tag:blogger.com,1999:blog-37222332021-05-11T16:06:32.458-05:00Computational ComplexityComputational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill GasarchLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger2836125tag:blogger.com,1999:blog-3722233.post-86096848150378953522021-05-09T19:08:00.002-05:002021-05-09T20:22:59.731-05:00Trump, Facebook, and ComplexityBlog<p> I care about the Facebook decision to ban Trump, but I do not have a strong opinion about it. I have heard arguments on both sides now, from up and down, and still somehow... I don't know how I feel. So instead of posting my opinion I post other opinions and my opinion of them.</p><p>1) Facebook is a private company. If they want to have liberal bias or a free for all or whatever then it is not the governments place to interfere. If enough people don't like what they see then they will lose customers. The invisible hand of the market will regulate it enough. Libertarians and honest small-gov republicans might believe this. On a personal level, I don't want someone else telling Lance and I that we can't block some comment; however, for now, more people use Facebook then read Complexity Blog. </p><p>2) Facebook is a private company but they need to follow standard business practices of having their uses sign an agreement and stick to it. Since the user signed the agreement, Facebook need only stick to that agreement. This is problematic in that (1) if the agreement is not that rigorous then Facebook can be arbitrary and capricious, but (2) if the agreement is to rigorous then people can game the system. Imagine if Lance and me had rule that you could not use profanity in the comments. Then someone could comment </p><p><i>People who think P vs NP is ind of ZFC can go Fortnow themselves. They are so full of</i> <i>Gasarch</i>.</p><p> (Something like this was the subplot of an episode of <i>The Good Fight</i>)</p><p>3) Facebook is so big that it has an obligation to let many voices be heard, within reason. This could lead to contradictions and confusions:</p><p>a) Facebook cannot ban political actors. What is a political actor? (Jon Voight is pro-trump and Dwayne ``The Rock'' Johnson is anti-trump, but that's not what I mean.) High level people in the two main parties qualify (how high level?). IMHO third parties (Libertarian and Green come to mind) need the most protection since they don't have as many other ways to get out their message and they are serious. (I wonder if Libertarians would object to the Government forcing Facebook to not ban them). What about the <a href="https://en.wikipedia.org/wiki/Gracie_Allen#Publicity_stunts">Surprise Party</a> or the <a href="https://en.wikipedia.org/wiki/Kanye_West#2020_presidential_campaign">Birthday Party</a> (which did have a platform see <a href="https://kanye2020.country/">here</a>). And what about people running for Mayors of small towns (much easier to do now with Facebook)? Should just running be enough to ban banning? </p><p>b) Facebook can ban posts that are a threat to public health and safety. I am thinking of anti-vaxers and insurrectionists, though I am always wary of making them free speech martyrs. </p><p>c) Fortunately a and b above have never conflicted. But they could. I can imagine a president who has lost an election urging his followers to storm the capitol. Then what should Facebook do? (ADDED LATER- A commenter points to a case where a and b conflicted that is not the obvious case.) </p><p>4) Facebook is so big that it has an obligation to block posts that put people in danger. This may have some of the same problems as point 3---who decides? </p><p>5) Facebook is so big and controls so much of the discourse that it should be heavily regulated (perhaps like a utility). This has some of the same problems as above- who decides how to regulate it and how?</p><p>6) As a country we want to encourage free speech and a diversity of viewpoints. There are times when blocking someone from posting may be <i>better for free speech</i> then letting them talk. When? When that person is advocating nonsensical views that stifle the public discussion. But I am talking about what the country should want. What do they want? What does Facebook want? Does either entity even know what they want? These are all ill defined questions. </p><p>7) Facebook is a monopoly so use Anti-Trust laws on it. Anti-Trust was originally intended to protect the consumer from price-gouging. Since Facebook is free this would require a new interpretation of antitrust. Judicial activism? The Justices solving a problem that the elected branches of government are currently unable to solve? Is that a bad precedent? What does it mean to break up Facebook anyway--- its a network and hence breaking it up probably doesn't make sense (maybe use MaxCut). </p><p>(ADDED LATER- a commenter pointed out that anti-trust is NOT just for consumer protection, but also about market manipulation to kill small innovators.) </p><p>8) Lets say that Facebook and Society and the Government and... whoever, finally agree on some sort of standards. Then we're done! Not so fast. Facebook is so vast that it would be hard to monitor everything. </p><p>9) As a side note- because Facebook and Twitter have banned or tagged some kinds of speech or even some people, there have been some alternative platforms set up. They always claim that they are PRO FREE SPEECH. Do liberals post on those sites? Do those sights ban anyone? Do they have SOME rules of discourse? I ask non rhetorically. </p><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com7tag:blogger.com,1999:blog-3722233.post-68328165009794788992021-05-06T08:07:00.001-05:002021-05-06T08:07:44.186-05:00Negotiations<p>So you got an offer to be an assistant professor in the computer science department at Prestigious U. Congratulations! </p><p>Time to negotiate your offer with the chair. Don't be nervous. This shouldn't be adversarial. Both of you have the same goal in mind--for you to come to Prestigious and be successful. </p><p>Let's discuss the different aspects of each package.</p><p><b>Research </b></p><p>Funds for supporting your research such as equipment, graduate student support, travel and postdocs. Here you should explain what you need to be successful. This will vary by subdiscipline, a systems researcher will need more equipment and students than a theorist. Keep in mind the university is giving you funds for 2-4 years to start your research, after which you are expected to fund your own research via grants.</p><p>I don't recommend taking on a postdoc right at the start of your first academic appointment. Postdocs require good mentoring while you need to spend the first year getting your research up and running. If you do ask for postdoc money, ask to have a flexible start time.</p><p>Many departments give course reductions to get your research going. I'd suggest asking to spend your first semester teaching a graduate topics course based on your thesis research to pick up some PhD students followed by a semester with no classes to get you research program going.</p><p><b>Salary</b></p><p>This includes actual salary, which is also the base for future raises, and summer salary in the first couple of years. Feel free to ask for more salary, but often these numbers are fixed for new assistant professors. There is more give if you take an academic job later in your career. You could also say something like, "Well if you can't give me more salary maybe you could give me another semester of grad student support?"</p><p><b>Partner</b></p><p>It seems 80% of the time, a job candidate has a partner that needs accommodating. Don't wait until the end of negotiations, bring it up early. The more time we have, the better we can help. Doesn't matter what job they want--we know people and we know people who know people.</p><p><b>Thesis</b></p><p>Many schools won't hire you as an assistant professor if you haven't finished your thesis. Has to do with college rankings work. Don't worry--they will generally give you some other role with the same package until you finish. This might delay your tenure clock though.</p><p><b>Delayed start time</b></p><p>A January start is usually fine with good reason but if you weren't planning to start until the fall of 2022 why are you on the market this year? If you do get the department to hold a position for you, remember you are also making a commitment--this is not an opportunity to try again for something better.</p><p><b>Overall</b></p><p>You may not get all that you want after a negotiation--don't take it personally. You shouldn't necessarily choose the place that gives you the biggest package. It's far more important in the long run that you pick a place where you can best succeed both professionally and personally, and the package is just a small piece of that puzzle.</p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com7tag:blogger.com,1999:blog-3722233.post-74744597726011257602021-05-02T14:33:00.000-05:002021-05-02T14:33:56.696-05:00The Mythical Man-Month, Hen-Day, and Cat-Minute (Fred Brooks Turned 90)<p><i> The Mythical Man-Month </i>is a great book which talks about the (obvious in retrospect) fact that putting more people on a project may slow it down. It was by Fred Brooks who turned 90 in April (he is still alive). It's a good read. I actually read it many years ago when I exchanged books with a Software Engineer I was dating- She lent me <i>The Mythical Man Month </i>which I found interesting, and I lent her <i>What is the name of this book by Smullyan </i>which she found amusing. Did this exchange of books help our relationship? We have now been married for many years, though its not clear if we can trace this to the exchange of books OR to the fact that she had KNUTH Volumes 1 and 3, and I had KNUTH Volume 2. </p><p> Fred Brooks: You have my thanks and of course Happy Birthday!</p><p>When I read The Mythical Man-Month I was reminded of a math problem I heard as a kid: </p><p>If a hen-and-half lays an egg-and-a-half in a day-and-a-half then how many eggs can seven hen lay in seven days? </p><p>My answer: if (3/2) hens lay (3/2) eggs in (3/2) days then that's 2/3 of an egg per hen-day, so the answer is </p><p>49* 2/3 = 32 and 2/3 eggs.</p><p>It did not bother me one whit that (1) you can't have 2/3 of an egg, and (2) Just like adding more people might slow down a project, adding more hens might end up being a bad idea-- especially if they are all crowded into the same chicken-coop and hence don't feel much like laying eggs.</p><p>Who was the first person to note that adding <i>more</i> people or hens might be a bad idea? I do not know, but here is an amusing, yet realistic, article by Mark Twain on what I would call <i>The mythical</i> <i>cat-minute. </i>My advisor Harry Lewis send it to me in the midst of an email exchange about <i>The Mythical</i> <i>Man-Month.</i> He got it from a student of his, Larry Denenberg. Here it is: </p><p><br /></p><p>CATS AND RATS</p><pre>The following piece first appeared in ``The Monthly Packet'' of February
1880 and is reprinted in _The_Magic_of_Lewis_Carroll_, edited by John
Fisher, Bramhall House, 1973.
