# The best article since a long time: “We have met the enemy and it is us” by Mark Johnston

The article is here. It is so good, in my opinion, that I can’t just give a quote from it.

Indeed, fact is: with all due respect for the publishers, librarians, even for the ISI bean-counters, science is primarily made by researchers, who are the most competent for taking decisions for their good. Only that we have forgot this and instead we rely on others, less competent, for reasons we are also to blame for.

This is good to recognize, not for us to feel guilty about, but  to take steps for taking back our power of decision.

Science is not a commercial activity, it does not feel good on the long term by being managed for attaining short-sighted goals. We are not the milk-providing cow of others, who take our raw product and packages it in fancy looking  clothes, for the sake of selling it.

On the other side, we have to find the courage of taking decisions for ourselves.  To  rely on “objective measures”, which are nothing else than means to avoid accountability, is to be afraid to take decisions.

This kind of change has to happen starting from the researchers involved in management of research. Because, in fact, the enemy is not quite “us”, but if this kind of change, which is for the benefit of science, is opposed by their inertia, then it is starting to look as being “them”.

______________

Related:

and even

# Bizarre wiki page on ISI (and comments about DORA and The Cost of Knowledge)

More and more people are supporting the  San Francisco Declaration on Research Assessment (DORA) .  Timothy Gowers, the initiator of The Cost of Knowledge movement, asks “Elsevier journals: has anything changed?” and writes

Greg Martin, a number theorist at UBC (the University of British Columbia in Vancouver) doesn’t think so, so he has decided to resign from the editorial board of Elsevier’s Journal of Number Theory.

Igor Pak rationalizes the apparent small effects in the real world of  the open access movement and asks   rhetorical questions:

Should all existing editorial boards revolt and all journals be electronic?  Or perhaps should we move to “pay-for-publishing” model?  Or even “crowd source refereeing”?  Well, now that the issue a bit cooled down, I think I figured out exactly what should happen to math journals.  Be patient – a long explanation is coming below.

DORA, in my opinion, can be considered a positive outcome of this movement (and of course, the Cost of Knowledge is only a drop in the sea of initiatives towards updating the research communication system from the medieval age to the present one). Let’s not be more pessimistic  than we should.

Or, maybe, should we?

Is the stumbling block  the publisher, or is it in the academic realm? Where is the weak link of this Research Banana Republic? Could it be in the entrenched opinions of a majority of researchers, based on a self-referential definition of academic impact which is built around “objective” measures?

I took a look at the wikipedia page on Thompson  ISI, to see what an open, non-partisan source is writing about it.

Here is an excerpt from this source:

This database allows a researcher to identify which articles have been cited most frequently, and who has cited them. The database not only provides an objective measure of the academic impact of the papers indexed in it, but also increases their impact by making them more visible and providing them with a quality label. There is some evidence suggesting that appearing in this database can double the number of citations received by a given paper.

An “objective measure of the academic impact”?  What is the evidence which backs this PR on wikipedia? The ISI was founded in the 1960 and “there is some evidence suggesting that appearing in this database can double the number of citations received by a given paper” in ONE article from 2013?

I clicked then on the Thomson Scientific & Healthcare  link and suggest you to do the same. Wikipedia has the following comments on the top of that page:

 This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (February 2008)

This article reads like a news release, or is otherwise written in an overly promotional tone. (January 2008)

# Call for analysis of the new UD video

Thanks to preda  and to appc23 for showing us the new UD video:

The previous post on this subject,  New discussion on UD (updated) , has lots of interesting comments. It has become difficult to make sense of the various proposals concerning the UD algorithm, therefore I made this new post which shall serve first as a place for new discussions, then it will be updated.

It is maybe the time to make sense a bit of the material existent (or linked to) on this blog. That is why I invite everybody who is willing to do this to make it’s own proposal, preferably with (either) programs or proofs or evidence (links). Especially, in a random order, this invitation is addressed to:

• Dave H
• preda
• 17genr
• JX
• appc23
• bcmpinc
• Shea
• Tony

but anybody which has something coherent to communicate is welcome to make a proposal which will blow our minds.

Make your respective proposals as detailed as you wish, take your time to make them convincing and then, if you agree, of course, we shall make feature posts here with each of them, in order to become easier to follow the different threads.

Let me finish, for the moment, by stating which points are the most important in my opinion, until now (I stress, in my opinion, feel free to contradict me):

• UD works like a sorting algorithm,
• cubemaps are used, but their main utility is to eliminate rotations wrt the POV from the problem,
• UD is not a rendering algorithm (or, at least, the most interesting part of UD is not one), it is an algorithm for fast searching the data needed to put a colour on each pixel,
• UD needs  to turn a cloud of points into a database, only once, operation which takes considerable more time than the searching algorithm part,
• does not need antialiasing
• does not raycasting for each pixel
• it is a mathematical breakthrough, though not a CS  or math technical one (i.e. does not need the latest edge CS or math research in order to make sense  of it, but it’s a beautiful idea).

