ours would be the first elite who hasn’t fallen for chimeras in thousands of years. I trust much more strongly the thousand year old record of human elites believing in nonsense.

Among those thinkers we now consider as part of the Enlightenment, you can find some like John Locke -whose ideas about government found their way to the US constitution via the founding fathers. John Locke’s religious ideas would be considered extreme by your own standards https://en.wikipedia.org/wiki/John_Locke#Religious_beliefs “With regard to the Bible Locke was very conservative. He retained the doctrine of the verbal inspiration of the Scriptures.The miracles were proofs of the divine nature of the biblical message. Locke was convinced that the entire content of the Bible was in agreement with human reason”. further “Although Locke was an advocate of tolerance, he urged the authorities not to tolerate atheism, because he thought the denial of God’s existence would undermine the social order and lead to chaos”.

Simply put, John Locke’s ideas are so much at the core of the founding fathers idea of government that Thomas Jefferson said https://en.wikipedia.org/wiki/Two_Treatises_of_Government#North_America “Bacon, Locke and Newton I consider them as the three greatest men that have ever lived, without any exception, and as having laid the foundation of those superstructures which have been raised in the Physical & Moral sciences”.

And please, spare me of an exercise of “historical fiction” of the kind I am so used to hear that John Locke and the like would be atheists had they lived in 2017. It is impossible to understate what Locke (and similar) contributed to our current world. Anybody can like his ideas after they have been practiced for 200+ years first in the US, then in the world at large. It takes a man of his genius to propose something like that in a context, XVII-th century Europe- that took for a given that “absolute monarchy” was the end of history when it came to government.

26. Scott Says:

venky #23: First, because the journalists are all over the world in various time zones, and are usually under deadline, and have complicated constraints of their own about when they can and can’t talk.

Second, because I lack the willpower to say, for example, that I’m only going to answer emails about this topic at these times during the week. If there’s easy work to be done, then I’ll always, always knock it off as a way of avoiding the hard work (indeed, answering this very comment is an example of that 😉 ). And as long as journalists know they can email me at will, the problem is that there will be a constant stream of easy work to distract me from hard work.

Third, because even office hours themselves—or classes, lunches, meetings, or anything whatsoever that’s at a set time in the day—are severe drains on my productivity. Besides (of course) having two kids, these are what stand between me and the sorts of insane hours, all-night paper-writing sessions, and uninterrupted 10-hour math binges that I had in grad school and postdoc—i.e., the period of my life when I actually got stuff done.

However, most of these things I do because they’re part of my job! Or because they contribute to the productivity of my students, to whom I feel an almost parental obligation. I now have to prioritize ruthlessly about the productivity sinks that aren’t matters of obligation.

27. Jon K. Says:

What about implementing a small consulting fee for the next year? This will cut down on demand by encouraging journalists to look for other quantum and/or complexity experts, but still allow you to be involved when a journalist or news outlet really wants to get *your* thoughts. The consulting fee could be calibrated to fit your desired work-life-balance utility function.

Monetize the brand! 🙂 You’ll be able to treat the family to dinner the next time you almost ruin an outing.

28. Atreat Says:

Jon K. with the market based solution for the win!

29. Sniffnoy Says:

TPWG #25:

This is pretty silly. Why does accepting some of Locke’s ideas necessitate accepting other unrelated ideas of his? Those seem very separable, especially considering how many — such as Jefferson who you mention — evidently did separate them.

30. jonas Says:

I welcome this decision. Unlike the science journals that really depend on researchers like you volunteering a significant amount of your time to referee their papers, journalists aren’t so dependent on you. They are prepared for people not willing to give them interviews, and are able to produce popular science articles of asymptotically the same quality even with this constraint. Plainly speaking, since most of them never really cared about what you said in the interviews, they’ll just keep inventing stuff.

In this case, they might say that quantum computing has no practical values, the research mathematician elites have always known this, and now that their deception has come to light, they’ve gone back to their old tactics of retiring to their ivory towers and not bothering to tell anything about their work to the general population. Quantum computing researcher Scott Aaronson, who had been one of the loudest voices in emphasizing how important quantum computing is, has declined to comment.

31. different Scott Says:

Scott #22: It’s worked at least once – I moved you off my ‘to pester’ list.

32. Erica Klarreich Says:

Scott, thank you for giving so much time to answering my questions over the years. Your insight, clarity, and sheer quotability have made my articles much more compelling than they would otherwise have been (and probably saved me from some embarrassing errors, too). I hope you enjoy your well-earned break.

33. Scott Says:

Jon K. #27 and Atreat #28: For that very reason, I do charge a pretty high consulting fee to talk about quantum computing to (e.g.) VCs and investment banks. For journalists, though, the problem with your proposal is that, as far as I know, reputable media outlets have a general policy of not paying sources. (And even if they were willing to pay, I’d feel bad about accepting it if I knew they couldn’t afford it.)

34. Scott Says:

jonas #30:

In this case, they might say that quantum computing has no practical values, the research mathematician elites have always known this, and now that their deception has come to light, they’ve gone back to their old tactics of retiring to their ivory towers and not bothering to tell anything about their work to the general population.

Don’t tempt me to renounce my oath a mere two days after making it… 😀

35. Scott Says:

Erica #32: Thanks!!

36. Ben Kuipers Says:

Someone (maybe him) told me about how Edsger W. Dijkstra handled the many review requests he received. If he had time to read the paper, write the review, and get it out in the next day’s mail, he did so. If not, he returned the manuscript in the next day’s mail, telling the editor he didn’t have time. (You can see this was some time ago.) This made for happy editors, as well as keeping his time manageable.

37. The problem with gatekeepers Says:

Sniffnoy #29

Did Thomas Jefferson separate them? Did he demonize John Locke’s religious ideas in the way some in academia demonize the same ideas today? I think that the answer to both questions is No. Thomas Jefferson had many faults, first among them was his condition as slave owner, but I don’t think he demonized religious people even though he himself, based on what I have read, was either a deist or an outright atheist. And BTW, before somebody accuses me of falling into https://en.wikipedia.org/wiki/Whig_history fallacious reasoning myself, I remind everyone that at the time Thomas Jefferson penned his most famous writings on liberty, slavery was already vehemently opposed by some colonialists. Slavery was officially abolished in Massachusetts in 1783, the year Americans won their war of independence against Britain, for example.

It is not silly to make clear what “Enlightenment” really was and put it into its proper historical context. I am not saying that Scott is guilty of equating “Enlightenment” with irreligiousity -since it is the first time I have seen him using the word- but I have been in too many interactions where a blunt metonymic fallacy – http://www.oxfordreference.com/view/10.1093/acref/9780199568758.001.0001/acref-9780199568758-e-1729 – was committed when using the word “Enlightenment”. The “Enlightenment” movement was pro-reason and anti-superstition. It was never “anti religious belief” as a whole -even though some Enlightenment figures were atheists- in the way the crop of New Atheists like Richard Dawkins have hijacked the word “bright”.

So I think the qualification is warranted. I let Scott elaborate on what he meant by “Enlightenment duties”.

38. Scott Says:

Gatekeepers #37: Not only is it entirely possible to be both religious and pro-Enlightenment, but I’d say that hundreds of millions of people are. To my mind, what “Enlightenment values” do demand in this sphere is a commitment to:

(1) Complete religious freedom and toleration, including the freedom to switch religions or renounce religion

(2) Religious pluralism—including a willingness to work and interact with people of other religious backgrounds as equals, not just as (e.g.) potential converts, or infidels whose souls need to be saved from damnation

(3) At least some degree of separation of church and state, including opposition to any religious tests for holding public office, and to the persecution of religious minorities

(4) Some baseline of humanistic values, including (e.g.) a belief in the political equality of the races and sexes, freedom of speech, toleration of the private sexual behavior of others (including homosexual behavior), and the rejection of legal recognition of “crimes” (blasphemy, heresy, sodomy, working on the Sabbath…) that only make sense in religious contexts

(5) A willingness to state one’s arguments in secular terms, and to acknowledge the possibility of being wrong and of new evidence or arguments changing the situation, whenever the arguments are meant to be persuasive to people of different religious backgrounds than one’s own (as in law, politics, history, philosophy, or science)

(6) Science and reason—including, most pointedly, the willingness to reinterpret (or amend, or treat as metaphorical, or selectively ignore) sacred scriptures when and if they conflict with the discoveries of science

Did I miss anything? 🙂

39. Sniffnoy Says:

Did Thomas Jefferson separate them? Did he demonize John Locke’s religious ideas in the way some in academia demonize the same ideas today? I think that the answer to both questions is No. Thomas Jefferson had many faults, first among them was his condition as slave owner, but I don’t think he demonized religious people even though he himself, based on what I have read, was either a deist or an outright atheist.