If 6 cats kill 6 rats in 6 minutes, how many will be needed to kill
100 rats in 50 minutes?
This is a good example of a phenomenon that often occurs in working
problems in double proportion; the answer looks all right at first, but,
when we come to test it, we find that, owing to peculiar circumstances in
the case, the solution is either impossible or else indefinite, and needing
further data. The 'peculiar circumstance' here is that fractional cats or
rats are excluded from consideration, and in consequence of this the
solution is, as we shall see, indefinite.
The solution, by the ordinary rules of Double Proportion, is 12 cats.
[Steps of Carroll's solution, in the notation of his time, omitted.]
But when we come to trace the history of this sanguinary scene through all
its horrid details, we find that at the end of 48 minutes 96 rats are dead,
and that there remain 4 live rats and 2 minutes to kill them in: the
question is, can this be done?
Now there are at least *four* different ways in which the original feat,
of 6 cats killing 6 rats in 6 minutes, may be achieved. For the sake of
clearness let us tabulate them:
A. All 6 cats are needed to kill a rat; and this they do in one minute,
the other rats standing meekly by, waiting for their turn.
B. 3 cats are needed to kill a rat, and they do it in 2 minutes.
C. 2 cats are needed, and do it in 3 minutes.
D. Each cat kills a rat all by itself, and takes 6 minutes to do it.
In cases A and B it is clear that the 12 cats (who are assumed to come
quite fresh from their 48 minutes of slaughter) can finish the affair in
the required time; but, in case C, it can only be done by supposing that 2
cats could kill two-thirds of a rat in 2 minutes; and in case D, by
supposing that a cat could kill one-third of a rat in two minutes. Neither
supposition is warranted by the data; nor could the fractional rats (even
if endowed with equal vitality) be fairly assigned to the different cats.
For my part, if I were a cat in case D, and did not find my claws in good
working order, I should certainly prefer to have my one-third-rat cut off
from the tail end.
In cases C and D, then, it is clear that we must provide extra cat-power.
In case C *less* than 2 extra cats would be of no use. If 2 were supplied,
and if they began killing their 4 rats at the beginning of the time, they
would finish them in 12 minutes, and have 36 minutes to spare, during which
they might weep, like Alexander, because there were not 12 more rats to
kill. In case D, one extra cat would suffice; it would kill its 4 rats in
24 minutes, and have 26 minutes to spare, during which it could have killed
another 4. But in neither case could any use be made of the last 2
minutes, except to half-kill rats---a barbarity we need not take into
consideration.
To sum up our results. If the 6 cats kill the 6 rats by method A or B,
the answer is 12; if by method C, 14; if by method D, 13.
This, then, is an instance of a solution made `indefinite' by the
circumstances of the case. If an instance of the `impossible' be desired,
take the following: `If a cat can kill a rat in a minute, how many would be
needed to kill it in the thousandth part of a second?' The *mathematical*
answer, of course, is `60,000,' and no doubt less than this would *not*
suffice; but would 60,000 suffice? I doubt it very much. I fancy that at
least 50,000 of the cats would never even see the rat, or have any idea of
what was going on.
Or take this: `If a cat can kill a rat in a minute, how long would it be
killing 60,000 rats?' Ah, how long, indeed! My private opinion is that
the rats would kill the cat.
</pre><div><br /></div><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com1tag:blogger.com,1999:blog-3722233.post-91521289886131498042021-04-25T21:01:00.000-05:002021-04-25T21:01:17.946-05:00Ferrer's Diagrams can be used to prove X theorems about partitions. What is X? <p>1978: I took an excellent ugrad course in combinatorics from James C Frauenthal (he sometimes wrote his name as the biniomial cofficient (J choose F)) and he covered Ferrer's diagrams. They are a nice way to prove equalities about types of partitions. See <a href="https://www.britannica.com/science/combinatorics/The-Ferrer-diagram">here</a> for a definition and a few examples. I have this (possibly false) memory that there were LOTS of partition theorems proven nicely with Ferrer's diagrams.</p><p>Fast forward to 2021:</p><p>2021: My TA Emily needs a topic to cover in Honors Discrete Math. I have this memory that there were LOTS of theorems about partitions proven with Ferrer's diagrams. We look at many websites on Ferrer diagrams and find only TWO examples:</p><p>The numb of partitions of n into k parts is the numb of partitions of n into parts the largest of which is k.</p><p><br /></p><p>The numb of partitions of n into \le k parts is the numb of partitions of n into parts the largest of which is \le k</p><p>We DO find many theorems about partitions such as this corollary to the Rogers-Ramanujan theorem:</p><p>The numb of partitions of n such that adjacent parts differ by at least 2 is the numb of partitions of n such that each partition is either \equiv 1 mod 5 or \equiv 4 mod 5.</p><p>This is a HARD theorem and there is no Ferrer-diagram or other elementary proof. </p><p>SO, I have one MEMORY but the reality seems different. Possibilities:</p><p>1) My memory is wrong. There really are only 2 examples (or some very small number).</p><p>2) There are other examples but I can't find them on the web. I HOPE this is true--- if someone knows of other ways to use Ferrer diagrams to get partition results, please comment. </p><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com10tag:blogger.com,1999:blog-3722233.post-11999072541690367892021-04-22T09:52:00.002-05:002021-04-22T09:54:27.771-05:00The Million Dollar Sermon<p>Illinois Tech has one of the greatest origin stories for a university. In 1890 Frank Gunsaulus, a pastor on the south side of Chicago, gave a sermon where he said "If I had a million dollars I would build a school to provide students from all backgrounds meaningful roles in a changing industrial society". Philip Armour, a wealthy industrialist in the congregation, went up to Gunsaulus after the sermon and said, "if you give me five years for this school, I'll give you the million dollars". Thus started the Armour Institute of Technology which after some mergers became the Illinois Institute of Technology.</p><p>The "million dollar sermon" really happened, though the exact wording and even the exact year are lost to posterity or, as speculated, hidden in a cornerstone of one of the original campus buildings. </p><p>In 1890 we were in the beginnings of the second industrial revolution, a revolution of communication, transportation, electrification and soon the assembly line. The first revolution happened a century earlier with mechanization and the steam engine. The third revolution was computers and automation, and we are now in the early parts of the fourth industrial revolution, one based on data and information. </p><p>There are many parallels between 1890 and today. Like 1890, the private economy is dominated by a small number of large companies that have an outsized influence in our society. Like 1890, technology is changing faster than we can manage it. Like 1890, many workers are finding their skills quickly outdated.</p><p>Today Gunsaulus's words ring truer than ever. We more than ever need to provide students of all backgrounds meaningful roles in a changing technological society. </p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com0tag:blogger.com,1999:blog-3722233.post-6287959816253771682021-04-18T21:01:00.001-05:002021-04-18T21:01:48.145-05:00An investment puzzle and speculation as to why some think its hard<p> This is a Guest Post by David Marcus. He gives a puzzle and its solution, which is interesting, and then speculates as to why some people get it wrong. </p><p>---------------------------------------------------------------------------</p><p>THE PROBLEM:</p><p>Investing Puzzle or Arithmetic Can Be Useful</p><p><br /></p><p>The following is an example of investment results that I saw in an</p><p>investment newsletter. There are two portfolios that use different</p><p>strategies. Both portfolios start with $1 million twenty years ago and</p><p>withdraw 5% each year. The idea is that you are retired and withdrawing</p><p>money to spend. Not all years are shown in the tables.</p><p><br /></p><p>Portfolio A</p><p><br /></p><p>Year Return Withdrawal Balance</p><p>2000 15.31% 57,655 1,095,445</p><p>2005 1.81% 59,962 1,139,273</p><p>2008 -12.65% 51,000 969,004</p><p>2009 34.26% 65,049 1,235,936</p><p>2010 11.94% 69,175 1,314,331</p><p>2015 -2.48% 64,935 1,233,764</p><p>2020 10.27% 66,935 1,271,765</p><p>Total Withdrawal: 1,685,190</p><p>Change in Balance: 27.18%</p><p>======</p><p>Portfolio B</p><p>Year Return Withdrawal Balance</p><p>2000 -0.95% 49,524 940,956</p><p>2005 3.80% 44,534 846,154</p><p>2008 -20.11% 35,922 682,523</p><p>2009 18.27% 40,360 766,833</p><p>2010 11.57% 42,777 812,764</p><p>2015 0.99% 50,767 964,567</p><p>2020 13.35% 65,602 1,246,433</p><p><br /></p><p>Total Withdrawal: 1,425,573</p><p>Change in Balance: 24.64%</p><p><br /></p><p>Portfolio A has a final balance that is 25,000 more than Portfolio B's and</p><p>had about 260,000 more in withdrawals. Does the example lend credence to</p><p>the Portfolio A strategy being better than the Portfolio B strategy?