It does seem like [n,n+1] is always unsolvable!

[9,8] -> [6,3,8] -> [6,2,1,8] -> [6,2,9] -> [8,9]

Indeed,

   [n, n-1] 
   [n-3, 3, n-1]
   [n-3, 2, 1, n-1]
   [n-3, 2, n]
   [n-1, n]

Works for all n greater than... 6?

Optimizing self-response! That fails for six because n-3 and 3 co-occur. With a slight modification we can make it work for all n>5

  [n, n-1]
  [2, n-2, n-1]
  [2, n-3, 1, n-1]
  [2, n-3, n]
  [n-1, n]

edit: and it's not hard to show that n<6 are impossible, so the solution above is optimal in that sense.

Yeah, the [n,n+1] is only a problem when there isn't enough wiggle room between the numbers. ex: [2,3] and [3,4]

[3,4]

--> [1,2,4] --> 4 can't split because 2/2 and 3/1 are invalid

--> 4 can't initially split because 2/2 and 3/1 are both invalid

[5,6] --> [5,4,2] --> [5,1,3,2] --> [6,3,2] --> [6,5]

[7,8] --> [7,3,5] --> [7,1,2,5] --> [8,2,5] --> [8,7]

When you add more numbers, you need more wiggle room. So, [4,5,6] is problematic and probably [5,6,7].

[4,5,6]

--> [3,1,5,6] --> 6 can't break into 3, nor 5/1. It can do 4/2, but then 5 can't split. 5 also can't split.

--> [4,2,3,6] --> [4,2,3,1,5] --> [6,4,5] --> 4 can't split into 2/2. It can split to 3/1 but then 5 can't split

--> 6 can't initially split at all because 3/3, 4/2, and 5/1 are invalid

Even if [6,7,8] has a solution, I'm sure [6,7,8,9] does not.

A solution for [6,7,8,9]:

6,7,8,9

6,3,4,8,9

6,3,4,8,2,7

9,4,8,2,7

9,4,8,2,1,6

9,4,3,5,2,1,6

9,7,5,2,1,6

9,7,5,3,6

9,7,8,6

9,5,2,8,6

9,5,2,1,7,6

9,5,3,7,6

9,8,7,6

Wow, well done! I found [6,7,8] as well:

6,7,8

6,7,5,3

6,7,1,4,3

6,8,4,3

6,8,7

6,3,5,7

6,2,1,5,7

8,1,5,7

8,6,7

8,4,2,1,6

8,4,3,6

8,7,6

Link to full pdf of the Report issued by Stanford's "special committee:" https://boardoftrustees.stanford.edu/wp-content/uploads/site...

Some extracts:

"There were repeated instances of manipulation of research data and/or subpar scientific practices from different people and in labs run by Dr. Tessier-Lavigne at different institutions"

"At various times when concerns with Dr. Tessier-Lavigne’s papers emerged—in 2001, the early 2010s, 2015-16, and March 2021—Dr.Tessier-Lavigne failed to decisively and forthrightly correct mistakes in the scientific record."

"However, a second theme emerged among some of the interviewees that the same lab culture also tended to reward the “winners” (that is, postdocs who could generate favorable results) and marginalize or diminish the “losers” (that is, postdocs who were unable or struggled to generate such data)"

Considering that Stanford's special committee has every reason to protect Tessier-Lavigne and damage control, the findings are quite damning.

Good on Theo Baker for continuing to provide a more critical perspective compared to the cushy political speak of the report.

Interesting that Stanford found the 2009 paper "lacked vigor" and Genentech found no-one "reported observing or knowing of any fraud, fabrication, or other intentional wrongdoing in the research leading to and reported in the 2009 Nature paper." [0]

So basically the euphemism "lacked vigor" = "wasn't scientific" but since it wasn't "intentional" or "known" no-one can be blamed for it? Am I the only one who doesn't really care if bad science is intentional or fraudulent? They should be judged on their science, which was objectively dogshit, not on their morality, which is subjectively dogshit, but conveniently can't be judged by the relevant parties because everyone involved got amnesia.

Maybe I'm being too harsh but shadiness in public health really irritates me.

[0] https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&c...

>For the five reviewed papers where Dr. Tessier-Lavigne was a principal author (sometimes referred to as the “primary papers”), the Scientific Panel has concluded that Dr. Tessier-Lavigne did not have actual knowledge of the manipulation of research data that occurred in his lab and was not reckless in failing to identify such manipulation prior to publication.

I've read some of the papers that contain duplicated data; such duplications can be seen as "honest errors" similar to typos (e.g. maybe the file names were too similar?). It would be negligent of MTL to overlook these, even if it would not be fraud.

This is so fun! Thank you for sharing it.

@pwnallthethings on Twitter makes exactly this point and I find it quite convincing. Link below. If (and this seems increasingly likely) this war drags on, we should try to attract and welcome as many Russian mathematicians, scientists, and engineers as we can before Putin forbids them from travelling.

This is why I find the recent cancellation of many public Russian individuals concerning. We should be offering them citizenship (I exaggerate!), not shaming and dropping them. Rossophobia against normal Russian citizens is counterproductive.

Thread: https://twitter.com/pwnallthethings/status/14979877099686051...

The choice is not dark magenta or bright yellow or bust though. A large spectrum of colors exist, and if we really wanted to not offend anyone, we could have chosen blue or green or pink or orange or any other color that couldn't possibly be a skin color (untill we meet easily-offended aliens of course).

Me too! I haven't even heard of Basecamp before, but now it has made it's way onto my whitelist of "sane companies worth working for." I really hope they survive this debacle and keep making good products.

This sounds hilarious. What are jug handles, and what are lefts?

To be a little pedantic, I'm not sure "under exaggerate" is a valid phrase. What you're looking for may be "under-report"?