So, in short, he did in fact separate the ideas. He agreed with some but not others, considering them separately rather than based on who originated them.

I was going to continue on in this line but rereading your original comment I’m getting the idea that your actual point was elsewhere and I’m not really responding to it, so, eh.

40. boo Says:

what do you think about the UFO footage release?

41. Scott Says:

boo #40: Is there anything about this that should cause me to take it more seriously, or even spend more seconds thinking about it, than 70 years of previous UFO claims—the investigation of which has taught us a lot about human psychology, and maybe about various aerial phenomena, but nothing positive at all about extraterrestrial intelligence?

Unexplained mysteries are all around us. Just yesterday, for example, I was absolutely certain that I turned the oven off, just as my wife told me to … yet the oven remained on and overcooked our dinner. Still, the bar for giving such phenomena international attention, or for speculating about an extraterrestrial origin for them, should probably be higher.

42. fred Says:

Scott
“do they “know” which individual person is looking at them? Whether it’s morning or night? Which room they’re currently in?”

They probably do, but they just don’t dwell on this fact as much as we do, they just move on to doing things that obsess them… like we all do! – how many humans actually marvel everyday at their own ability to know in which room they’re currently in? Or that they’re alive and breathing? Versus going for the next thing to do (looking down their cell phone) or thinking about some hypothetical future or reminiscing on the past?

In his book “My view of the world”, Erwin Schrodinger puts things upside down a bit by noticing that individual consciousness is what all start with, and what we each call “the world” is but an internal construct entirely within our own hermetic sphere of consciousness.
What’s miraculous to him is how all those entirely private spheres of consciousness somehow manage to become aware of each other, and how all those private world constructs within them end up merging into the concept of a physical reality (he argues that because of that process, the concept of a physical reality is really “metaphysical”).
The way we recognize others as similar to us is first through mimicry. Animals and human babies all do it. Behaving like something we think is similar to us is a way to connect deeply (that’s also probably why/how the sense of self evolved).

Then beyond that there is language.

There’s fascinating evidence that animals can be as aware as we are http://www.koko.org/sign-language

43. The problem with gatekeepers Says:

Scott #38

Thanks for clarifying. I hold those same values and yes, I am also a Christian. In fact, Jesus himself could be classified as an Enlightenment figure according to this definition. He was pro separation of church and state (Matthew 22:21), he was definitely tolerant with other religious traditions of his time with teachings such as the parable of the Good Samaritan (Luke 10:25-37) and if there is anybody who knows what’s like to be killed by religious intolerance, well, that’s Him.

I am glad you are making this clear.

Sniffnoy #39

Jefferson still went as far as signaling John Locke, the whole person, as a great man. Well, in fact, he even signaled Isaac Newton -whose religious convictions were even more extreme than Locke’s- as a great man. This notion that he considered in his praise only the ideas from these men that he agreed with is your own editing, not something supported by the quote I provided. A typical example of over-fitting religious animosity into a famous person’s writing if you were to ask me.

44. Atreat Says:

“Just yesterday, for example, I was absolutely certain that I turned the oven off, just as my wife told me to…”

Little Green Men running amok in your house gaslighting you. Literally. Tee hee.

45. jonas Says:

As for the tax, I’m a bit late, but I believe Jorge Cham’s reaction wasn’t linked in the previous thread about it: http://phdcomics.com/comics/archive.php?comicid=1985

46. Andrew G Says:

Re: Unrelated Update #1

Let’s dispel with the myth once and for all that babies / dogs / cats don’t know what they’re doing. They know exactly what they’re doing!

47. John Sidles Says:

Scott asks (circa #38)  “Did I miss anything [in summarizing ‘Enlightenment Values’]?”

The quick answer: Scott’s list is solidly grounded in Enlightenment history.

Specifically, in Jonathan Israel’s Enlightenment Contested: Philosophy, Modernity, and the Emancipation of Man 1670-1752 (p. 866) we read:

Radical Enlightenment conceived as a package of basic concepts and values may be summarized in eight cardinal points:

JI.1 adoption of philosophical (mathematical-historical) reason as the only and exclusive criterion of what is true;

JI.2 rejection of all supernatural agency, magic, disembodied spirits, and divine providence;

JI.3 equality of all mankind (racial and sexual);

JI.4 secular ‘universalism’ in ethics anchored in equality and chiefly stressing equity, justice, and charity;

JI.5 comprehensive toleration and freedom of thought based on independent critical thinking;

JI.6 personal liberty of lifestyle and sexual conduct between consenting adults;

JI.7 freedom of expression, political criticism, and the press, in the public sphere.

JI.8 democratic republicanism as the most legitimate form of politics.

Comparing Shtetl Optimized Enlightenment Values with Jonathan Israel’s pointwise, we find:

Scott Aaron’s Enlightenment Values (SA.*) …
compared to Jonathan Israel’s (JI.*)

SA.1 ⇆ JI.5
SA.2 ⇆ JI.3⊕7
SA.3 ⇆ JI.7⊕8
SA.4 ⇆ JI.4⊕6
SA.5 ⇆ JI.1
SA.6 ⇆ JI.2

The bottom line: Shtetl Optimized’s enlightened values closely accord with the historical Enlightenment values that Jonathan Israel summarizes.

A sharply contrasting alt-right critique of Enlightenment values is provided by Andrew Joyce’s three-part jeremiad “Pariah to Messiah: The Engineered Apotheosis of Baruch Spinoza“, which appeared in the (Putin-assisted?) Occidental Observer: White Identity, Interests, and Culture (March, 2013).

To refocus our attention on quantum science, let’s consider the cardinal points of enlightened Quantum Supremacy (QuSu) versus enlightened Quantum Skepticism (QuSP). Using Jonathan Israel’s summary as a template yields only two (of eight) cardinal points that differ between QuSu and QuSk:

Enlightened Quantum Supremacy (QuSu) and enlightened Quantum Skepticism (QuSk), each conceived as a package of basic concepts and values, may be summarized in eight cardinal points (here ‘QuS*’ labels points in common):

—–
QuSu.1 adoption of unitary dynamics and projective measurements, on Hilbert spaces of countably many dimensions, as the privileged model of computational processes;

QuSk.1 adoption of quantum electrodynamics (QED), on Hilbert spaces of uncountably many dimensions, as the privileged model of computational processes;
—–

QuS*.2 (shared) rejection of all hidden variable models;

QuS*.3 (shared) scalability as a sine qua non of technological practicality;

—–
QuSu.4 quantum dynamical ‘universality’, anchored in complexity theory, and chiefly stressing that there exist physically realizable quantum dynamical processes whose classical unravellings are (postulated to be) fundamentally incompatible with the Extended Church-Turing thesis;

QuSk.4 thermodynamic ‘universality’, anchored in macroscopically localized entropy-densities, and chiefly stressing that classical unravellings of physically realizable quantum electrodynamical processes are (postulated to be) universally compatible with the Extended Church-Turing thesis;
—–

QuS*.5 (shared) comprehensive algorithmic freedom based on practical hardware engineering;

QuS*.6 (shared) liberty of hardware instantiation of computational processes;

QuS*.7 (shared) freedom of pedagogic discourse and scientific criticism in the public sphere;

QuS*.8 (shared) peer reviewed publication as the most legitimate form of scientific communication.

One take-away lesson for science-popularizers is simple this: from an enlightened scientific perspective, Quantum Supremacy and Quantum Skepticism are, fundamentally, much more alike than different.

48. Sniffnoy Says:

TPWG #43: Right, see, I’m not talking about what he “considered in his praise”, I’m talking about what he agreed with. I see no particular reason why the former might be relevant to anything, and as such had not considered it might be something you were talking about. So like I said we seem to have been talking past each other, and I’m not really sure this is going anywhere useful.

49. boo Says:

Scott this footage was released by official sources https://www.nytimes.com/2017/12/16/us/politics/pentagon-program-ufo-harry-reid.html!!!!!!!

Also what is the tex for
?
P = NP

???????