</p><p>---------------------------------------------------------------------------</p><p>THE ANSWER:</p><p>Investing Puzzle or Arithmetic Can Be Useful: Analysis</p><p><br /></p><p>Summary: The two portfolios have about the same performance over the 20</p><p>years. The difference is mainly due to Portfolio A having a good year or</p><p>years near the beginning before much money was withdrawn. The example</p><p>merely shows that it is better to withdraw money after a gain rather than</p><p>before.</p><p><br /></p><p>Detailed Analysis:</p><p><br /></p><p>The scenario is: Start with X = $1 million. Withdraw 5% a year.</p><p><br /></p><p>Define "gain factor" to be 1 plus the percentage return. For example, if a</p><p>portfolio returns 5%, then the gain factor is 1.05.</p><p><br /></p><p>Let A_j, j = 1, ..., 20, be the gain factors each year for portfolio A.</p><p><br /></p><p>Let B_j, j = 1, ..., 20 be the gain factors each year for portfolio B.</p><p><br /></p><p>The final amount in portfolio A is</p><p><br /></p><p> F = X * A_1 * 0.95 * A_2 * 0.95 * ... * A_20 * 0.95 .</p><p><br /></p><p>The final amount in portfolio B is</p><p><br /></p><p> G = X * B_1 * 0.95 * B_2 * 0.95 * ... * B_20 * 0.95 .</p><p><br /></p><p>From the "Change in Balance" values or the balances for year 2020, we see</p><p>that F and G are almost the same:</p><p><br /></p><p> F = 1.271865 * X,</p><p> G = 1.246433 * X.</p><p><br /></p><p>But, as we learned in elementary school, multiplication is commutative, so</p><p><br /></p><p> F = X * 0.95^20 * \prod_{j=1}^20 A_j,</p><p> G = X * 0.95^20 * \prod_{j=1}^20 B_j.</p><p><br /></p><p>Since F and G are almost the same, the total gains (product of the gain</p><p>factors) for the two portfolios are almost the same, i.e.,</p><p><br /></p><p> \prod_{j=1}^20 A_j \approx \prod_{j=1}^20 B_j.</p><p><br /></p><p>Then what accounts for the big difference in the amounts withdrawn?</p><p>Portfolio A must have had some good years near the beginning. (We see in</p><p>the tables that Portfolio A did better in 2000 than Portfolio B.) So, all</p><p>the example shows is that it is better to withdraw your money after your</p><p>gains rather than before.</p><p><br /></p><p>To take an extreme example, suppose an investment is going to go up 100%</p><p>this year. It is better to take your money out at the end of the year</p><p>(after the gain) than at the beginning of the year (before the gain). This</p><p>is a triviality.</p><p><br /></p><p>The example tells us nothing useful about the two strategies.</p><p><br /></p><p>Note: The total gains aren't exactly the same, but the timing of the yearly</p><p>gains is what is driving the results. We have (rounding off)</p><p> ( F - G ) / 0.95^20 = 70942.81 .</p><p>So, if there had been no withdrawals, the difference in the portfolio</p><p>balances would have been about $71,000, much less than the $260,000 +</p><p>$25,000 difference with the withdrawals.</p><p>---------------------------------------------------------</p><p>WHY IS THIS HARD FOR PEOPLE?</p><p>Many people have trouble with this puzzle. The difficulty may be that such</p><p>people don't make a mental model (or a written model) of the process that</p><p>is producing the balance. If you write down (or have in your head) a</p><p>formula for the balance, then you see that the gain factors are independent</p><p>of the withdrawal factors. That is, we could withdraw more or less money,</p><p>or even deposit money, without affecting the gain factors we would use in</p><p>the model. This then leads us to consider the gain factors on their own,</p><p>and to recognize that the gain factors are the true measures of how the</p><p>strategies perform.</p><p><br /></p><p><br /></p><div><br /></div>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com10tag:blogger.com,1999:blog-3722233.post-39881262523595407082021-04-15T07:31:00.000-05:002021-04-15T07:31:15.733-05:00Ordering Beauty<p>First, congratulations to fellow complexity theorist and <a href="https://www.scottaaronson.com/blog/">blogger</a> Scott Aaronson for <a href="https://awards.acm.org/about/2020-acm-prize">receiving the 2020 ACM Prize in Computing</a> for "groundbreaking contributions to quantum computing". The prize is ACM's highest honor for mid-career researchers. Well deserved! </p><p>Now back to our regularly scheduled post...</p><p>Every freshman at Cornell back in 1981 had to take two seminar courses, basically one-shot courses in an usually humanities area which required no prerequisites but lots of writing. I took my first course in philosophy. The instructor, a PhD student, at one point described his research, a philosophical argument that there is an intrinsic total ordering of beauty, say that Beethoven would always sit above the Beatles, no matter the beholder. I didn't believe him then and still don't today. A few months ago the Washington Post ran a story with the same theme entitled <a href="https://www.washingtonpost.com/entertainment/maradona-messi-ronaldo-zlatan-shakespeare-beatles/2020/12/23/27654712-38a9-11eb-9276-ae0ca72729be_story.html">Maradona was great, and maybe the greatest. Can we make similar claims about artists?</a></p><p>Somehow we have this belief when it comes to conference submissions, that there is some perfect ordering of the submissions and a good PC can suss it out. That's not really how it works. Let's say a conference has an accept rate of 30%. Typically 10% of the submissions are strong and will be accepted by any committee. About half the submissions are just okay or worse and would be rejected. The other 40% of the submissions will be chosen seemingly randomly based on the tastes of the specific members of the program committee. Experiments in the NeurIPS and ESA conferences have bourn this out. </p><p>Why not make the randomness explicit instead of implicit? Have the PC divide the papers into three piles, definite accepts, definite rejects and the middle. Take the third group and randomly choose which ones to accept. It will create a more interesting program. Also randomness removes biases, randomness doesn't care about gender, race and nationality or whether the authors are at senior professors at MIT or first year grad students at Southern North Dakota. </p><p>We put far too much weight on getting accepted into a conference given the implicit randomness of a PC. If we make the randomness explicit that would devalue that weight. We would have to judge researchers on the quality of their research instead of their luck in conferences.</p><p>Given that conferences, especially the virtual ones, have no real limits on the number of papers and talks, you might say why not just accept all the papers in the middle. Works for me.</p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com6tag:blogger.com,1999:blog-3722233.post-81471478310524805352021-04-11T23:12:00.000-05:002021-04-11T23:12:49.976-05:00Is the following reaction to getting the first COVID shot logical?<p> Alice works at a charity that puts together bag and box lunches for children.</p><p><br />They all wear masks and they are 12 feet apart and very careful, and nobody there has gotten COVID.</p><p>Then Alice gets here first COVID shot and says:</p><p><br /></p><p><i>I am not going to work for that charity until I have had my second shot and waited 4 weeks so I am immune. </i></p><p><i><br /></i></p><p>She is really scared of getting COVID NOW that she is on the verge of being immune. </p><p><br /></p><p>Is that logical? She was not scared before. So does it make sense to be scared now? I see where she is coming from emotionally, but is there a logical argument for her viewpoint? I ask nonrhetorically.</p><p><br /></p><p>bill g. </p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com11tag:blogger.com,1999:blog-3722233.post-7097049136232446462021-04-08T07:57:00.002-05:002021-04-08T08:30:21.341-05:00Quantum Stories<p>Scott Aaronson <a href="https://www.scottaaronson.com/blog/?p=5387">wrote last month</a> about the hype over quantum computing. I'd thought I'd drop a few stories.</p><p>I was once asked to review a grant proposal (outside the US) that claimed it would find a quantum algorithm for NP-hard problems. I wrote a scathing review but the grant was funded because I failed to prove that it was impossible. I replied that they should fund my research to teleport people from Chicago to Paris because they couldn't prove I couldn't do it. I never got a response.