Almost finished, but I have to explain a bit my attitude about UD.  I am thorn between my curiosity about this, explained in other posts (for example by it’s partial overlap with the goals of Digital Materialization), and the fact that I don’t want this blog to be absorbed into this subject only. I have my ideas concerning a possible UD algorithm, especially from a math viewpoint, but unless I produce a program, I can’t know if I’m right or wrong (and I am not willing to try yet, because I am sympathetic with the underdog Dell and also because it would take me at least several months to get off the rust from my programming brain and I am not yet willing to spent real research time on this). Suppose I’m wrong, therefore, and let’s try to find it in a collaborative, open way. If we succeed then I would be very happy, in particular because it would get out of my mind.

# New article on graphic lambda calculus

Up to date, this is the most comprehensive introduction to graphic lambda calculus. Is available as arxiv:1305.5786. It does not contain all the material on the subject, but it is, I hope, a fair exposition of what you can do with it. See also the tutorial page on graphic lambda calculus on this blog.

Two points:

• it shows that it can be used for much more than just visually representing lambda calculus for pedagogical reasons, you can turn it into a programming language which mixes differential calculus, manipulation of spatial quantities, with lambda calculus,
• it is the visual language appropriated for giving a rigorous formulation of the constructions done in Computing with space.

If you have comments or corrections to make, or peer-reviews, let me know! For the moment I can’t stand to look at it, I have to detach a bit, but it would surely benefit from a fresh eye.

________

UPDATE: The article has been accepted for publication in Wolfram’s  Complex Systems. This is  good news for the emergent algebras – computing with space subject. (Btw, thumbs up for the reviewing process, which made me update the previous version  arXiv:1207.0332  to a much more comprehensive presentation, which also benefited from several postings on this blog and from one question on mathoverflow.)

# What is an author buying from a Gold OA publisher?

1. Is the author a customer of a Gold OA publisher?

I think it is.

2. What is the author paying for, as a customer?

I think the author pays for the peer-review service.

3. What offers the Gold OA publisher  for the money?

I think it offers only the peer-review service, because
– dissemination can be done by the author by submitting to arxiv, for example,
– +Mike Taylor  says that the Gold OA publisher offer the service of assembling an editorial board, but who wants to buy an editorial board? No, the authors pays for the peer-review process, which is managed by the editorial board, true, which is assembled by the publisher. So the end-product is the peer-review and the author pays for that.
– almost 100% automated services, like formatting, citation-web services, hosting the article are very low value services today.

However, it might be argued that the Gold OA publisher offers also the service of satisfying the author’s vanity, as the legacy publishers do.

4. Why no Gold OA publisher present itself as a seller of the peer-review service?

Have no idea.

5. Why is the peer-review service valuable?

Because:
– it spares time for the reader, who will select more likely a peer-reviewed  paper to read,
– it is a filter for the technical quality of the articles,
– it helps authors to write better articles, as an effect of the referees comments,
– it is also a tool for influencing the opinions of the community, by spinning up some research subjects and downplaying others.

Also on G+ here.

# Democratic changes in OA can be only reactive. We need daring private initiatives

Democratic changes in OA can be only reactive. That means one step back with respect to active opposition to change, methodically pursued by interests of a small but powerful minority of big players in the publishing game (i.e. publishers themselves and their academic management friends, sometimes overlapping). And even more, one might say that democratic changes are even two steps back with respect to strategic decisions taken by the said big players. It’s only speculation, but for example the admirable DORA could throw us in the future into the arms of the newly acquired Mendeley.

By democratic changes I mean those which are agreed by a significant part of the research community.

So, what else? Privately supported changes. By this I mean support of any potentially viral solution for getting us out from this tarpit war. It’s clear that Gold OA is the immediate future change agreed by the big players, although it’s just as useless  as the actual research communication system based on traditional publication. Why waste another 10 years on this bad idea, only to repeat afterwards that it is already technically possible to disseminate knowledge without making the authors (or public funding agencies which support those) pay for nothing?

The advantage of a new dissemination system is already acknowledged, namely it is far more convenient, economically speaking, to profit from the outcomes of low Coase cost research collaborations, than to keep paying a hand of people who offer an obsolete service and don’t want to adapt to the new world of the net.

This point of view is stressed already in my Seven years forecast (i.e. until 2020), part 5:

In seven years all  successful changes of the process of dissemination of knowledge will turn out to be among those born from private initiatives,

Wish I have a crystal ball,  though I only have some hope.

UPDATE: Oh, yeah, maybe the uber-library idea is not the right thing. Yes, everybody wishes for a world library at a click distance, but that’s not all. That’s like “what can we do with cars? Well, let’s make them like coaches, only without the horse. The rich guys will love them.” And boum! the car concept became a success from the moment they were mass-produced.

UPDATE 2: Maybe relevant for the idea from  the first update, Cameron Neylon’s post “The bravery of librarians” ends with the question:

What can we do to create a world where we need to rely less on the bravery of librarians and therefore benefit so much more from it?

______________

# Freedom sector of graphic lambda calculus

Yes, graphic lambda calculus has a freedom sector. Which means in that sector you can do anything you like (modulo some garbage, though). It’s yet not clear to me if this means a kind of universality property of graphic lambda calculus.