50. Scott Says:

boo #49: But I remember as a teenager in the 90s, the other teenagers I knew who were UFO buffs were always talking about “official sources,” the CIA and the Pentagon, unexplained footage, all the same basic ingredients. And then I learned, e.g. from reading Carl Sagan, that those have been the basic ingredients of UFOlogy ever since the subject “took off” (har har) shortly after WWII—by complete coincidence, the exact same time when the public was first being inundated with movies about spacemen, and also the exact same time when the Air Force really did start doing all sorts of aerial shenanigans that it tried to keep secret.

Yet again and again and again, the previous cases, when they could be resolved at all, had ordinary terrestrial explanations. Of course I don’t know that the same will be true this time around … but at some point, it becomes like the story of the guy who used to believe that lightning came from an angry Zeus, but then someone teaches him Maxwell’s equations, so he revises his belief to say that most lightning is explainable by Maxwell’s equations, and only some of it comes from angry Zeus.

It’s like, try to step back for one minute from the immediate puzzle! Look instead at the reference class of similar puzzles, and try to find general principles that would give the right answers for most of them! Think about it like a Bayesian! (This, not coincidentally, is exactly what I recommended years ago for thinking about the JFK assassination.)

51. Scott Says:

Gatekeepers #25:

Prediction: the moratorium won’t last in any meaningful way. You yourself seem to hint at that when you say “exceptions can be made when and if there’s a serious claim to have achieved quantum supremacy, or in other special cases”.

That “special case” provision is so vague that it can encompass almost anything.

The spotlight is addictive. Instead of denying your love affair with the popularization of computer science ideas, you should embrace it wholeheartedly. You could be the Carl Sagan of computer science in this age, if you wanted to.

That sounds nice, but if I wanted to achieve even 1% of Sagan’s productivity at (e.g.) writing popular books, then I’d indeed need to become much more ruthless at managing my time!

I will be passing off almost all media requests this year to my colleagues, because that’s something I want to try, and because this post will let me. But even if I only passed off (say) half of them, writing the post would still have been a win in terms of time.

52. Sniffnoy Says:

Scott #50:

Somehow I don’t think boo actually meant that seriously, and instead was trying to imitate your FAQ…

53. The problem with gatekeepers Says:

Scott #51

I think you should definitely consider becoming “Carl Sagan”-like. In fact, forget about “Carl Sagan”, each of us is different. I don’t like when I am asked to be like “someone else”, so I don’t like to ask others to do so.

My point here is that it seems you have a knack for communicating computer science ideas to the public at large that escapes other experts in the field of theoretical computer science. From personal experience having worked with, and continue to work with, very smart technical people, not everybody in computer science has this gift. It’s already hard to have experts in computer science understand each other points when they discuss non trivial issues. Having the public know about these issues in very important, particularly given that debates about what AI will accomplish or its limits aside, I have no doubt that we are in a path in that will make the computer systems of tomorrow even more complex than those of today. And their impact in society will also be greater. At the same time, and this is something that Carl Sagan mentioned during one of his last interviews, it seems that the ability of the public at large to understand these issues seems going down. I have stopped counting the number of conversations that I have tried to have with regular folks about the danger of Google, Apple and the like tracking everybody’s smartphone GPS position data that can be correlated with their identity and online tracking only to be told “I have nothing to hide, I don’t care”. I get the feeling that if these same people were asked to live with a video camera taping their daily lives at home they would not be as understanding and yet, I find the former type of tracking way more dangerous for privacy. My take is that most regular folks do not understand computing on large amounts of data as a technology.

On a more personal note, when I was growing up, I got a lot of inspiration from Carl Sagan’s documentaries. Nobody in my family had ever pursued a career in science so other than the encouragement I got from my high school teachers, Carl Sagan was the closest I had as an informal mentor as I navigated college life and beyond.

So all this to say that becoming a public computer science intellectual could be, depending on your personal preferences of course, more rewarding than leading an obscure intellectual life that gets rewarded with things like membership in the National Academy of Engineering or the National Academy of Science. The public doesn’t generally know who these people are and very few of them are remembered after their deaths unless they have done something of significance that affects society at large. I bet Carl Sagan has had more impact for science as a whole through the number of people he inspired to become scientists or engineers than most of the people who were elected to the National Academy of Science at the time he was refused membership to the same.

54. boo Says:

Scott this is my theory. Part of the $22million was spent on this footage to increase credibility of the program? Plausible? Or is this one of the rare Zeus jolts (I am taking your exceptional Zeus jolts literally that they come from Zeus (unless you imply something else))? 55. xyz Says: Something that’s been annoying me about the AI risk community is the use of unnecessary specialized jargon counterproductive to communicating with a wide audience. The worst is “singleton”, “hegemon” is the term of art everywhere else, and I see no obvious reason not to use it other than a desire to signal one’s membership in the AI risk community. And while I detest the Great Mouse of Darkness as much as anyone, it seems to me that referencing “paperclip maximizers” and either explaning what that means at length or hoping that your listeners will be bothered to google the phrase is a bit silly when one could just refer them to the single most famous animated short of all time. 56. Dan Staley Says: I think it’s absolutely imperative that Scott immediately break his moratorium in order to comment on these new revelations about his oven. 57. Raoul Ohio Says: xyz #55: Are “singleton” and “hegemon” related? I thought “singleton” was a OOP GOF Pattern (to use some unnecessary jargon), and “hegemon” was something PoMoPoPo’s (Post Modern Political Posers) yammered about. 58. xyz Says: Raoul Ohio #57 I imagine OOP is where the word hails from originally, but I see it used to mean “a power nexus that can defeat all challengers” a fair bit, most often in the context of FOOM scenarios. I just don’t see the point of coining a new term for that when a perfectly servicable one already exists. 59. Kenneth W. Regan Says: One comment to the linked 2011 item with the “Minus Sign Test”: Deutsch in 1984-85 really did believe that the quantum machine model he had then was capable of hypercomputation. If I recall correctly from my own over-the-shoulders peering while the greats of the Oxford Maths Institute debated this, the argument came down to something about infinite random sequences where an intensional definition seems to be non-r.e. but was equivalent to an extensional one that is r.e. So his argument was refuted, and I don’t know what became of any writeup of it. The actual 1985 paper came out different. 60. amy Says: Atreat #44: you mean as in…soda? 61. Scott Says: Ken #59: Interesting historical tidbit! Even more recently, Deutsch has written things that elide the distinction between computability and complexity more than I’m comfortable with, although I think he’s gotten better about that. The argument that you describe sounds like one I’ve been involved with many times myself, when people ask me why the randomness of quantum measurement outcomes doesn’t already refute the Church-Turing Thesis, or why it shouldn’t already be considered “hypercomputational.” In response, I try to impress on them what a weak and pathetic form of “hypercomputation” that is, compared to what one might have hoped for! If it did refute the Church-Turing Thesis, all that would really mean was that we weren’t careful enough in stating the thesis. We should restate it to encompass probabilistic Turing machines, in which case we’re right back where we started. (Of course it’s also true that probabilistic TMs don’t let us decide any languages beyond what deterministic TMs let us decide. They do, however, let us perform other tasks that are deterministically impossible, like “given n as input, output an algorithmically incompressible string of length n, with high success probability.”) 62. Uncle Brad Says: xyz #58 I see no future for you in marketing. 63. JohnK Says: Scott, Why is the tax bill “cruel & monstrous?” I’m not totally up on it, but it doesn’t seem so bad to me from what I do know. 64. The problem with gatekeepers Says: JohnK #63, As Margaret Thatcher already noticed, a common theme in leftists is the belief that they have a God given right to spend other people’s money anyway they wish. In their worldview, taxation is not thief -as it is in my own- but rather an entitlement that the “enlightened bureaucrats” in government have to spend money collected via the coercive force of government as they see fit. Any time there is less money from taxation at the hands of those bureaucrats and more money in the taxpayer’s pockets, the “enlightened bureaucrats” scream. It’s like this idea that is popular among Silicon Valley tycoons of a universal minimum income. Let’s consider for a second how perverse this idea is. So, people like Larry Page, Sergey Brin, Mark Zuckerberg, Elon Musk, etc have taken automation to the extreme to the point that many people lack the necessary skills to keep up and will necessarily be unemployed. Instead of volunteering their own money or their own companies’ money to compensate those affected by their misdeeds, they want the rest of us to pay for it. Cases like this is what the term “limousine liberal” was coined for. 65. Scott Says: JohnK #63: Well, it amounts to a massive transfer of wealth from the poor and middle-class to the rich, at exactly the time when inequality in the US has become 1929-level severe and we ought to be changing the tax code in the opposite direction. Some of it, like eliminating the SALT deduction, is fundamentally unjust and upends assumptions people have planned their lives around. And it’s opposed by most of the American public and by almost all economists, and was rammed through Congress without any serious debate. Probably even worse than the bill itself is the contempt for democracy that the process of passing it revealed, with Trump and Congressional Republicans just telling bald-faced lies (e.g., that the bill would actually hurt rich people like Trump), and suppressing analysis from the Treasury department about the bill’s terrible effects, because they knew this thing had no honest defense. Worse yet, not only does the bill add$1.5 trillion to the debt (exposing the hypocrisy of the Republican “”debt hawks””), but it’s designed to explode in everyone’s faces a few years from now—when we’ll be faced with a choice between increasing the debt by much more even than $1.5 trillion, or else raising taxes on most of the American public in order to pay for the giant giveaway to the rich. Meanwhile, even more horrible crap was added on, like repealing the individual mandate (!) and drilling in the Arctic National Wildlife Refuge, as part of a successful “Shock Doctrine” strategy to overwhelm the opposition. AFAIK, lowering the corporate tax rate could maybe, possibly have been economically defended, as part of a package that would also include benefits for the poor and middle-class. But the rest of it is just pure looting of the public treasury to reward Republican campaign donors at the expense of the country’s future. Like seriously: what is the rational defense of any of this, that differentiates it in any way from the corruption that regularly occurs in Third World banana republics? 66. The problem with gatekeepers Says: Scott #65 Let’s be real here. The SALT deduction benefited overwhelmingly the upper middle class people who live in expensive, blue states such as California or New York. Most people used the deduction to deduce a combination of state taxes and local property taxes. Given that for a married couple, the standard deduction has doubled to 20K, keeping things as they were would have benefited only people who would have deduced more than 20K in these two concepts. They don’t look poor people to me. This deduction was being subsidized by people who were not upper middle class from California, New York or elsewhere. I don’t feel sorry for these people. They were living above their means subsidized by the rest of us. 67. Michael Says: Also, the tax bill limits deductions for state and local taxes to$10,000.00, which is a way of punishing blue states, which often have higher taxes than red states.