</p><div>I was at an NSF sponsored meeting on quantum computing. I suggested, as a complexity theorist, that we need to explore the limits of quantum computing. A senior researcher said we shouldn't mention that in the report or it might hurt our chances of funding the field if they think quantum computing might not be a complete success.</div><p>I went to a Microsoft Faculty Research Summit which had a big focus on quantum computing. I complained of the quantum computing hype. My friends in the field denied the hype. Later at the summit a research head said that Microsoft will solve world hunger with quantum computing.</p><p>I was meeting with a congressional staffer who had worked on the National Quantum Initiative which coincidentally was being announced that day. I said something about high risk, high reward. He looked shocked--nobody had told him before that quantum computing is a speculative technology.</p><p>Quantum computing has generated a large number of beautiful and challenging scientific questions. Thinking about quantum has helped generate classical complexity and algorithmic results. But quantum computing having a real-world impact in the near or mid-term is unlikely. Most scientists I know working directly in quantum research are honest about the limitations and challenges in quantum computing. But somehow that message is not often getting to the next layers up, the policy makers, the research managers, the university administrators, the media and the venture capitalists. </p><p>But who knows, maybe some quantum heuristic that doesn't need much entanglement will change the world tomorrow. I can't prove it's impossible.</p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com7tag:blogger.com,1999:blog-3722233.post-75016436261208463752021-04-04T23:30:00.000-05:002021-04-04T23:30:18.887-05:00Do any NP-reductions use deep mathematics? Non-rheticallyBILL: Lets say we didn't know that FACTORING NPC --> NP=coNP.<div>then what direction would we think Factoring in P or NPC? </div><div><br />STUDENT: In P. After all, Number Theory is a deep subject and I can imagine some deep Theorem in it leading to FACTORING in P. </div><div><br /></div><div>BILL: That cuts both ways. I can imagine some deep theorem in NT being the key to showing </div><div><br /></div><div>FACTORING poly-reduces to SAT</div><div><br /></div><div>STUDENT: </div><div>Deep mathematics HAS been used for algorithms. Factoring algs is one example, The graph minor theorem yielding MANY problems in P is another. Can you give me an example where deep mathematics has been used for an NPC reduction?</div><div><br /></div><div>BILL: Oh. Gee. I do not know of any. </div><div><br /></div><div>STUDENT: If only you had some mechanism to ask the theory community. Maybe you could call it a web log, or weblog.</div><div><br /></div><div>BILL: If only...</div><div><br />QUESTIONS</div><div>1) Are there any NPC reductions that use deep math? (I realize that the phrase `deep math' is not well defined,)</div><div><br /></div><div>2) Are there other reductions that use deep math?</div><div><br /></div><div>3) If P NE NP then: </div><div>For all epsilon there is no approx-alg for MAX3SAT which yields \ge (7/8 + epsilon)OPT</div><div><br /></div><div>For all delta there is no approx-alg for CLIQ which yields > n^{-delta} OPT</div><div><br /></div><div>No approx-alg for SET COVER which yields \ge (ln n + o(1))OPT. </div><div><br /></div><div>All of these proofs use the PCP machinery or something similar. My impression is that the original PCP theorem, while long, hard, and impressive, did not use deep math. I have a vague memory of some paper or PhD thesis stating that the ONLY theorem needed was that a poly of degree d over a finite field has \le d roots. </div><div><br /></div><div>However to get the optimal lower bounds seemed to use some deep math. But I am more ASKING than telling. </div>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com17tag:blogger.com,1999:blog-3722233.post-23699884090490117312021-04-01T08:22:00.000-05:002021-04-01T08:22:38.658-05:00Want to Buy a Theorem?<p>This is embarrassing to admit but after a few badly timed trades on GameStop options I find myself a bit tight on money. To raise some cash, I reluctantly decided to sell one of my prized possessions, one of my theorems.</p><p><b>For Sale</b>: Boolean formula satisfiability cannot be solved in both logarithmic space and quasilinear time. For a more formal and slightly more general statement and a proof, see <a href="https://doi.org/10.1006/jcss.1999.1671">this paper</a>.</p><p><b>Bidding starts</b> at 12 BTC (about $705,000). </p><p><b>The winning bid, upon verified payment, will receive:</b></p><p></p><ul style="text-align: left;"><li>The ability to give the theorem the name of your choice such as your own name, your best friend's mother's name or "Teddy McTheoremface".</li><li>A non-fungible token (NFT) attesting ownership of the theorem and the name you have chosen for it.</li><li>Anyone citing this result will be required to note that you own it and use the name you chose above. You cannot, however, limit the use of the theorem or receive compensation for its use. </li><li>By virtue of owning this theorem you will a Fortnow number of zero. This immediately gives you an Erdős number of 2. If you have previously written a paper with Paul Erdős then both of us will now have an Erdős number of 1.</li></ul><div><b>Frequently Asked Questions</b></div><div><b><br /></b></div><div><b>Q: </b>Why this theorem?</div><div><b><br /></b></div><div><b>A: </b>The theorem is in one of my few solely authored papers and I can't afford to share the proceeds of the sale. </div><div><br /></div><div><b>Q: </b>Doesn't Ryan Williams and others have <a href="http://pages.cs.wisc.edu/~dieter/Papers/sat-lb-survey-fttcs.pdf">stronger theorems</a>?</div><div><br /></div><div><b>A: </b>The results are incomparable. Ryan gives bounds on a single algorithm with low time and space. My theorem allows different machines for the time and space bounds.</div><div><br /></div><div>Also, to the best of my knowledge, Ryan's theorem is not for sale.</div><div><br /></div><div><b>Q: </b>Doesn't the proof of the theorem rely on other people's theorems such as Nepomnjascii? Shouldn't he get some of the value from this sale?</div><div><br /></div><div><b>A: </b>I'm not selling the proof of the theorem, just the theorem itself.</div><div><br /></div><div><b>Q: </b>If I purchase this theorem will I get to write next year's April Fools post?</div><div><br /></div><div><b>A: </b>No.</div><p></p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com2tag:blogger.com,1999:blog-3722233.post-78504049149136985152021-03-29T07:47:00.002-05:002021-03-29T08:05:29.979-05:00Slicing the Hypercube<p>Here's a neat result I heard about at <a href="https://www.dagstuhl.de/en/program/calendar/semhp/?semnr=21121">virtual Dagstuhl</a> last week, a new lower bound on the number of hyperplanes that cuts all the edges of a hypercube.</p><p>A n-dimensional hypercube has 2<sup>n</sup> vertices corresponding to the binary strings of length n. Edges are between two vertices that differ in exactly one bit, for a total of (n/2) 2<sup>n</sup> edges. Hypercubes played a <a href="https://blog.computationalcomplexity.org/2019/07/degree-and-sensitivity.html">large role</a> in Hao Huang's recent proof of the sensitivity conjecture. </p><p>A hyperplane is just a linear inequality in x<sub>1</sub>,…,x<sub>n</sub> the bits of the string corresponding to a vertex. An edge is cut if the inequality is true for one vertex and false for the other.</p><p>With n hyperplanes you can cut all the edges in two very different ways. </p><p></p><ul style="text-align: left;"><li>The hyperplanes x<sub>i</sub> > 0 for each i. These are n orthogonal hyperplanes.</li><li>The hyperplanes x<sub>1</sub>+…+x<sub>n</sub> > i for each i from 0 to n-1. These are n parallel hyperplanes.</li></ul><div>Do you need n hyperplanes to cut all the edges? Mike Paterson found 5 explicit hyperplanes that cuts all the edges of a 6-dimensional hypercube (see <a href="https://doi.org/10.1017/CBO9780511662089.009">survey</a> by Mike Saks). Scaling that up means you need 5n/6 hyperplanes to cut an n-dimensional hypercube. That remains the best known upper bound.</div><div><br /></div><div>For the lower bound, in 1971 Patrick O'Neil <a href="https://doi.org/10.1016/0012-365X(71)90025-2">showed</a> that any hyperplane can cut at most O(n<sup>0.5</sup>) fraction of the edges (sharp by the hyperplane x<sub>1</sub>+…+x<sub>n</sub> > n/2). Thus you need at least O(n<sup>0.5</sup>) hyperplanes which for 50 years was the best known bound.</div><div><br /></div><div>Gil Yehuda and Amir Yehudayoff have <a href="https://arxiv.org/abs/2102.05536">given a new lower bound</a> of O(n<sup>0.57</sup>). The paper gives a O(n<sup>0.51</sup>) bound but Yehudayoff said in a talk last week the bound has been improved.</div><div><br /></div><div>Yehudayoff didn't go into much details in his 20 minute talk but the proofs uses geometry, probability and antichains. </div><div><br /></div><div>The result has some applications to complexity, namely you need at least n<sup>1.57</sup> wires in a depth-two threshold circuit for parity. But the main fun is the question itself, that we finally made progress and there is still a long way to go.