This post is a written record of mt thoughts after reading “WTF? The University of California sides with publishers against the public” by Michael Eisen.

I suspected and privately said to reluctant ears that there is something profoundly dishonest, in principle, in the system of fabricating research papers for the love of the number of them, BUT (and the emphasis is here) it works because many researchers love it. Well, maybe not many and maybe not especially the young ones, but many of the researchers with established reputation constructed in the interior of this system.

Is this a naive thought? Surely is for the two categories of people in the academia who sustain it: a big, maybe a majority, maybe not, class of mediocre researchers, formed by those who find a sure and opportunistic path to promotion, tenure, etc, by producing a kind of structured noise which looks like research and, a second class, of managers of the academic realm, having direct interest into the system, mainly, I suspect, because it provides access to power over other people lives. (The second class may be  populated by former members of the first, this follows logically from the fact that if the promotion system is based on massive mediocre crap production then the best among the producers tend to be selected by the system.)

My preferred comparison of the fall in the making of the actual academic system is described in “Another parable of academic publishing: the fall of 19th century academic art“. Continuing the comparison, it is true that the production of independent artists surely contained (and still contains now-a-days) a lot of garbage, but it is also true that the academic production of paintings was massively mediocre.  What to choose — diversity, from very bad to very good to out of the scale exploratory art — or — uniform mediocrity, with rare dashes of solid, good, surprising or even exceptional academic paintings?  In the past, diversity won.

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1. This post is not directed  against UC.  At least UC made a statement which is criticised in the post by Michael Eisen. On the contrary, the vast majority of smaller, or less visible  academic institutions don’t even make clear their respective positions on this matter. In the background business goes as usual.
2. See also the very well written previous post by Eisen, “The Past, Present and Future of Scholarly Publishing “. Just a small quote from the post:

Tonight, I will describe how we got to this ridiculous place. How twenty years of avarice from publishers, conservatism from researchers, fecklessness from universities and funders, and a basic lack of common sense from everyone has made the research community and public miss the manifest opportunities created by the Internet to transform how scholars communicate their ideas and discoveries.

# Carry propagation-free number systems and a kind of approximate groups (I)

Avizienis introduced a signed-digit number representation which allows fast, carry propagation-free addition (A. Avizienis, Signed-digit number representation for fast parallel arithmetic, IRE Trans. Comput., vol. EC-10, pp. 389-400, 1961, see also B. Parhami, Carry-Free Addition of Recoded Binary Signed-Digit Numbers, IEEE Trans. Computers, Vol. 37, No. 11, pp. 1470-1476, November 1988.)

Here, just for fun, I shall use a kind of approximate groups to define a carry-free addition-like operation.

1. The hypothesis is: you have three finite sets $A$, $B$, $K$, all sitting in a group $G$. I shall suppose that the group $G$ is commutative, although it seems that’s not really needed further if one takes a bit of care. In order to reflect this, I shall use  $+$ for the group operation on $G$, but I shall write $M N$  for the set of all elements of the form  $x + y$ with $x \in M$ and $y \in N$.

We know the following about the three (non-empty, of course) sets $A, B, K$:

1. $B \subset A$,
2. $0 \in B$, $0 \in K$, $A = -A$, $B = -B$, $K = -K$,
3. $\mid B \mid = \mid K \mid$   (where $\mid M \mid$ is the cardinal of the finite set $M$),
4. $A A B \subset A K$  (that’s what qualifies $A$ as a kind of an approximate group).

Let now choose a bijective function $\phi: K \rightarrow B$ and two functions $\psi: AAB \rightarrow A$ and $\chi: AAB \rightarrow K$ such that

(1)   for any $x, y \in A$ and any $b \in B$ we have $x+y+b = \psi(x+y+b) + \chi(x+y+b)$.

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2. Let $X$ be the family of functions defined on $\mathbb{Z}$ with values in $A$, with compact support, i.e. if $x: \mathbb{Z} \rightarrow A$ belongs to $X$, then only a finite number of $k \in \mathbb{Z}$ have the property that $x_{k} = x(k) \not = 0$.  The element $0 \in X$ is defined by $x_{k} = 0$ for any $k \in \mathbb{Z}$.  If $x \in X$ with $x \not = 0$ then $ind(x) \in \mathbb{Z}$ is the smallest index $k \in \mathbb{Z}$ with $x_{k} \not = 0$.

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3.  The structure introduced at 1. allows the definition of an operation $*$ on $X$. The definition of the operation is inspired from a carry-free addition algorithm.