68. The problem with gatekeepers Says:

Here is another popular deduction that benefits mostly those already rich,

“Federal housing policy transfers lots of money to rich homeowners, a bit less to middle-class homeowners, and practically nothing to poor renters.”

The tax bill kept it, but lowered the max amount of loans that are eligible for it from 1 million to 750K. Again, you tell me which Americans buy these homes. It ain’t the poor.

Slate, which cannot be labeled as Republican, let alone pro-Trump, published a very provocative article about the upper middle class 2 years ago,

“The Upper Middle Class Is Ruining America
And I want it to stop.”

So yeah, let’s at the very minimum agree that the tax code was already weaponized to favor these people. I don’t know if the tax bill will deliver on the promises Trump made -projections based on economic analysis alone are mostly junk because economics is dismal science- but to say that the previous regime was awesome, and that the new regime is awful is misleading. It was awesome for a subset of the American people (25 % at most). Now it will be a bit less good for them, but others will see more money in their pockets than with the previous regime. That’s good news for them.

69. asdf Says:

Scott #61, http://jdh.hamkins.org/infinite-chess-dartmouth-2014/ and related posts mention that in infinite chess (edgeless board), there are positions where if white and black both are required to use computable strategies, white can win; but if computability is not required (randomness is available?) then black can draw. I haven’t read the paper yet so don’t know how much incomputability is actually required.

70. CScuriosity Says:

Does P=NP mean the end of the world? Everything human brain can do a computer can and so a csapien replaces sapiens?

71. Scott Says:

CScuriosity #70: No, I wouldn’t say P=NP means “the end of the world”—in particular, as I said in my survey, it’s neither necessary nor sufficient for an AI singularity—but if P=NP and the algorithm could actually be run in practice, it would certainly be a very different world.

72. Scott Says:

asdf #69: Cool! Of course, even if we agreed that the ability to generate infinitely many random bits was “uncomputable in a more interesting sense” than the ability to generate finitely many, it would still require infinite time, putting it outside the scope of what I normally think of as “the physical Church-Turing Thesis.”

73. CScuriosity Says:

I do not understand ‘Conversely, while a proof of P = NP might hasten a robot uprising, it wouldn’t guarantee one. For again, what P?= NP asks is not whether all creativity can be automated, but only creativity whose fruits can quickly be verified by computer programs’. What is a problem related to creativity that is not in P if P=NP and SAT has linear time algorithm with benign constants?

74. Scott Says:

CScuriosity #73: There might or might be any such problem. Indeed, if you believe the brain is essentially a classical computer, then everything humans can do should be captured by the class P, regardless of whether or not P=NP!

But even so, even if someone proved tomorrow that P=NP, via an efficient-in-practice algorithm that they handed you … if you wanted to use their breakthrough to automate human creativity, you would still face the problem of writing down the actual NP verifier for whatever creative task you wanted to automate. E.g., if you wanted your computer to generate great novels, then you’d still have to figure out how to get your computer to recognize great novels when shown them, before your magical P=NP code could help you.

Now, you might believe that programming a computer to recognize great novels must be possible, since you can recognize great novels and “your brain is just a Turing machine”—but even then, believing that the program exists and actually producing it would be two different things, just like in the world of today.

And yes, you might be able to use P=NP in a second place, to speed up machine learning or whatever and thereby help create a fast program to recognize great novels (which could then, by P=NP, be converted into a fast program to generate great novels). My only point was that you’d still be left with a nontrivial problem there.

75. CScuriosity Says:

Ok I see the point. So if someone publishes a 7n time complexity algorithm for 3SAT there will be something that prevents you to make use of full potential of 3SAT thereby preventing the end of the world (sounds like matrix stuff but I think traditional institutions like money based, knowledge based, altruism based, entertainment based might collapse and a third world war realistically unpreventable).

76. Daniel Says:

Twitler’s the guy who sent the people marked with blue checks to the gas chambers, right?

77. asdf Says:

CScuriosity, if you reject the idea that the brain is a classical computer, then even if P=NP but assuming P!=PSPACE, it’s conceivable that a computer could never play generalized chess as well as a human. Sadly for this theory, computers already outplay humans…

Scott #72, I’m not sure which version of infinite chess that computability result considers, but quite a few of the results are about the version with an infinite board and a finite number of pieces, so all positions must be won or drawn in finite time. You still get positions with transfinite game values, like “white to mate in omega” but that means black has to pick a finite number n and make a move selected by that n. After seeing black’s choice, white can now mate in n. So it’s bounded by omega since n can be as large as black likes, but not infinite.

78. Scott Says:

asdf #77: Cool! Can you tell me anything further about how that goes? In particular, I assume that a “White to mate in omega” situation would have to involve Black encoding the value of n by moving a rook, bishop, or queen n squares? Because otherwise—if Black encoded n piecemeal via a sequence of moves—then Black could just continue those moves forever (increasing n without bound) to force a draw, a la König’s Lemma.

79. asdf Says:

Scott, yes, move the rook n squares to make white mate in n is the general idea. You can have higher ordinal values that way too, provably up to omega**4 on a 2-d chessboard and omega_1 (i.e. all the countable ordinals) on a 3-d board, and conjecturally omega_1 on 2-d.

Here’s the MO thread that set it off:

https://mathoverflow.net/questions/63423/checkmate-in-omega-moves

Here’s a mate-in-omega position:

https://i.stack.imgur.com/TaMqW.jpg

It’s part of Joel David Hamkins’ lengthy answer containing a lot of other diagrams and a pointer to his joint paper:

https://mathoverflow.net/a/122250

80. asdf Says:

Added: looking at the MO thread again, it looks like the uncomputable-strategy draw does depend on having infinitely many pieces, and also with finitely many pieces the ordinal values all have to be recursive (which makes sense). Oh well.

Maybe randomness can help win the “who can name the bigger number” game. A and B each have to constructively specify a number N on a fixed size piece of paper, the bigger N wins, and A and B both can use the axioms of Peano arithmetic but B can also roll dice. So B can generate more axioms of the sort “X has arithmetic complexity greater than k” which are true with high probability, then use those axioms in naming a number…

81. anon Says:

Scott #12 &
Mateus #11:

Would a junior researcher’s (academic) career really benfit from the media attention??
How junior?