</div><p></p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com0tag:blogger.com,1999:blog-3722233.post-60408468431180469342021-03-25T21:58:00.002-05:002021-04-29T22:27:12.440-05:00The key to my Taylor series problem: Buddy can you spare a penny, nickel, dime, or quarter<p> In my last blog post I posed a question about finding the coeff of x^100 in a particular Taylor Series. The question and answer are given <a href="https://www.cs.umd.edu/users/gasarch/BLOGPAPERS/taylorcoins.pdf">here</a>:</p><p><br /></p><p>The key to the problem was to recognize that it was asking how many ways you can make change of a dollar using pennies, nickels, dimes, and quarters. This can be done by hand (its 242). </p><p>1) Someone who I gave the problem to solved it by available software, but when he saw the answer was 242 he realized how to do it via making change.</p><p><br /></p><p>2) How hard would this problem be to do completely by hand- say as a Putnam Problem? Its hard for me to say since I started with the trick and then found the problem. </p><p><br /></p><p>3) Is this a well known trick? </p><p><br /></p><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com3tag:blogger.com,1999:blog-3722233.post-74481141903199868342021-03-22T14:21:00.003-05:002021-03-22T14:21:55.452-05:00A Taylor Series Problem <p> I post a problem today and its solution on Thursday.</p><p>Comments are fine, though if you don't want to get a hint, don't read them. </p><p><br /></p><p>Find the coefficient of x<sup>100</sup> in the Taylor series for the rational function which has </p><p><br /></p><p>numerator 1 </p><p>and denominator</p><p><br /></p><p>x<sup>41</sup> - x<sup>40</sup> - x<sup>36</sup> + x<sup>35</sup> -x<sup>31</sup> + x<sup>30</sup> + x<sup>26</sup> - x<sup>25</sup>- x<sup>16</sup> + x<sup>15</sup> + x<sup>11</sup> - x<sup>10</sup> + x<sup>6</sup> - x<sup>5</sup> -x+1</p><p><br /></p><p>For better readability see my pdf file with the problem in it <a href="http://www.cs.umd.edu/~gasarch/BLOGPAPERS/taylorcoinsprob.pdf">here</a></p><p><br /></p><p>Is there a clever way to do the problem? If the way to do it was to actually do the Taylor series then </p><p>1) I wouldn't post it</p><p>2) I probably could not do it (or it would take too long to bother) though maybe there are freely available programs that could. </p><p><br /></p><p>So yes, there is a clever solution. At least I think it's clever. </p><p><br /></p><p><br /></p>
gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com12tag:blogger.com,1999:blog-3722233.post-91018421771466363342021-03-17T14:57:00.001-05:002021-03-18T07:34:12.924-05:00I read the news today oh boy<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-NMc_aH4Gb9o/YFJR2J9R5BI/AAAAAAAB61M/Mez6sk3EWO4mP5AZxnxUM_JszhYdaNZvACLcBGAsYHQ/s400/lovasz.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="300" data-original-width="400" height="150" src="https://1.bp.blogspot.com/-NMc_aH4Gb9o/YFJR2J9R5BI/AAAAAAAB61M/Mez6sk3EWO4mP5AZxnxUM_JszhYdaNZvACLcBGAsYHQ/w200-h150/lovasz.jpg" width="200" /></a><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-PzuRktxYKx4/YFJR4Z5NBrI/AAAAAAAB61Q/imp2GYxDJWwYxffkU9deF93T3-lA7m-ZgCLcBGAsYHQ/s260/avi.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="194" data-original-width="260" height="149" src="https://1.bp.blogspot.com/-PzuRktxYKx4/YFJR4Z5NBrI/AAAAAAAB61Q/imp2GYxDJWwYxffkU9deF93T3-lA7m-ZgCLcBGAsYHQ/w200-h149/avi.jpg" width="200" /></a></div></div><br /><br />I'm absolutely elated that <a href="https://www.abelprize.no/c76389/seksjon/vis.html?tid=76390&strukt_tid=76389">Lázló Lovász and Avi Wigderson won the Abel Prize</a>. More from the <a href="https://www.nytimes.com/2021/03/17/science/abel-prize-mathematics.html">New York Times</a>, <a href="https://www.quantamagazine.org/avi-wigderson-and-laszlo-lovasz-win-abel-prize-20210317/">Quanta Magazine</a> and <a href="https://gilkalai.wordpress.com/2021/03/17/cheerful-news-in-difficult-times-the-abel-prize-is-awarded-to-laszlo-lovasz-and-avi-wigderson/">Gil Kalai</a>. Another example of how complexity theory and theoretical computer science has reached the upper echelons of mathematics.<p></p><p>I'm horrified of the <a href="https://www.nbcnews.com/news/us-news/3-dead-shooting-georgia-massage-parlor-suspect-loose-n1261262">spa shootings in Atlanta</a>. I've driven by those spas many times when I lived there. </p><p>I'm saddened by the <a href="https://www.mills.edu/announcement/index.php">closing of Mills College</a> in Oakland, California. I lived in a dorm Berkeley rented at Mills College during my <a href="https://blog.computationalcomplexity.org/2006/04/one-miserable-year.html">crazy year there</a>.</p><p>I've got mixed emotions about the <a href="https://www.nytimes.com/2021/03/17/obituaries/james-levine-dead.html">death of James Levine</a>. What he did musically with the Metropolitan opera and orchestra was nothing short of incredible. What he did to the young people he abused is inexcusable. I remember watching a Met taped videocast of Die Walküre with my daughter, enjoying the production but telling her "Do you realize we are watching an opera composed by an anti-Semite and conducted by a child molester?" Can you separate art from artist?</p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com6tag:blogger.com,1999:blog-3722233.post-79567281270254728022021-03-15T00:52:00.000-05:002021-03-15T00:52:27.845-05:00I didn't understand The Art Market before the NFT sale, and I understand it less now<p> (This post is a sequel to my post from Feb 13, 2007 which you can find <a href="https://blog.computationalcomplexity.org/search?q=rare">here</a>. While the gap from 2007 until 2021 seems large, its not as long as the gap between Knuth Vol 3 and Knuth Vol 4, nor as long as the gap between Stan Freberg Vinyl Record History of America Part I and his CD History of America Part 2, both novelty records, and quite good.)</p><p>My 2017 post was about people posting a clip on youtube and calling it `rare footage of...' </p><p><br /></p><p>My point was: How can something be rare if its on you tube?</p><p>I also pondered: if someone can make a REALLY REALLY GOOD copy of the Mona Lisa, that is at talent that should be respected and such a person should be able to sell it for about the same price as the original (not sure if I want the copy to be worth A LOT or the original to be worth LESS than it is.)</p><p>IF Art is to-look-at-cause-its-pretty then it should not matter who the artist is. </p><p>IF Art is an investment then that could be risky since it does not have intrinsic value. </p><p>IF Art is neither to-look-at or an investment then... What is it? We'll see below that one answer might be Bragging Rights. </p><p>This is NOT a RANT, this is an admitance of my lack of understanding. (Spell check things admitance is not a word. Maybe its admitence. No, Hmmm.) </p><p>And now there is a new wrinkle in all of this: </p><p>69 million for a NFT (Non-Fungable Token) of an art work:<a href="https://variety.com/2021/digital/news/nft-craze-beeple-jpeg-artwork-69-million-1234928289/">story here</a></p><p>1) What is the buyer getting? Bragging rights?</p><p>2) Can anyone SEE the art but doesn't OWN it? I don't know..</p><p>3) If someone hacked in and got a perfect copy of the art and posted it on a website, would that be theft? Nothing was taken. </p><p>4) In the normal art world does it happen that prices go DOWN because people wake up and say WHAT? Why did I EVER think that White on White was worth 10 million dollars? </p><p>5) Might this happen here also? </p><p>6) Is My Feb 13 blog, which is in a diff format (or I didn't know how to use the blogger interface then) going to one day be worth something?</p><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com5tag:blogger.com,1999:blog-3722233.post-90441505699541775172021-03-12T09:12:00.002-06:002021-03-13T11:16:00.166-06:00Cake Cutting in Overtime<p>There's a new <a href="https://www.foxsports.com/stories/nfl/baltimore-ravens-coach-john-harbaugh-overtime-rule">proposal out of Baltimore</a> for a new way to handle overtime in National Football League games. This post is about American Football, soccer has its own overtime issues we won't talk about here.</p><p>Instead of randomly choosing who gets the ball, which gives an advantage to the team on offense, the Raven's coach John Harbaugh suggests a "spot and choose" rule based on cake cutting. One team picks a starting position and the other team decides whether to be on offense or defense.</p><p>Sounds intriguing but there's a problem. In cake cutting, if you cut off a crumb, everyone would definitely choose the rest of the cake. But in football suppose the spotting team chose the offensive's team one-yard line (99 yards needed for a touchdown). For spot and choose to work the one-yard line would have to be an obvious choice for defense. But many teams might still choose starting at the one-year line on offense. There's a chance you can march down the field and if not you can always punt it away. So the team that gets to choose whether to be on offense could get an advantage no matter what the spotting team did.