Definition 1. If both $x, y \in X$ are equal to $0$ then $x*y = 0$. Otherwise, let $j \in \mathbb{Z}$ be the smallest index $k$ such that one of $x_{k}$ or $y_{k}$ is different than $0$.  The element $z = x*y$ is defined by the following algorithm:

1. $z_{k} = 0$ for any $k < j$,
2. let $t_{j} = 0$$k = j$. Repeat:

$p_{k} = x_{k} + y_{k} + t_{k}$

$z_{k} = \psi(p_{k})$

$t_{k+1} = \phi(\chi(p_{k}))$

$k \rightarrow k+1$

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4.  We may choose the functions $\phi, \psi, \chi$ such that the operation $*$ is starting to become interesting. Before doing this, let’s remark that:

• the operation $*$ is commutative as a consequence of the fact that $+$ is commutative,
• the operation $*$ is conical, i.e. it admits the shift $\delta: X \rightarrow X$, $\delta(x)(k+1) = x_{k}$ as automorphism ( a property encountered before for dilation structures on ultrametric spaces, see  arXiv:0709.2224  )

Proposition 1.  If the functions $\phi, \chi, \psi$ satisfy the following:

1. $\phi(0) = \chi(0) = \psi(0) = 0$
2. $\chi(x) = 0$ for any $x \in A$
3. $\psi(-x) = - \psi(x)$$\phi(-x) = -\phi(x)$ for any $x \in A A B$, $\chi(-x) = -\chi(x)$ for any $x \in K$,

then $(X, *)$ is a conical quasigroup.

# Big sets of oriented Reidemeister moves which don’t generate all moves

The article  “Minimal generating sets of Reidemeister moves“ by Michael Polyak gives some minimal generating sets of all oriented Reidemeister moves. The question I am asking in this post is this: how big can be non-generating sets of moves?

The oriented Reidemeister moves are the following (I shall use the same names as Polyak, but with the letter $\Omega$  replaced by the letter $R$):

• four oriented Reidemeister moves of type 1:

• four oriented Reidemeister moves of type 2:

• eight oriented Reidemeister moves of type 3:

Among these moves, some are more powerful than others, as witnessed by the following

Theorem. The set of twelve Reidemeister moves formed by:

• four moves of type 1
• two moves of type 2, namely R2a and R2b
• six moves of type 3, namely R3b, R3c, R3d, R3e, R3f, R3g

does not generate the remaining moves R2c, R2d, R3a and R3h.

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I postpone the proof for another time, here I just want to emphasize that the moves R2c, R2d, R3a and R3h are more special than the rest of them. The proof which I have is via the graphic lambda calculus, but probably other proofs exists. Please tell me if you know a proof of this theorem.

UPDATE: see a proof at mathoverflow.

# Writing research articles vs writing blog posts

Is there any difference between writing a research article and writing a blog post on a research subject? This is what I would like to understand.

In my mind research articles should become a subset of … how should I call them, maybe “research posts”.  There are obvious advantages on the side of the research posts, as well as some disadvantages. I think it is revealing that the advantages have an objective flavour, while the disadvantages have more of a subjective one, mostly being related to the bad image the blog posts have among the “serious” researchers.

I have already experimented with this idea:

• the Tutorial on graphic lambda calculus has served as the template for  arXiv:1302.0778   On graphic lambda calculus and the dual of the graphic beta move,
• the post Geometric Ruzsa triangle inequalities and metric spaces with dilations became  arXiv:1304.3358  Geometric Ruzsa triangle inequality in metric spaces with dilations, with very few modifications,
• I just submitted on arXiv  the article arXiv:1304.3694 Origin of emergent algebras, based on the posts The origin of emergent algebras, part II and part III, as well as parts of Emergent algebra as combinatory logic (part I),
• now I am struggling with writing a shorter (and somehow dumber) version of arXiv:1207.0332  Local and global moves on locally planar trivalent graphs, lambda calculus and $\lambda$-Scale, because I was too hurried and spoiled by the freedom this blog gives me to do research, so in the first version of the article I just write too much, without enough motivation. Therefore I decided (based on a peer-review which I appreciated) to concentrate first only on what the graphic lambda calculus can do with the gates corresponding to the application, the abstraction and the fan-out:  the lambda calculus part of the graphic lambda calculus, along with the braids formalism part. The emergent algebra part is for later.

The format of the articles  from this list is as much as possible similar with the one of the research posts.  As an example I mention  the use of links inside  the text, including direct links to the (preferably OA) versions of the cited articles. See the post Idiot things that we we do in our papers out of sheer habit by Mike Taylor for more examples of the same “habits” which I already renounced in some of my papers.