82. Fang Zhang Says:

You speak of the Minus Sign Test, but is there a way to popularize quantum computing without getting to the depth of complex numbers? I know that all quantum computation can be done with just real gates, but I also feel that any popularization need to assure the readers that quantum computing is physical, and I can’t think of a way to explain the underlying physics without complex numbers. (Of course, then people may still think it’s not *really* physical…)

83. Scott Says:

Fang Zhang #82: Try Feynman’s QED book! He never mentions “complex numbers,” just says that you have to add up a bunch of arrows to find how likely a particle is to end up somewhere.

Of course, someone who understands it might still doubt that that’s how the world could actually work. But popularizing QC without getting across that that’s how the world does work (as far as physics can tell) strikes me as an unsolvable problem. It would be like trying to popularize evolution without getting into humans and fish having a common ancestor, because if you told people that then they might doubt the whole story.

84. just a thought Says:

Lazy Journalists?

It’s a lot easier for them to come up with a story if they don’t have to do the lion’s share of the research. And if there are errors, well they can blame them on the interviewee. But if the material is good, that reflects positively on them.

Not that that’s a reason to run from interviews, just to be judicious about which will be the best investment of your time, IMO.

PS – just found your blog, and enjoy what I’ve read so far. If you have links to what you think are some of your best interviews, it might be fun to read a few, especially if you cover material there that isn’t here.


text:
# Trying to simplify a permeability expression

1. Jun 4, 2006

### NEWO

I'm just looking through some work I did a while back and trying to simplify an expression,

epsilon_{0}epsilon_{r}=epsilon

is there an expression for

mu_{0}mu_{r}?

2. Jun 4, 2006

### Hootenanny

Staff Emeritus
The relative permeability is defined as

$$\mu_{r} = \frac{\mu}{\mu_{0}} \Leftrightarrow \mu = \mu_{0}\cdot\mu_{r}$$

3. Jun 4, 2006

cool cheers

format: plain


text:
# Trig substitution problem

## Homework Statement

Evaluate the following integrals or state that they diverge. Use proper notation.

Integral from 0 to 2 of (x+1)/Square root(4-x^2)

## The Attempt at a Solution

I just substituted x = 2sin(theta) thus dx = 2cos(theta)

I got to the point where it is .5(integral from 0 to 2 of 2tan(theta)) + .5(integral from 0 to 2 of sec(theta)).

I think theres an easier approach at the problem.

suggestions?

Related Calculus and Beyond Homework Help News on Phys.org
Partial fractions.

I think trig subst. is a good way. The limits of integration will change since you went from x to theta.

dextercioby
Homework Helper
So instead of going from 0 to 2, they go from 0 to $\pi/2$.

Ya, that's it. Why do people have to take all the fun out of a problem? Why not leave a hint as a hint? This one-up business is boring.

Gib Z
Homework Helper
$$\int\frac{x+1}{4-x^2} dx =\frac{3}{4} \int \frac{1}{2-x} dx - \frac{1}{4}\int \frac{1}{2+x} dx$$. Far too simple from there, the only reason I posted even this far was because I wanted to do it as well :)

Gib Z
Homework Helper
Shoot me in the face, i didnt see the sqrt...

hello friend

solution

Integral from 0 to 2 of (x+1)/Square root(4-x^2) dx

let x=2sin(&)
dx=2cos(&)d&

=Integral from 0 to [PLAIN]https://www.physicsforums.com/latex_images/12/1253579-0.png [Broken] of (2sin&+1)(2cos&)/2cos& d&

=Integral from 0 to [PLAIN]https://www.physicsforums.com/latex_images/12/1253579-0.png [Broken] of (2sin&+1) d&

i think know it is easy to solve


text:
# Temperature difference conductor to surface

This is the temperature difference between the conductor and the surface.

Symbol
$\Delta \theta_{ce}$
Unit
K
Formulae
$\theta_{c} - \theta_{e}$
Related
$\theta_{c}$
$\theta_{e}$
Used in
$\theta_{c}$


text:
Talks
Fall 2018

# Algorithmic Polynomials

Tuesday, September 11th, 2018 11:30 am12:00 pm

Speaker:

The approximate degree of a Boolean function f(x_1,x_2,...,x_n) is the minimum degree of a real polynomial that approximates f pointwise within 1/3. Upper bounds on approximate degree have a variety of applications in learning theory, diferential privacy, and algorithm design in general. Nearly all known upper bounds on approximate degree arise in an existential manner from bounds on quantum query complexity. We develop a first-principles, classical approach to the polynomial approximation of Boolean functions. We use it to give the first constructive upper bounds on the approximate degree of several fundamental problems:

(i) $O(n^{\frac{3}{4}-\frac{1}{4(2^{k}-1)}})$ for the k-element distinctness problem;

(ii) $O(n^{1-\frac{1}{k+1}})$ for the k-subset sum problem;

(iii) $O(n^{1-\frac{1}{k+1}})$ for any k-DNF or k-CNF formula;

(iv) $O(n^{3/4})$ for the surjectivity problem.

In all cases, we obtain explicit, closed-form approximating polynomials that are unrelated to the quantum arguments from previous work. Our first three results match the bounds from quantum query complexity.
Our fourth result improves polynomially on the Theta(n) quantum query complexity of the problem and refutes the conjecture by several experts that surjectivity has approximate degree Omega(n). In particular, we exhibit the first natural problem with a polynomial gap between approximate degree and quantum query complexity.

AttachmentSize
3.13 MB


text:
# When do you use the Dickey Fuller Test and the Ljung-Box Test?

When do you use the Dickey Fuller Test and the Ljung-Box Test?

They seem to serve the same purpose?

I think that the Durbin-Watson statistics just checks for autocorrelation at lag 1.

• The Dickey-Fuller test addresses the question of whether the time series of interest has a unit root.
• The Ljung-Box and the Durbin-Watson tests help assess whether the time series of interest is autocorrelated.

These are two different questions. According to the tag description of a unit root,

A unit root is a property of a non-stationary time series which can lead to spurious regressions and wrong inference. A series $$y_t = y_{t-1} + e_t$$ with $$e_t \sim i.i.d.(0,\sigma^2)$$* has a unit root if it can be expressed as $$(1-L)y_t = e_t$$ where $$L$$ is the lag operator. Then the characteristic equation of the above process has one unit root. A property of the unit root is that when an $$I(1)$$ autoregressive process is first differenced, it becomes an $$I(0)$$ process, i.e. it will be stationary.

According to the tag description of autocorrelation,

Autocorrelation (serial correlation) is the correlation of a series of data with itself at some lag. For example, if a given value were higher than average, it might be more likely than not that the next value would also be higher than average; if so, there is a positive autocorrelation at lag 1.

The autocorrelation for a time series, between times $$s$$ and $$t$$ is defined as:

$$R(s,t) = \frac{\mathbb{E}[(X_t - \mu)(X_s - \mu)]}{\sigma_t \sigma_s}$$

where $$\mathbb{E}$$ is the expected value operation.

Some differences between the Ljung-Box (LB) and the Durbin-Watson (DW) tests

• LB tests a joint null hypothesis of autocorrelation at a set of lags being equal to zero, while DW tests a null hypothesis of autocorrelation at a single lag being equal to zero.
• LB test can be applied to any selected group of lags (though usually the first $$k$$ for some natural number $$k$$), while DW tests autocorrelation at lag 1 specifically.

*It is enough that $$e_t$$ is a stationary process or an I(0) process which are almost the same.


text:
# 1 Summary/Abstract

Rapidly increasing inflation rates and worsening effects of climate change are dramatically increasing the financial impacts of disasters. Within the United States, the Federal Emergency Management Agency (FEMA) is responsible for providing federal resources to support states and territories during the response phase as well as tracking the financial costs. All tiers of government would benefit from knowing which disaster declaration characteristics would change the amount of financial support from FEMA. This analysis utilizes machine learning technology to predict the funds requested by states or territories from FEMA as well as the funds eventually obligated to states or territories from FEMA for a disaster declaration. In particular, three models are considered: decision tree, bagged tree, and random forest. Cross-validation and bootstrap re-sampling structures are utilized, depending on the model, and the fits of the models are evaluated using the root mean square error (RMSE) statistic. The bagged tree model employing bootstrap re-sampling best fit both the requested and obligated fund models; however, future studies should consider other machine learning models as well as further refinement of the tuning parameters for the ones considered in this analysis. The prediction capabilities created by such models have the potential to dramatically improve comprehension of the key factors affecting financial disaster relief support.

