The Mystical Bond Between Man and Machine
16 July 2018 | 4:55 pm

You just can't watch a movie these days without being inundated with trailers. First came Axl, a movie about a boys love for a military robotic dog.

 

"It's only a robot," says his father. "It's an intelligent robot" replies the kid. Then comes the generic ET-like story of the government coming for the robot.

Next came a trailer for a movie that start off with Hailee Steinfeld discovering a VW bug with the background voice going "The driver don't pick the car. The car picks the driver". I'm thinking it's either a new Herbie movie or Transformers. Spoiler: Transformers.


"There's a mystical bond between man and machine" the voice intones. Followed by action that looks just like Axl.

Movie love for machines is hardly new. You can go back to Her or Short Circuit or even Metropolis in 1927. But in an age that parents worry about their kids being rude to Alexa perhaps this mystical bond is starting to get just a little too real.

The Six Degrees of VDW
12 July 2018 | 5:33 am

 A long long time ago  a HS student, Justin Kruskal (Clyde's  son)  was working with me on upper bounds on some Poly VDW numbers (see here for a statement of PVDW). His school required that he have an application.  Here is what he ended up doing: rather than argue that PVDW had an application he argued that Ramsey Theory itself had applications, and since this was part of Ramsey Theory it had an application.

How many degrees of separation were there from his work and the so called application.

  1. The best (at the time) Matrix Multiplication algorithm used 3-free sets.
  2. 3-free sets are used to get lower bounds on VDW numbers.
  3. Lower bounds on VDW numbers are related to upper bounds on VDW numbers
  4. Upper bounds on VDW are related to upper bounds on PVDW numbers.
Only 4 degrees!  The people in charge of the HS projects recognized that it was good work and hence gave him a pass on the lack of real applications. Or they didn't quite notice the lack of applications. He DID end up being one of five students who got to give a talk on his project to the entire school.

When you say that your work has applications is it direct? one degree off? two? Are all theorems no more than six degrees away from  an application? Depends on how you define degree and application.

The Muffin Problem
10 July 2018 | 5:11 pm

I've been meaning to post on THE MUFFIN PROBLEM for at least a year. Its a project I've been working on for two years, but every time I wanted to post on it I thought.


I'm in the middle of a new result. I'll wait until I get it!

However, I was sort of forced to finally post on it since Ken Regan (with my blessing) posted on it. In fact its better this way- you can goto his post for the math and I get to just tell you other stuff.

The problem was first defined by Alan Frank in a math email list in 2009.

I'll  define the problem, though for more math details goto Ken's post:  here.

You have m muffins and s students. You want to give each student m/s piece and
divide the muffins to maximize the min piece. Let f(m,s) be the size of the min piece
in an optimal divide-and-distribute procedure.

Go and READ his post, or skim it, and then come back.

Okay, you're back. Some informal comments now that you know the problem and the math

1) I saw the problem in a pamplet at the 12th Gathering for Gardner. Yada Yada Yada I have 8 co-authors and 200 pages, and a paper in FUN with algorihtms You never know when a problem will strike you and be worth working on!
(The 8 coauthors are Guangiqi Cui, John Dickerson, Naveen Dursula, William Gasarch, Erik Metz,
Jacob Prinze, Naveen Raman, Daniel Smolyak, Sung Hyun Yoo. The 200 pages are here. The FUN with algorithms paper, only 20 pages, is here)

2) Many of the co-authors are HS students. The problem needs very little advanced mathematics (though Ken thinks it might connect to some advanced math later). This is a PRO (HS students can work on it, people can understand it) and a CON (maybe harder math would get us more unified results)

3) The way the research had gone is a microcosm for math and science progress:

We proved f(m,s) = (m/s)f(s,m)  (already known in 2009) by Erich Friedman in that math email list)

Hence we need only look at m>s.

First theorem: we got a simple function FC such that

f(m,s)  ≤ FC(m,s)

for MANY m,s we got f(m,s) = FC(m,s).

GREAT! - conjecture f(m,s) = FC(m,s)

We found some exceptions, and a way to get better upper bounds called INT.

GREAT! - conjecture f(m,s) = MIN(FC(m,s),INT(m,s))

We found some exceptions, and a way to get better upper bounds called ... We now have

conjecture

f(m,s) = MIN(FC(m,s), INT(m,s), ERIK(m,s), JACOB(m,s), ERIKPLUS(m,s), BILL(m,s))

and it looks like we still have a few exceptions.

This is how science and math works- you make conjectures which are false but the refutations lead
to better and better results.

Also, we have over time mechanized the theorems, a project called:

Making Erik Obsolete

since Erik is very clever at these problems, but we would like to not have to rely on that.

4) I have worked hard on this problem as is clear from this: picture




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