The new  habit of giving exactly the link to the article, instead of a numbered citation in the bibliography, as well as giving the link to ANY  source which is used in the research article (as for example a wikipedia page for a first time encounter of a term, along with the invitation for further study from another sources), is clearly one of the advantages a blog post has over a traditionally written article.

However, it is difficult to find the good balance between the extreme freedom of a blog post and the more constraint one of a research article (although the blog of Terence Tao is a very good example – maybe the best I know about – that such a balance may be attainable).

My guess is that at some point open peer-review  and this change of habits concerning writing research articles will meet.________________

UPDATE: See the post Blogging as post-publication peer review: reasonable or unfair?  by Dorothy Bishop, as well as the comment by Phillip Lord which I reproduce here:

Why stop there? If Author self-publishing can provide rapid feedback on “properly” published science, then they can also provide dissemination of that science in the first place.
Scientific publishing has too long been about credit and promotion. It’s time it returned to what it really should be and what it originally was: communication.

# Packing arrows (II) and the strand networks sector

I continue from   Packing and unpacking arrows in graphic lambda calculus  and I want now to describe another sector of the graphic lambda calculus, called the strand networks sector.

Strand networks are a close relative to spin networks (in fact they may be used as primitives, together with some algebraic tricks in order to define spin networks). See the beautiful article  by Roger Penrose, Angular momentum: an approach to combinatorial space-time, in Quantum Theory and Beyond, ed. T. Bastin, Cambridge University Press, Cambridge, 1971.   where strand networks appear in and around figure 17.

However the strand networks which I shall write about here are oriented. Moreover, a more apt name for those would be “states of strand networks”.  The main thing to retain is that the algebraic glue can be put over them (for example, as concerns free algebras generated by those, counting states, grouping them into equivalence classes which are the real strand networks and so on).

In graphic lambda calculus we may consider graphs in $GRAPH$ which are obtained by the following procedure. We start with a  finite collection of loops and we clip together, as we please, strands from these loops. How can we do this? Is simple, we choose our strands we want to clip together and the we cross them with an arrow. Here is an example for three strands:

We want to make this clipping permanent, so to say, therefore we apply as many graphic beta moves as are needed, three in this example:

The beautiful thing about this procedure is that in the middle of the graph from the right hand side we have now three arrows with the same orientation. So, let’s pack them into one arrow.  The packing procedure for three arrows, with the same orientation, is the following:

So, we pack the arrows, we connect them and we unpack afterwards.

With the previous trick, we may define now decorated arrows of strand networks, but mind that we have bundles, packs of oriented strands, so the decoration has to be more precise than just indicating the number of strands.

That is about all, only we have to be careful to discern among clipped strands which become decorated arrows and clipped strands which become nodes of the strand network. But this is rather obvious, if you think about.

Conclusion. Let’s think about the purpose of the algebraic glue which is needed in order to define a spin network and then an evolving spin network. As you can see all comes down to another way of deciding which is the sequence of applications of (graphic) beta moves, which is this time probabilistic. It is another type of computation than the one from the lambda calculus sector, where we use the combinators and zippers (as well as some strategy of evaluation) in order to make a classical computation. So at the level of graphic lambda calculus, it becomes transparent that both are computations, but with slightly different strategies. (This is a kind of a theorem, but to put it in a precise form one has to make ornate notations and unnecessary orderings, so it would be just a manifestation of  the cartesian disease, which we don’t need.) The last point to mention is that, compared to the lambda calculus strategy (based on combinators plus choice of evaluation), this computation which comes from physics, is more cartesian disease free.

# New discussion on UD (updated)

This post is for a new discussion on UD, because the older ones “Discussion about how an UD algorithm might work” and “Unlimited detail challenge: the most easy formulation” have lots of comments.

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UPDATE: It looks like Oliver Kreylos    (go and read his blog as well)   extremely interesting work on LiDAR Visualization is very close to Bruce Dell’s  Geoverse. Thanks to Dave H. (see comments further) for letting me know about this.  It is more and more puzzling why UD  was welcomed by so much rejection and so many hate messages when, it turns out, slowly but surely, that’s one of the future hot topics.

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Please post here any new comment and I shall update this post with relevant information. We are close to a solution (maybe different than the original), thanks to several contributors, this project begins to look like a real collaborative one.

Note: please don’t get worried if your comment does not appear immediately, this might be due to the fact that it contains links (which is good!) or other quirks of the wordpress filtering of comments, which makes that sometimes I have to approve comments by people who already have previous approved comments. (Also, mind that the first comment you make have to be approved, the following ones are free of approval, unless the previous remarks apply.)

Let’s talk!