# 2 Introduction

On November 8, 1988, United States (US) President Ronald Reagan signed the Robert T. Stafford Disaster Relief and Emergency Act into law, which formalizes the disaster declaration process and specifies the response responsibilities for each tier of government (Moss, Schellhamer, & Berman, 2009). Under this law, when a disaster occurs, the affected area (local or state representatives) conducts a damage assessment to estimate the amount of support required from the federal government. That assessment goes through the state government to the Federal Emergency Management Agency (FEMA) to the Department of Homeland Security (DHS) to the US President, who ultimately decides whether the affected region should receive an emergency declaration, a major disaster declaration, or neither (McCarthy, 2009). FEMA then deploys resources from across the federal government to support the disaster region, the volume and type of which depend upon the declaration type. However, the federal government does not necessarily incur all of the cost of these resources. Under most circumstances, this pay structure more accurately reflects a reimbursement model; that is, the states or territories submit requests to the FEMA for reimbursement after the expenses have occurred. However, there is then a reconciliation process by which the total funds a state or territory receives is often different than the original request. This process, explained in greater detail below, involves numerous parameters that are not always obvious to non-FEMA representatives. As such, this analysis endeavors to discern the key predictors for receiving federal funding relief under a disaster declaration.

## 2.1 Disaster Declaration Process

When a disaster occurs, the onus for requesting assistance begins at the local government. The local officials must have enacted their own emergency operations plans and demonstrate the need for more resources than the local entities can provide. Once this threshold is crossed, the municipal or county leader submits a formal request to the state governor for assistance by requesting a state disaster declaration (McCarthy, 2009). If the governor approves such a request, state resources are mobilized to assist the affected area, but the local government is still the primary leading entity for the emergency management response. If the state has fully enacted their emergency response plans and further assistance is still required, the governor requests the state emergency management agency to conduct a state-level Preliminary Damage Assessment (PDA). These assessments aim to estimate the impact of the disaster on individuals, infrastructure, and government agencies (Moss et al., 2009). As federal resources are extraordinarily expensive, state governors utilize PDAs to ensure federal assistance is only requested when absolutely necessary. If the governor does decide that federal resources are required, a formal request is submitted by the governor’s office through the regional FEMA office. This request includes the PDA, barring a few exceptional circumstances for catastrophic events, and a list of requested federal resources, including the anticipated duration and cost of each resource (Moss et al., 2009). The regional FEMA office ensures the request is complete before sending it to a special declaration processing unit in FEMA headquarters, which further add to the request by incorporating detailed statistics about the region and their own assessment of needs and costs (McCarthy, 2009). The declaration processing unit then submits the request to the FEMA Administrator, who must make a recommendation for the President. The request and the recommendation are then submitted to the President, who ultimately decides whether or not to grant the declaration request. The President is not bound by the FEMA Administrator’s recommendation, and, in the event the President denies the request, the governor is permitted to submit an appeal based on further damage assessments (Moss et al., 2009). If the request is approved, FEMA becomes the primary agency to coordinate resource allocation and support the local response. The approval from the President also specifies which programs are authorized as well as the federal/state cost-sharing ratio (FEMA, 2021).

## 2.2 Newly Available Data

The federal government funding process was further refined as part of the Sandy Recovery Improvement Act of 2013 as well as The Disaster Recovery Reform Act of 2019 (FEMA, 2021). These laws require FEMA to publicly provide the information regarding federal government resources paid for by state and federal government funds for each disaster declaration. As a result, the OpenFEMA Data Sets website now exists and provides information summarizing disaster declarations and mission assignments. While these acts have improved the accessible information, little has been done to draw conclusions from these data for predicting the financial impacts of disasters. Due to the federal government legislative process, these datasets have been publicly available for less than two years, during which the preponderance of the emergency management community was dedicated to managing the COVID-19 pandemic. To date, there is one published paper using predictive modeling to examine disaster declarations; however, it is only published in Spanish, and the authors do not have a reliable means of translation (Araujo Pérez, 2019). Based on an approximate translation, the authors used a logistic regression to predict whether or not a presidential declaration would be awarded in the state of Maryland, utilizing Maryland data 2003 - 2017 (Araujo Pérez, 2019). Given this newly available data from the federal government, there are numerous potential predictive models to be considered.

It would greatly benefit the federal government to be able to predict the amount of funding required for a disaster based on parameters known at the onset of the incident, as it would allow for improved funds flow and budgeting practices. Moreover, it would benefit states and territories to know which parameters increase the amount of federal government support in the aftermath of a disaster. Modeling approaches that include machine learning algorithms have been demonstrated to have extensive prediction capability for large datasets. As such, this analysis will examine the use of machine learning models in predicting FEMA expenses for a federally-declared disaster. In particular, a decision tree, bagged tree, and random forest model will be used to predict requested and obligated FEMA funds.

# 3 Materials and Methods

## 3.1 Data and Processing

The data were obtained from the OpenFEMA Data Sets website (OpenFEMA Data Sets FEMA.gov, n.d.) as well as the US Department of Agriculture Economic Research Service website (USDA ERS - County-level Data Sets, n.d.). The mission assignments data was cleaned to represent the requested and obligated FEMA funds for each disaster declaration for each state or territory. Summary variables were created for total number of federal agencies involved in resource assistance, the amount of funding requested by the state or territory from FEMA, the amount of funding allocated to the state or territory from FEMA, and the average cost share for FEMA of the resources provided. Similarly, the disaster declaration summaries were also summarized to represent the unique disaster declarations for each state, bounded to the same time frame as the mission assignments data. Feature engineering was performed to create variables for incident duration, response duration, month of declaration, and year of the incident. The population data from the US Department of Agriculture Economic Research Service was incorporated into the disaster summary data, after creating a variable for state. The mission assignment data and declaration data were then joined to create a comprehensive dataset that was used for analysis. At this point in the analysis, Google developer data (Developer, n.d.) was added to specify coordinates of each date, and the outcomes of interest were subset to include only circumstances in which the federal government provided funding (e.g. only positive requested or obligated amounts).

Prior to fitting the models, the data were subset based on outcome of interest, and the least frequent disaster types were added to the “Other” category, due to the limited values in certain categories. The outcomes of interest were also log transformed to better represent the distribution of disaster relief funding. At this point, three outliers were removed from the analysis, as each had a negative value of the log transform of the outcomes of interest.

## 3.2 Parameters Considered

Ultimately, the following parameters were considered in the analysis: state, longitude/latitude of state, state population, state number of counties, the FEMA Region to which the state belonged, declaration type, month and year of the first date of the event, duration of the incident, duration of the response efforts, when the Individual/Household, Public Assistance, and Hazard Mitigation Programs were awarded to any county in the state as well as the percent of counties receiving each program, number of federal agencies involved in the response, and the average FEMA cost share for the resources provided to the state under the declaration.

## 3.3 Model Development

Four models were considered for the prediction analysis, and each were fit for both outcomes of interest (e.g. requested and obligated funds). The data were split such that 66.7% were used for training the models and the remaining 33.3% were used for testing the final chosen model. Spatial cross-validation was used for all models, using a five-fold resampling structure. The tidymodels framework utilized in the analysis does not support a repreated spatial cross-validation resampling structure, as is standard in typical cross-validation.

## 3.4 Model Definition

There are numerous machine learning models that could be applied to the research question, but this analysis focuses primarily on two different types of models: tree-based and regularization-based. The tree-based models were chosen as the primary users of the prediction algorithms are non-statisticians, and such models are among the easiest machine learning models to interpret and understand (James, Witten, Hastie, & Tibshirani, 2021). However, to robustly consider the machine learning methodology, two regularization-based methods were also included in the analysis. Broadly, regularization allows variables to be included in a model with less weight than other variables by reducing the value of the variable’s coefficient (Hastie, Tibshirani, & Friedman, 2016).

• Decision Tree (DT): Also known as a classification and regression tree (CART), the DT examines each predictor and splits the outcome at a value of the predictor that leads to the best performance increase in the model. The tree development continues until a certain threshold criteria is met, such as number of observations in each leaf of the tree. A DT model is often the most intuitive machine learning algorithm, but it also typically has a reduced performance compared to other models (Boehmke & Greenwell, 2019).

• Random Forest (RF): A slightly more sophisticated model, a RF model aims to reduce the variance by building a tree for each re-sampling of the existing data. However, instead of considering all possible predictors at each decision tree split, the split occurs based on the best predictors of a random sample of all predictors. This method allows for de-correlation in the trees by avoiding the default nature of decision trees that aim to include as many predictors as possible. Each individual tree is then averaged to find the final model. RF models are also more difficult to interpret than standard decision tree models (Breiman, 2001).

