Acronyms and PHP
21 September 2017 | 11:57 pm

Whenever I teach discrete math and use FML to mean Formula the students laugh since its a common acroynm for  Fuck My Life. Now they laugh, and I say I know why you are laughing, I know what it means  and they laugh even harder.

BUT it got me thinking: Pigeonhole Principle! There are more things we want short acroynms for then there are short acroynms. Below are some I thought of. I am sure there are others, in fact I am sure there are websites of such, but I wanted to see which ones I just happen to know.

AMS- American Math Society and much much more:see here

DOA-

Dead on Arrival

Department of Aging. Scary!

ERA-

Earned Run Average in Baseball,

Equal Rights Amendment in politics

PCP-

Phencyclidine, a drug that you should never take.

Prob. Checkable Proofs. Obscure to the pubic but not to us.

IRA- 

Irish Republic Army

Internal Retirement Account

Several companies have had rumors they fund terrorism because they were giving their employees IRA's. The headline `Company X funds IRA's' could be misunderstood.


SAT-

Standard Aptitute Test

Satisfiability (of Boolena Formulas) Obscure to the pubic but not to us. Actually it may get less obscure as more ``proofs'' resolving P vs NP come out.

SJW

Single Jewish Female (in classified ads- more on that later). I think SJF is more common.

Social Justice Warrior (sounds like a good thing but might not be)

Classified ads are a source of many acronyms which can be used to teach combinatorics.

{S,M,W,D,G}{B,C,H,J,W}{M,F}


S-single, M-married, W-widowed, D-Divorced, G-Gay (this one I've seen alone making me wonder
about S/M/W/D? I've also seen four-letter acronyms to disambiguate).

B- black, C-Christian, H-Hispanic,  J-Jewish, W-White.

M,F- Male, Female, though I am sure there are ways to say other genders.

Great for combinatorics! especially if you add in other ones (like BD)

WTF-

Wisconsin  Tourism Federation

You know what else it means so I won't say it (this is a G-rated blog). When I first saw it I thought `what the fuck?- how could they have screwed up so badly?'


TEACHING TOOL- when teaching PHP (Pigeon hole Principle, not the language PHP which stands for Hypertex PreProcessing, not quite in order, or Personal Home Page) you can use the the fact that

number of concepts GREATER THAN  number of 3-letter combos

leads to some 3-letter combos will be used more than once.


A problem I thought was interesting- now...
18 September 2017 | 4:36 am

On Nate Silver's page he sometimes (might be once a week) has a column edited by Oliver Roeder of problems. Pretty much math problems though sometimes not quite.

Some are math problems that I have seen before (e.g., hat problems). I don't bother submitting since that would just be goofy. I would be  ringer.

Some are math problems that I have not seen before, I try to do, I fail, but read the answer and am enlightened. I call that a win.

But some are math problems that I have not seen before, I try to do, I fail, but when I see the solution its a computer simulation or something else that isn't quite as interesting as I had hoped.

I describe one of those now; however, I ask if it can be made more interesting.

The problems is from this column: here

I paraphrase:  Let A be the numbers {1,2,3,...,100}.  A sequence is nice if  (1) it begins with any number in A, (2) every number is from A and is either a factor of multiple of the number just before it, and (3) no number can appear more than once.  Find the LONGEST nice sequence

Example of a nice sequence: 

4, 12, 24, 6, 60, 30, 10, 100, 25, 5, 1, 97

I worked on it

1) By hand I came up with a nice sequence of length 42. This was FUN! You can either have fun trying to find a long nice sequence or you can look at mine here.

2) I tried to prove that it was optimal, hoping that either I would find its optimal or be guided to a longer sequence. Neither happened. More important is that this was NOT FUN.

3) I looked forward to the solution that would be in the next column and would be enlightening. 

4) The next column, which did have the solution, is here! The answer was a sequence of length 77 found by a program that also verified there was no longer sequence. The sequence itself was mildly enlightening in that I found some tricks I didn't know about, but the lack of a real lower bound proof was disappointing.

They mentioned that this is a longest path problem (Graph is {1,..,100} edges are between numbers that are either multiples of factors) and that such problems are NP-complete. That gave the impression that THIS problem is hard since its a case of an NP-complete problem. Thats not quite right- its possible that this type of graph has a quick solution.

But I would like YOU the readers to help me turn lemon into lemonade.

1) Is there a short proof that 77 is optimal?  Is there a short proof that (say) there is no sequence of length 83.  I picked 83 at random.  One can easily prove there is no sequence of length 100.

2) Is the following problem in P or NPC or if-NPC-then-bad-thing-happen:

Given (n,k) is there a nice sequence of {1,...,n} of length at least k. (n is in binary, k is in unary, so that the problem is in NP.)

I suspect not NPC.

3) Is the following problem in P or NPC or ...

Given a set of numbers A and a number k, is there a nice sequence of elements of A of length at least k (k in unary).

Might be NPC if one can code any graph into such a set.

Might be in P since the input has a long length.

4) Is the following solvable: given a puzzle in the Riddler, determine ahead of time if its going to be interesting? Clyde Kruskal and I have a way to solve this- every even numbered column I read the problem and the solution and tell him if its interesting, and he does the same for odd number columns.



Random Storm Thoughts
14 September 2017 | 4:36 pm

It's Monday as I write this post from home. Atlanta, for the first time ever, is in a tropical storm warning. Georgia Tech is closed today and tomorrow. I'm just waiting for the power to go out. But whatever will happen here won't even count as a minor inconvenience compared to those in Houston, the Caribbean and Florida. Our hearts goes out to all those affected by these terrible storms.

Did global warming help make Harvey and Irma as dangerous as they became? Hard to believe we have an administration that won't even consider the question and keeps busy eliminating "climate change" from research papers. Here's a lengthy list cataloging Trump's war on science. 

Tesla temporarily upgraded to its Florida Owners' cars giving them an extra 30 miles of battery life. Glad they did this but it begs the question why Tesla restricted the battery life in the first place. Reminds of when in the 1970's you wanted a faster IBM computer, you paid more and an IBM technician would come and turn the appropriate screw. Competition prevents software-inhibitors to hardware. Who will be Tesla's competitors?

During all this turmoil the follow question by Elchanan Mossel had me oddly obsessed: Suppose you flip a six-sided die. What is the expected number of dice throws needed until you get a six given that all the throws ended up being even numbers? My intuition was wrong though when Tim Gowers falls into the same trap I don't feel so bad. I wrote a short Python program to convince me, and the program itself suggested a proof.

Updates on Thursday: I never did lose power though many other Georgia Tech faculty did. The New York Times also covered the Tesla update. 


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