</p><p>I still like the idea of "spot and choose". Maybe you let the first team choose not only the yard line but what down to start. Because no one would start at their one yard line at 4th down.</p><p>Are there variations for spot and choose in other sports? I like using game theory to figure out how to play actual games. </p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com6tag:blogger.com,1999:blog-3722233.post-612767423473052782021-03-07T20:35:00.003-06:002021-03-07T20:35:50.342-06:00When do I need to warn about Spoilers? <p>In a recent post <a href="https://blog.computationalcomplexity.org/2021/02/using-number-of-phds-as-measure-of.html">here</a> I mentioned in passing a plot point from the last season of The Big Bang Theory. Note that the last season was in 2019. WARNING- do not read that post if you are watching The Big Bang Theory and do not want a plot point revealed. </p><p>Someone who perhaps thinks Lance and I are the same person (are we? See <a href="https://blog.computationalcomplexity.org/2014/04/i-am-bill-gasarch.html">here</a>) left Lance a tweet complaining about the spoiler. At least I think they are complaining. The tweet is in Spanish and its <a href="https://twitter.com/deoxyt2/status/1366120364070338560">here</a>.</p><p>Either</p><p>1) Some country is two years behind America on showing The Big Bang Theory. </p><p>2) The person who tweeted has them on DVR (or something like that) and is watching them a few years after they air (I watched Firefly on a DVD I borrowed from a friend 10 years after it went off he air. Ask your grandparents what a DVD used to be.) </p><p>3) They are kidding us and making fun of the notion of spoilers.</p><p>This raises the question: When is it okay to post spoilers without warning? A few random thoughts:</p><p>1) ``Don't tell me who won the superb owl! I have it on tape and want to watch it without knowing who won!'' This always seemed odd to me. Routing for events to happen that have already happened seems weird to me. When I was 10 years old I was in New York listening to a Knicks-Celtics Basketball game on the radio and during halftime I accidentally found a Boston radio station that had the game 30 minutes later (I did not realize that the channel I was on originally was 30 minutes behind). So I heard how the game ended, then switched back <i>listening to a game knowing how it would end. </i>I didn't route for my team (the Knicks, who lost) but it just felt very weird listening to it. If I had thought of it I might have noticed how the different broadcasts differ and got a paper out of the data, but as a 10 year old I was not thinking about how to pad my resume quite yet. </p><p>2) I like seeing a mystery twice- first time I don't know who did it, second time I do but can look for clues I missed the first time.</p><p>3) I would have thought 2 years after a show is off the air its fine to spoil. But... maybe not.</p><p>4) It also matters how important the plot point is. I didn't think the plot point I revealed was that important. </p><p>5) Many TV shows are predictable so I am not sure what `spoiler' even means. If I said to Darling:</p><p><i> The bad guy is an unimportant character we meet in the first 10 minutes.</i></p><p>that does not show I've seen it before. It shows that I am a master of TV-logic.</p><p>6) With Arc TV shows this is more of a problem. While it was possible to spoil an episode (Captain Kir will survive but Ensign Red Shirt will bite the dust) it was impossible to spoil a long-term arc. TV has gotten to complicated. And I say that without having watched Game of Thrones. </p><p><br /></p><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com7tag:blogger.com,1999:blog-3722233.post-56638843250468904612021-02-28T11:42:00.000-06:002021-02-28T11:42:00.815-06:00Using number-of-PhD's as a measure of smartness is stupid. <p>In <i>Thor:Ragnorak</i> Bruce Banner mentions that he has 7 PhDs. Gee, I wonder how he managed to slip that into a conversation casually. Later in the movie:</p><p><br /></p><p>Bruce: I don't know how to fly one of those (it an Alien Spacecraft)</p><p>Thor: You're a scientist. Use one of your PhD's </p><p>Bruce: None of them are for flying alien spaceships.</p><p><br /></p><p>On the episode <i>Double Date </i>of Archer (Season 11, Episode 6) Gabrielle notes that she has 2 PhD's whereas Lana only has 1 PhD. </p><p><br /></p><p>I am sure there are other examples of a work of fiction using <i>number of PhDs </i>as a way to say that someone is smart. In reality the number of PhD's one has is... not really a thing. </p><p>In reality if a scientist wants to do work in another field they... do work in that field.</p><p>Godel did research in Physics in the 1950's, but it would have been silly to go back and get a PhD in it.</p><p>Fortnow did research in Economics, but it would have been silly to go back and get a PhD in it. </p><p>Amy Farrah Fowler worked in neurobiology and then in Physics. Her Nobel prize in physics (with Sheldon Cooper) is impressive, getting a PhD in Physics would be ... odd. Imagine someone looking at here resume: <i>She has a Nobel Prize in Physics, but does she have a PhD? Did she pass her qualifying</i> <i>exams?</i> This is the flip side of what I mentioned in a prior post about PhD's: <i>Not only does Dr. Doom want to take over the world, but his PhD is from The University of Latveria, which is not accredited. </i></p><p>There are other examples.</p><p>There ARE some people who get two PhDs for reasons of job market or other such things. That's absolutely fine of course. However, I wonder if in the real world they brag about it. I doubt it. </p><p>Is there anyone who has 3 PhDs? I would assume yes, but again, I wonder if they brag about it. Or should. </p><p>WHY do TV and movies use number-of-PhDs as a sign of genius? I do not know- especially since there are BETTER ways say someone is a genius in a way the audience can understand: number-of-Nobel-prizes, number-of-times-mentioned-in-complexityblog, number of Dundie's (see <a href="https://theoffice.fandom.com/wiki/Dundie">here</a>), etc. </p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com14tag:blogger.com,1999:blog-3722233.post-22022488280095628002021-02-25T08:19:00.000-06:002021-02-25T08:19:22.435-06:00Complexity is the Enemy of Speed<p>The title of this post came from an <a href="https://www.wsj.com/articles/connecticuts-covid-vaccine-lesson-11614124012">opinion piece</a> in the Wall Street Journal yesterday on vaccine distribution. Many attempts to get the vaccines to the right groups first have slowed down distribution and sometime even caused <a href="https://www.nbcnews.com/news/us-news/thousands-covid-19-vaccines-wind-garbage-because-fed-state-guidelines-n1254364">vaccines to go to waste</a>. Rules to help spread vaccines across minority groups often backfire. Often when some rules lead to inequity, we try to fix it with more rules when we need less much less. Attempts to distribute vaccines to multiple medical and pharmacy sites have made it difficult to get appointments even if you are eligible.</p><p>Randomness is the simplest way to fairness. The movie Contagion got it right, just choose birthdays by picking balls from a bin to distribute the vaccine. Then people can just show up at a few chosen sites with proof of birthday. No need to sign up.</p><p>You could argue to add back conditions like age, medical conditions, jobs but that just leads you down the same problematic path. The fastest way to get past this pandemic is to get vaccines into arms. Trust the randomness.</p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com6tag:blogger.com,1999:blog-3722233.post-63985373581101728582021-02-22T23:36:00.000-06:002021-02-22T23:36:15.128-06:00Good Names and Bad Names of Game Shows and theorems<p> In my post on Alex Trebek, see <a href="https://blog.computationalcomplexity.org/2020/11/alex-trebekwhat-is-todays-post-about.html">here</a>, I noted that <i>Jeopardy!</i> is not a good name for the game show since it doesn't tell you much about the show. Perhaps <i>Answers and Questions </i>is a better name.</p><p>The following game shows have names that tell you something about the game and hence have better names: </p><p>Wheel of Fortune, The Price is Right, Lets make a Deal, Beautiful women have suitcases full of money (the original name for Deal-No Deal), Win Ben Stein's Money, Beat the Geeks. </p><p>In Math we often name a concept after a person. While this may be a good way to honor someone, the name does not tell us much about the concept and it leads to statements like:</p><p><br /></p><p><i>A Calabi-Yau manifold is a compact complex Kahler manifold with a trivial first Chern class. </i></p><p><i>A Kahler manifold is a Hermitian manifold for which the Hermitian form is closed.