• Least Absolute Shrinkage and Selection Operator (LASSO): LASSO balances the goodness of fit with a penalty for the coefficients, calculated by the respective absolute value. This methodology allows coefficients to go to zero and thus be dropped from the model. The disadvantage of the LASSO model comes predominantly in the form of selection of just one variable from highly correlated variables, ignoring the rest entirely (Roth, 2004).

• Elastic Net (EN): Of particular use in circumstances with correlations between predictor variables, an EN model further adds to a LASSO model by incorporating a mixture parameter in addition to the overall weight given of the penalty. The mixture parameter determines the distribution of the penalty, which is the sum of the LASSO regularization component as well as a new regularization component, which is calculated by squaring the magnitude of the coefficient, and then all coefficients are shrunk by the same factor (Zou & Hastie, 2005).

## 3.5 Model Performance Evaluation

The standard metric for evaluating regression models is the root mean square error (RMSE), which is the square root of the mean of the square of all error. It is formally defined as: $RMSE = \sqrt{\frac {1}{n} \sum_{i = 1}^{n}{(S_i - O_i)^2}}$ where Oi are the observations, Si are the predicted values of the outcome, and n is the number of observations in the analysis. RMSE is scale dependent, but the lower the RMSE, the better the model performance.

## 3.6 Software

This analysis was conducted in R 1.4, using Rstudio 4.1 on a Windows Server operating system (Team, 2021). The following R packages were utilized: here (Müller, 2020), tidyverse (Wickham et al., 2019), tidymodels (Kuhn & Wickham, 2020), skimr (Waring et al., 2021), spatialsample (Silge, 2021), broom.mixed (Bolker & Robinson, 2021), rpart.plot (Milborrow, 2021), vip (Greenwell & Boehmke, 2020), doParallel (Corporation & Weston, 2020), ranger (Wright & Ziegler, 2017), viridis (Garnier et al., 2021), maps (Richard A. Becker, Ray Brownrigg. Enhancements by Thomas P Minka, & Deckmyn., 2021), table1 (Rich, 2021), cowplot (Wilke, 2020), scales (Wickham & Seidel, 2020), gtsummary (Sjoberg, Whiting, Curry, Lavery, & Larmarange, 2021), car (Fox & Weisberg, 2019), ggplot2 (Wickham, 2016), and summarytools (Comtois, 2021). All processing and analysis code can be found in the supplementary materials.

# 4 Results

## 4.1 Outcomes of Interest

A total 3266 disaster declarations were included in this analysis, ranging from February 2012 to November 2021. On average, $40,600,000 (SD =$255,000,000) were requested in FEMA funding, and $40,700,000 (SD =$256,000,000) were obligated in FEMA funding. A total 51 states and territories were represented in the analysis, and on average, the FEMA cost-share was 96.4% (SD = 5.73%). Figure 4.1 shows the almost identical density distribution of the two outcomes of interest, which is further confirmed by the correlation plot between the two shown in figure 4.2.


text:
Jul 15, 2017

The answers are $\left(b\right) = 4.95 m {s}^{-} 1$ and $\left(c\right) = 495 m {s}^{-} 1$

#### Explanation:

Part $\left(a\right)$

When the shot is released, there is a recoil of the gun, but momentum is conserved

${m}_{g} {v}_{g} = - {m}_{b} {v}_{b}$

The gun recoils in the opposie direction.

Part $\left(b\right)$

The height $h = 1.25 m$

Mass of the bullet is $m = 0.005 k g$

Mass of the target is $M = 0.495 k g$

Let the speed of the bullet $+$ target be $= v m {s}^{-} 1$

Then,

$K E = P E$

$\frac{1}{2} \cdot \left(m + M\right) {v}^{2} = \left(m + M\right) g h$

$v = \sqrt{2 g h} = \sqrt{2 \cdot 9.8 \cdot 1.25}$

$= \sqrt{24.5}$

$= 4.95 m {s}^{-} 1$

Part $\left(c\right)$

Let the velocity of the bullet before hitting the target is $= u m {s}^{-} 1$

Then , by the law of conservation of momentum

$\mu + M \cdot 0 = \left(m + M\right) \cdot v$

$u = \frac{m + M}{m} \cdot v$

$= \frac{0.495 + 0.005}{0.005} \cdot 4.95$

$= \frac{0.5}{0.005} \cdot 4.95$

$= 495 m {s}^{-} 1$


text:
## Chandrasekhar Venkat Raman

Chandrasekhar Venkat Raman, also known as Sir CV Raman, was a Physicist, Mathematician and a Nobel Laureate. Venkat (his first name) was a Tamil Brahmin and was the second of the eight children of his parents. He was born at Thiruvanaikaval, near Tiruchirappalli on 7th November 1888. He was the second of their eight children. His father was a lecturer in Mathematics and physics which helped him aspire careers in the same fields.

Here is how his life progressed:

• At an early age, Raman moved to Visakhapatnam.
• Started studying in St. Aloysius Anglo-Indian High School.
• After his graduation he was selected into government services where he worked for years.
• In 1917, Raman resigned from his government service and took up the newly created Palit Professorship in Physics at the University of Calcutta at the age of 28.

On February 28, 1928, (the reason National Science Day is celebrated in India) through his experiments on the scattering of light, he discovered the Raman effect. C. V. Raman was awarded the 1930 Physics Nobel Prize for this.

# Raman Effect

In contrast to other conventional branches of spectroscopy, Raman spectroscopy deals with the scattering of light & not with its absorption.

Chandrasekhar Venkat Raman discovered in 1928 that if light of a definite frequency is passed through any substance in gaseous, liquid or solid state, the light scattered at right angles contains radiations not only of the original frequency (Rayleigh Scattering)  but also of some other frequencies which are generally lower but occasionally higher than the frequency of the incident light.

The phenomenon of scattering of light by a substance when the frequencies of radiations scattered at right angles are different (generally lower and only occasionally higher) from the frequency of the incident light, is known as Raman Scattering or Raman effect.
The lines of lower frequencies as known as Stokes lines while those of higher frequencies are called anti-stokes lines.

If $f$  is the frequency of the incident light &  $f’$  that of a particular line in the scattered spectrum, then the difference   $f-f’$ is known as the Raman Frequency. This frequency is independent of the frequency of the incident light. It is constant and is characteristic of the substance exposed to the incident light.

A striking feature of Raman Scattering is that Raman Frequencies are identical, within the limits of experimental error, with those obtained from rotation-vibration (infrared) spectra of the substance.
Here is a home-made video explaining the Raman Scattering of Yellow light:

And here is another video guide for Raman Scattering:

• Raman Spectroscopy can be used not only for gases but also for liquids & solids for which the infrared spectra are so diffuse as to be of little quantitative value.
• Raman Effect is exhibited not only by polar molecules but also by non-polar molecules such as $O_2$, $N_2$, $Cl_2$ etc.
• The rotation-vibration changes in non-polar molecules can be observed only by Raman Spectroscopy.
• The most important advantage of Raman Spectra is that it involves measurement of frequencies of scattered radiations, which are only slightly different from the frequencies of incident radiations. Thus, by appropriate choice of the incident radiations, the scattered spectral lines are brought into a convenient region of the spectrum, generally in the visible region where they are easily observed. The measurement of the corresponding infrared spectra is much more difficult.

### Uses

•  Investigation of biological systems such as the polypeptides and the proteins in aqueous solution.
•  Determination of the structures of molecules.

# Classical Theory of Raman Effect

The classical theory of Raman effect, also called the polarizability theory, was developed by G. Placzek in 1934. I shall discuss it briefly here. It is known from electrostatics that the electric field $E$ associated with the electromagnetic radiation induces a dipole moment $\mu$ in the molecule, given by
$\mu = \alpha E$ …….(1)
where $\alpha$ is the polarizability of the molecule. The electric field vector $E$ itself is given by
$E = E_0 \sin \omega t = E_0 \sin 2\pi \nu t$ ……(2)
where $E_0$ is the amplitude of the vibrating electric field vector and $\nu$ is the frequency of the incident light radiation.

Thus, from equations (1) & (2),
$\mu= \alpha E_0 \sin 2\pi \nu t$ …..(3)
Such an oscillating dipole emits radiation of its own oscillation with a frequency $\nu$ , giving the Rayleigh scattered beam. If, however, the polarizability varies slightly with molecular vibration, we can write
$\alpha =\alpha_0 + \frac {d \alpha} {dq} q$ …..(4)
where the coordinate q describes the molecular vibration. We can also write q as:
$q=q_0 \sin 2\pi \nu_m t$ …..(5)
Where $q_0$ is the amplitude of the molecular vibration and $\nu_m$ is its (molecular) frequency. From equations. 4 & 5, we have
$\alpha =\alpha_0 + \frac {d\alpha} {dq} q_0 \sin 2\pi \nu_m t$ …..(6)
Substituting for $alpha$   in (3), we have
$\mu= \alpha_0 E_0 \sin 2\pi \nu t + \frac {d\alpha}{dq} q_0 E_0 \sin 2\pi \nu t \sin 2\pi \nu_m t$ …….(7)
Making use of the trigonometric relation $\sin x \sin y = \frac{1}{2} [\cos (x-y) -\cos (x+y) ]$ this equation reduces to:
$\mu= \alpha_0 E_0 \sin 2\pi \nu t + \frac {1}{2} \frac {d\alpha}{dq} q_0 E_0 [\cos 2\pi (\nu – \nu_m) t – \cos 2\pi (\nu+\nu_m) t]$ ……(8)
Thus, we find that the oscillating dipole has three distinct frequency components:

• The exciting frequency $\nu$ with amplitude $\alpha_0 E_0$
• $\nu – \nu_m$
• $\nu + \nu_m$ (2 & 3 with very small amplitudes of $\frac {1}{2} \frac {d\alpha}{dq} q_0 E_0$

Hence, the Raman spectrum of a vibrating molecule consists of a relatively intense band at the incident frequency and two very weak bands at frequencies slightly above and below that of the intense band.

If, however, the molecular vibration does not change the polarizability of the molecule then $(d\alpha / dq )=0$ so that the dipole oscillates only at the frequency of the incident (exciting) radiation. The same is true for the molecular rotation. We conclude that for a molecular vibration or rotation to be active in the Raman Spectrum, it must cause a change in the molecular polarizability, i.e., $d\alpha/dq \ne 0$ …….(9)

Homo-nuclear diatomic molecules such as $\mathbf {H_2 , N_2 , O_2}$ which do not show IR Spectra since they don’t possess a permanent dipole moment, do show Raman spectra since their vibration is accompanied by a change in polarizability of the molecule. As a consequence of the change in polarizability, there occurs a change in the induced dipole moment at the vibrational frequency.

REFERENCES:-

• Principles in Physical Chemistry, Puri, Sharma & Pathania
• Physics Chemistry, Atkins
• Spectroscopy, Raj Kumar

1. Anonymous says:

sir super, thanks you so much

2. sir, send problems& relavented formulas in raman spector scope. says:

thank you sir , your effort gives me life to my dreame,

3. PURATCHIDASAN.M says:

good

4. Ramarao pampana says:

Gauravtiwari ji felt happy for the details of ramaneffect and illestrations furnished in ur website thanks

5. The #BirthAnniversary of one of the most prominent #Indian #scientists in history, Sir #CVRaman was on 07th Nov. Let us all pay a #heartfelt #tribute to him on cvraman.tributes.in.
He was the first Indian person to win the Nobel Prize in science for his illustrious 1930 discovery, which is known as the “Raman Effect”.

In case you wish to create a tribute for your loved ones as well, please give us a missed call on +91-9643105042.
Our associates will get in touch with you.
You can also create a profile yourself on – tributes.in
https://cvraman.tributes.in

6. Thanks for sharing this. I am a Non-medical student at Panjab University. IIn Bsc there is topic on Raman effect. you had explain the topic very well.

7. Myrbsenotes says:

Good job amazing explanation

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text:
# Why can high variance help you in Heckman (1998) but not Aigner and Cain (1977)?

Heckman (1998) argues that, if the bar for acceptance is high (so most applicants are rejected), then belonging to a group who quality has high variance tends to help you. The argument is something like this: if employers only hire people whose quality exceeds a certain cutoff, but most people fail the cutoff, then if your group's distribution of quality has higher variance it will have more mass above the cutoff.

Aigner and Cain (1977) also discuss variance based discrimination. Assuming that you send a signal equal to your group's mean, the only effect of higher variance is to dissuade risk averse employers to hire you. There is no Heckman style mechanism where high variance can help you if most people get rejected.

I would be very grateful if someone could explain what leads to this contrast.

My (possibly confused) thoughts on this: the Heckman model makes sense if employers decide whether to grant an interview based on whether the probability that someone's quality is above a certain level exceeds a certain cutoff. But that is a crazy hiring rule! Instead, they should just look at whether expected quality exceeds a certain cutoff (to be fair to Heckman, this is supposed to be the hiring rule.)

OK suppose that this is the hiring rule: can high variance still help you (in the context of an audit/correspondence study)? Well, I can see how this works if the researcher perfectly controls on one dimension (e.g. what the auditors say) but doesn't control on another (e.g. attractiveness), and one group has higher variance on that second dimension, which means more of them get over the bar. But that logic totally breaks down in correspondence studies (supposedly also a target). Here the employer does not get to see some realisation from a distribution of quality that is unobserved by the researcher. At best, the employer can say: that group's high variance, so more likely to exceed the cutoff. But that brings us back to the crazy hiring strategy already discussed.

• I think the different results simply come from the different hiring rules. In Heckman all people above the cutoff get hired, while in Aigner wnd Cain there is no cutoff and employers maximize the expected skill of of potential employees in their hiring decision. The Heckman cutoff rule is not as crazy as you think. Many universities will accept all candidates above a threshold of 'skill' (as mine does), but some seek to maximize the average skill of the cohort. – BB King Apr 6 '18 at 8:02

Say you have two distributions, $G$ and $H$ with equal means supported on (say) $[0,1]$ and $H$ is second-order stochastically dominated by $G$. Then, for any concave increasing $u$, we'll have $$\int udG \geq \int udH$$ This would correspond to Aigner and Cain, where the risk averse firm would prefer to hire an agent from distribution G.

However, now suppose that $G$ and $H$ are distributions of talent (with the same stochastic ordering i.e. $H \succ_{C} G$). One equivalent notion to this idea is that distribution $G$ can be obtained by fusing" together part of the mass of $H$, i.e. by collapsing part of the mass to its respective barycenter. Given this, it is easy to see that there is always a cutoff $\eta \in [0,1]$ such that $H(\eta) \geq G(\eta)$.

This corresponds to Heckman's result--if the job is sufficiently demanding, then it will be (at least weakly better) to be part of the high variance population. Moreover, note that this by no means depends on the expected quality of the agent. There are simply more of the highest quality people in the group with distribution $H$ than in the group with distribution $G$. They are not just more likely to exceed the cutoff, there are more of them that exceed the cutoff.

Another way to think about the hiring problem is as follows: say a firm wants to hire one person but receives applications from $10$ applicants, $5$ from group $A$ and $5$ from group $B$. A candidate's quality is unknown and it it ranges from $[0,1]$ continuously. Suppose also for the sake of simplicity that the firm may observe the candidate's group (and so knows what distribution he/she is drawn from): the distribution of quality for group $A$ is given by $G$ and the distribution of quality for group $B$ is given by $H$. Interviewing a candidate fully reveals a candidate's type, but the firm has the budget to interview only $4$ candidates. Whom should they interview?

The answer is simple: all four candidates interviewed should be from group $B$ (which has distribution $H$). Why? Because we can think about a candidate's quality as a random variable $X_{i}$ and thus the firm wants to maximize $\mathbb{E}[Z]$ where $$Z:=\max\big\{X_{1},X_{2},X_{3},X_{4}\big\}$$ Since $H \succ_{C} G$, $$\mathbb{E}_{H^{4}}[Z] \geq \mathbb{E}_{G^{4}}[Z]$$

Note also that $H \succ_{C} G$ $\Rightarrow$ $Var(H) \geq Var(G)$ but not $\Leftarrow$. In this sort of thing, I think it is stochastic dominance and not variance that is the apposite metric.

• +1. Perhaps for future readers it would make sense to explain SOSD a bit. For example one could show a simple graph of two CDFs so that it is more intuitive for readers unfamiliar with the concept. – BB King Apr 6 '18 at 8:05
• Thanks for this! So I guess Aigner/Cain is the right model if the employer can only interview one candidate in a correspondence study, but Heckman is the right model if the firm can interview many candidates? – afreelunch Apr 6 '18 at 12:22


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