</i></p><p><i>A Hermitian manifold is the complex analog of the Riemann manifold. </i></p><p>(These examples are from an article I will point to later---I do not understand <i>any </i>of these terms, though I once knew what a <i>Riemann manifold</i> was. I heard the term <i>Kahler Manifold </i>in the song <a href="https://www.youtube.com/watch?v=2rjbtsX7twc">Bohemian Gravity</a>. It's at about the 4 minute 30 second place.) </p><p>While I am amused by the name <i>Victoria Delfino Problems</i> (probably the only realtor who has problems in math named after her, see my post <a href="https://blog.computationalcomplexity.org/2021/02/the-victoria-delfino-problems-example.html">here</a>) it's not a descriptive way to name open problems in descriptive set theory. </p><p><br /></p><p>Sometimes a name becomes SO connected to a concept that it IS descriptive, e.g.:</p><p><i>The first proof of VDW's theorem yields ACKERMAN-LIKE bounds. </i></p><p>but you cannot count on that happening AND it is only descriptive to people already somewhat in the field. </p><p><br /></p><p>What to do? <a href="http://nautil.us/issue/89/the-dark-side/why-mathematicians-should-stop-naming-things-after-each-other">This</a> article makes the ballian point that we should STOP DOING THIS and that the person who first proves the theorem should name it in a way that tells you something about the concept. I would agree. But this can still be hard to really do.</p><p><br /></p><p>In my book on Muffin Mathematics (see <a href="https://www.amazon.com/Mathematical-Muffin-Morsels-Problem-Mathematics/dp/9811215170">here</a>) I have a sequence of methods called</p><p>Floor Ceiling, Half, Mid, Interval, Easy-Buddy-Match, Hard-Buddy-Match, Gap, Train. </p><p>There was one more method that I didn't quite name, but I used the phrase `Scott Muffin Problem' to honors Scott Huddleton who came up with the method, in my description of it. </p><p>All but the last concept were given ballian names. Even so, you would need to read the book to see why the names make sense. Still, that would be easier than trying to figure out what a Calabi-Yau manifold is. </p><p><br /></p><p></p><br />gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com8tag:blogger.com,1999:blog-3722233.post-6992308318083450842021-02-14T14:23:00.000-06:002021-02-14T14:23:02.530-06:00Two examples of Journalists being... Wrong. One BIG one small<p> Journalists sometimes get things wrong.</p><p>This is not news, but it is interesting when you KNOW they are wrong. </p><p>1) Scott Aaronson has a GREAT example regarding an IMPORTANT story. I recommend you to read his blog post <a href="https://www.scottaaronson.com/blog/?p=5310">here</a>. Most of the comments are good also, though they go off on some tangents (e.g., is the Universal Basic Income a progressive idea?)</p><p><br /></p><p>2) I have my own example. It is far less important than the one Scott discusses; however, inspired by Scott, I will discuss it. My example also involves Scott, but that's a coincidence. </p><p>Quanta Magazine emailed me that they wanted to talk to me about an upcoming article on <i>The Busy</i> <i>Beaver Problem</i>. Why me? Because Scott's (same Scott as above!) survey/open problems column appeared in the SIGACT News Open Problem Column that I edit. </p><p>This sounded fine (Spoiler Alert: It was fine, the errors they made were odd, not harmful).</p><p>Here is the Quanta Article (though I do not know if it is behind paywalls- I can never tell if I am getting access because I have a UMCP account of or anyone can have access or if I am breaking copyright laws by posting the link): <a href="https://www.quantamagazine.org/the-busy-beaver-game-illuminates-the-fundamental-limits-of-math-20201210/">here</a></p><p>Here is Scotts article: <a href="https://www.scottaaronson.com/papers/bb.pdf">here</a></p><p>The interviewer asked me </p><p>a) Why did I ask Scott to write the article?</p><p>ANSWER: He had a blog post on it, and I was skeptical of why these numbers are interesting, so I asked a question in the comments. He gave a great answer, so I asked him if he wanted to write a column for my open problems column. Actually I asked him if either he or perhaps a grad student would do it- I assumed he would be too busy since his `day job' is quantum computing. However, much to my surprise and delight he said YES he would do it.</p><p>b) Is the Busy Beaver Function important?</p><p>ANSWER: In my opinion the actual numbers are not that important but its really neat that (a) we know some of them, and (b) they are far smaller than I would have thought. Also these numbers are interesting for the following reason: there is some n so that proving </p><p>BB(n)=whatever it equals</p><p> is Ind of Peano Arithmetic. When I hear that I think the number must be really large. Its not. Its 27. NEAT! And stronger theories are related to bigger numbers. This is a way to order theories. For ZF they have something in the 700's- MUCH SMALLER than I would have thought. Scott and others can even relate BB to open problems in Math! </p><p>There were some other questions also, but I don't recall what they were. </p><p>SO when the article came they mentioned me once, and its... not quite wrong but odd:</p><p><i>William Gasarch, a computer science professor at the University of Maryland College Park,</i></p><p><i>said he's less intrigued by the prospect of pinning down the Busy Beaver numbers than by </i></p><p><i>``the general concept that its actually uncomputable.'' He and other mathematicians are mainly interested in using the yardstick for gauging the difficulty of important open problems in mathematics--or for figuring out what is mathematically knowable at all. </i></p><p><br /></p><p>The oddest thing about the paragraph is they do not mention my connection to Scott and the article he wrote! I reread the article looking for something like `<i>Scotts article appeared in the SIGACT News</i> <i>Open Problems column edited by William Gasarch' </i>Nothing of that sort appears. </p><p>Without that its not clear why they are soliciting my opinion. My colleague Clyde says this is GOOD: people will ASSUME I am some sort of expert. Am I an expert? I proofread Scott's paper so... there is that...</p><p>Also I come off as more down on BB than I really am. </p><p>Did I claim that Mathematicians are more interested in using it as a yardstick. Actually I may have said something like that. I don't know if its true. That's my bad- I should have said that I am interested in that.</p><p>After the article came out I asked the interviewer why my role was not in the article. He said it was cut by the editor. </p><p>NOW- NONE of this is important, but even on small and easily correctable things, they get it wrong. So imagine what happens on hard issues that are harder to get right. </p><p><br /></p><p>MISC: One comment on Scott's blog was about the Gell-Mann amnesia effect, see this article on it:</p><p><a href="https://www.tefter.io/bookmarks/45454/readable">here</a><br /></p><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com5tag:blogger.com,1999:blog-3722233.post-84741383957157370502021-02-07T22:55:00.003-06:002021-02-09T00:25:21.286-06:00The Victoria Delfino Problems: an example of math problems named after a non-mathematician<p> If you Google <b>Victoria Delfino </b>you will find that she is a real estate agent in LA (well, one of the Victoria Delfino's you find is such). After this blog is posted you may well get this post on the first Google page. </p><p>If you Google <b>Victoria Delfino Problems</b> you will find a paper:</p><p><a href="https://andrescaicedo.files.wordpress.com/2008/04/vdp-finalversion-withreferences.pdf">The fourteen Victoria Delfino Problems and their Status in the year 2015</a></p><p>(ADDED LATER: a comment pointed me to an updated version, so you can see that- I got to a pay wall.) </p><p>How did a real estate agent get honored by having 14 problems in descriptive set theory named after her?</p><p>Possibilities before I tell you which one.</p><p>1) Real estate is her day job. Her hobby is Descriptive Set Theory. Recall that Fermat was a lawyer (or something like that- see <a href="https://en.wikipedia.org/wiki/Pierre_de_Fermat">his Wikipedia page</a>) so perhaps she is similar. Doubtful- I think math is too hard for that now. Or at least descriptive set theory is too hard for that now. </p><p>2) She just happened to remark one day,<i> Gee, I wonder if</i></p><p><i> ZFC + SEP(Sigma_3^1) + # implies DET(Delta_2^1).</i> </p><p>Its just the kind of thing someone might just say. That was problem 4 of the 14. </p><p>3) There are two Victoria Delfino's- one is a realtor, one is a mathematician. While plausible, that would not be worth blogging about. </p><p>4) And now the truth: Victoria was the realtor who helped Moschovakis (a descriptive set theorist who I will henceforth describe as M) buy his house. When Tony Martin (another Desc. Set Theorist) moved to UCLA, M referred him to Victoria and she did indeed help Tony find a house. Victoria gave M a large commission which he tried to turn down. She did not want it returned, so M used the money to fund five problems. Later problems were added, but for no money. The article <i>The Fourteen... </i>linked to above has the full story. It also has the curious line: </p><p><i>Contrary to popular belief, no monetary prize is attached to further problems. </i></p><p>I didn't think any of this was so well known as to have popular believes. </p><p>ANYWAY, this is an example of a math problem named after a non-math person. Are there others? Will the name stick? Probably not- already 12 of the 14 are solved. I have noted in a prior blog (<a href="https://blog.computationalcomplexity.org/2009/08/how-much-credit-should-conjecturer-get_14.html">here</a>) once a conjecture gets proven, the one who made the conjecture gets forgotten. Or in this case the person who the conjectures is named after. </p><p>So are there other open problems in math named after non-math people? How about Theorems?</p><p>Near Misses: </p><p>Pythagoras: Not clear what he had to do with the theorem that bears his name. </p><p>L'hopital's Rule: the story could be a blog in itself, and in fact it is! Not mind, but someone else: <a href="https://andrescaicedo.wordpress.com/2013/11/05/credit/">here</a>. However L'hopital was a mathematician. </p><p>Sheldon's conjecture (see <a href="https://blog.computationalcomplexity.org/2019/10/the-sheldon-conjecture-too-late-for.html">here</a>) was named after a FICTIONAL physicist. Note that Sheldon inspired the conjecture but did not make it. It has been solved. </p><p>The Governor's Theorem (see <a href="https://blog.computationalcomplexity.org/2013/08/how-much-trig-does-your-governor-know.html">here</a>) was named because Jeb Bush was asked for the angles of a 3-4-5 right triangle (not a fair question). </p><p>The Monty Hall Paradox.</p><p>SO- are there Open Problems, Theorems, Lemmas, any math concepts, named after non-math people? I really mean non-STEM people. If a Physicist or an Engineer or a Chemist or Biologist or... has their name on something, that would not really be what I want.</p><p>(ADDED LATER - someone emailed me two oddly-named math things:</p><p>Belphegor's prime, <span style="background-color: white; color: #222222; font-family: Arial, Helvetica, sans-serif; font-size: small;">see </span><a href="https://en.wikipedia.org/wiki/Belphegor%27s_prime">here</a></p><p>Morrie's law- odd since Morrie is the FIRST name of who the name is honoring, see <a href="https://en.wikipedia.org/wiki/Morrie%27s_law">here</a> </p><p>)</p><p><br /></p><p>Are there any other open problems in descriptive set theory named after realtors?</p><p><i><br /></i></p><p><br /></p><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com7tag:blogger.com,1999:blog-3722233.post-79912313674610367242021-02-03T07:26:00.000-06:002021-02-03T07:26:25.479-06:00A Blood Donation Puzzle<p>In the US you can donate whole blood every eight weeks. Suppose Elvira does exactly that. Will she hit every date of the year? For example, if Elvira gave blood today, will she in some future year give blood on the 4th of July? Can we figure it out without having to rely on a computer simulation or even a calculator?</p><p>Let's make the assumptions that the blood center is open every day and that Elvira gives blood exactly every 56 days for eternity. </p><p>A year has 365 days which is relatively prime to 56=2<sup>3</sup>*7 since 365 mod 2 =1 and 365 mod 7 = 1. By the <a href="https://en.wikipedia.org/wiki/Chinese_remainder_theorem">Chinese remainder theorem</a> her next 365 blood donations will be on 365 distinct dates. If Elvira started giving blood at age 17, she will have hit every date at age 73.</p><p>That was easy but wrong. We have to account for those pesky leap years.</p><p>In a four year span, there will be one leap day. The total days in four years (using modular arithmetic) will still be odd and 5 mod 7, so still relatively prime to 56. So Elvira will donate on every day on the calendar exactly four times, except February 29th which she will hit once, over a period 56*4=224 years. </p><p>Alas not quite. Years ending 00 are not leap years, unless the year is divisible by 400. 2000 was a leap year but 2100 won't be. Any stretch of 224 years will hit at least one of those 00 non-leap years.</p><p>In 400 years, there will be 97 leap years. Since a regular year is 1 mod 7 days and a leap year is 2 mod 7 days, 400 years will be 497 mod 7 days. Since 497=71*7, 400 years has a multiple of 7 days. Every 400 years we have exactly the same calendar. February 3, 2421 is also a Wednesday.</p><p>The cycle of blood donations will repeat every 3200 years, the number of years in the least common multiple of 56 and the odd multiple of seven number of days in 400 years. But we can no longer directly apply the Chinese remainder theorem and argue that every day of the year will be hit. In those 3200 years Elvira will have over 20,000 blood donations. If the dates were chosen randomly the expected number to hit all dates would be 2372 by <a href="https://en.wikipedia.org/wiki/Coupon_collector%27s_problem">coupon collector</a>. So one would expect Elvira would hit every day, but that's not a proof.</p><p>So I had to dust off my Python skills and do the computer simulation after all. No matter what day Elvira starts donating she will eventually hit every date of the year. If Elvira starts donating today, she would give blood on the 4th of July for the first time in 2035 and <a href="https://docs.google.com/document/d/10aTFv5UUWfsrkKmVeud_r2VObfS1_J1tJflMeWld2w4/edit?usp=sharing">hit all dates</a> on January 8, 2087 after 431 donations. The longest sequence is 3235 donations starting April 25, 2140 and hitting all dates on February 29, 2636.</p>Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.com4tag:blogger.com,1999:blog-3722233.post-88093940017863874912021-01-31T15:50:00.003-06:002021-02-14T14:29:26.294-06:00Grading policies during Covid-No easy answers<p> Because of COVID (my spellecheck says covid and Covid are not words, but COVID is) various schools have done various things to make school less traumatic. Students already have problems, either getting COVID or having their friends got family get it (I've had four relatives get it, and one died) . Some do not adjust to learning online. Some do not have good computer connection to learn on line. So what is a good policy? Here are some things I have either seen schools do or heard that they might do.</p><p><br /></p><p>1) Be more generous with Tuition-Refunds if a student has to withdraw. </p><p>2) Be more generous with Housing-Refunds if a students comes to campus thinking it will be courses on campus and there are no courses on campus. Or if a student has to withdraw. </p><p>3) Make the deadlines for dropping-without-a-W, or taking-it-pass-fail, later in the semester. </p><p>4) Tell the teachers to `just teach them the bare min they need for the next course.'</p><p>5) Allow students to take courses P/F in their major and still allow them to count, so a student might get a D in Discrete Math and be able to go on in the major. </p><p>6) How far to extend deadlines? How is this: extend deadline to make it P/F until the last day of classes (but before the final) and then after the final is given, the school changes its mind and says - OH, you can change to P/F now if you want to.</p><p>7) Allow either an absolute number (say 7) or a fraction (say 1/3) of the courses to be changed to P/F by the last day of class.</p><p>8) Combine 6 or 7 with saying NO- a D is an F for a P/F course. Perhaps only if its in the major, but that maybe hard to work out. since majors can change. Some schools do A-B-C-NO CREDIT, where the NC grade does not go into the GPA.</p><p>9) Give standard letter grades and tell the students to tough it out. Recall the following inspirational quotes</p><p>When the going gets tough, the tough go shopping</p><p>When the going gets tough, the tough take a nap</p><p>If at first you don't succeed, quit. Why make a damn fool of yourself. </p><p>If at first you don't succeed, then skydiving is not for you. </p><p>10) Decide later in the term what to do depending on who yells the loudest. </p><p>11) Any combination of the above that makes sense, and even some that don't. </p><p><br /></p><p>On the one hand, there are students who are going through very hard times because of COVID and should be given a break. On the other hand, we want to give people a good education and give grades that are meaningful (the logic of how to give grades in normal times is another issue for another blog post). </p><p>What is your school doing? Is it working? What does it mean to be working?</p><p>The problems I am talking about are first-world problems or even champagne-problems. I know there are people who have far worse problems then getting a bad grade or dropping courses.</p><p><br /></p>gasarchhttp://www.blogger.com/profile/03004932739846901628noreply@blogger.com4