The starting point is the procedure of packing arrows explained in this post.  This procedure can be seen in the following way:

Here, the left and right void circles with the respective arrows represent: the one from the left is a generic out arrow which exits from a gate and the one from the right is a generic in arrow which enters in a gate.

This gives the following idea: replace the inputs and the outputs of the gates from graphic lambda calculus by the following graphs (the green wiggly arrow means “replace”):

For example, look how it’s done for the $\curlywedge$ graph. Technically we define new macros, one for each elementary gate. Let’s call these macros “the free gates”.

These free gates define the free sector of the graphic lambda calculus, which consists all graphs made by free gates, along with the move of cutting or gluing arrows.

The free sector has inside a copy of the whole graphic lambda calculus, with the condition of adding a local move of elimination of garbage, which is the local move of elimination (goes only one way, not both) of any graph which is not made by free gates with at most, say, 100 arrows + gates. This move is needed, for example, for the case of emulating the graphic beta move with free gates, where we are left with some garbage consisting of one $\lambda$ gate and one $\curlywedge$ gate, seen as disconnected graphs.

# The good, the bad and the iawful: OA, measures of scientific output and bad legislation

What happens in the real world, the one of the  powers that be, as concerns open access, peer-review and communication of research results? Let’s see.

Funding agencies, institutions that employ scientists, and scientists themselves, all have a desire, and need, to assess the quality and impact of scientific outputs. It is thus imperative that scientific output is measured accurately and evaluated wisely. […]

A number of themes run through these recommendations:

• the need to eliminate the use of journal-based metrics, such as Journal Impact Factors, in funding, appointment, and promotion considerations;
• the need to assess research on its own merits rather than on the basis of the journal in which the research is published; and
• the need to capitalize on the opportunities provided by online publication (such as relaxing unnecessary limits on the number of words, figures, and references in articles, and exploring new indicators of significance and impact).

Read it. Disseminate it. Sign it.

________________

The bad:  The apparatus of research assessment is driven by the academic publishing industry and has become entirely self-serving. In this article by  Peter Coles you find:

The involvement of  a company like Elsevier in this system just demonstrates the extent to which the machinery of research assessment is driven by the academic publishing industry. The REF is now pretty much the only reason why we have to use traditional journals. It would be better for research, better for public accountability and better economically if we all published our research free of charge in open archives. It wouldn’t be good for academic publishing houses, however, so they’re naturally very keen to keep things just the way they are. The saddest thing is that we’re all so cowed by the system that we see no alternative but to participate in this scam.

________________

The iawful:  From this g+ post by Peter Suber we find out that:

Elsevier, NewsCorp, Facebook, and Yahoo are some of the major players in NetChoice, an industry group “promoting convenience, choice, and commerce on the net.”

NetChoice has a watch list for bad legislation that it calls iAWFUL (Internet Advocates’ Watchlist for Ugly Laws). The latest version of iAWFUL includes the White House OA directive plus the state-level OA bills in California, Illinois, and North Dakota. (Yes, there was a bill in ND, and no, NetChoice doesn’t seem to know about the OA bill in NY.)
http://www.netchoice.org/2013-may-iawful/

Insofar as NetChoice has an argument for opposing these OA initiatives, it’s a crude bolus of false assertions and assumptions. I haven’t seen this kind of motivated distortion since the days of PRISM and the Research Works Act.
http://www.netchoice.org/2013-may-iawful/4-forcing-journals-to-make-their-works-publicly-available/

UPDATE (23.05.2013):Elsevier distances itself from open-access article

The publisher Elsevier has disassociated itself from an article by a trade association it belongs to that condemns proposed open-access mandates in several US states.

________________

So, things happen … eventually. But slowly. I bet many of us, not entangled with the high politics or management in academia, wish for a faster pace.  For my part, I would rather play the Game. It has a very low Coase cost, you know?

________________

UPDATE:  if you still wonder  about Gold OA, is it good? is it bad?, here is a tweet about Elsevier and iawful:

# Sets, lists and order of moves in graphic lambda calculus

Suppose that we want to group together three arrows in graphic lambda calculus. We have this:

We want to group them together such that later, by performing graphic beta moves, the first arrow available to be 11′, then 22′, then 33′. Moreover, we want to group the arrows such that we don’t have to make choices concerning the order of the graphic beta moves, i.e. such that there is only one way to unpack the arrows. The solution is to “pack” the arrows into a variant of a list. Lists have been defined here, in relation to currying.

Basically we take a zipper and we close it.  Further we see how to unpack this list.

The dashed red curve encircles the only place where we can use a graphic beta move. The first move frees the 11′ arrow and then there is only one place where we can do a graphic beta move, which frees the 22′ arrow and finally a last move frees the 33′ arrow and produces a loop which can be eliminated.

The uniqueness of the order of moves is true, in fact, if we accept as valid beta moves only those from left to right (i.e. those which eliminate gates). Otherwise we can go back and forth with a beta move as long as we want.

There is another way to pack the three arrows, under the form of another graph, which could aptly be called a “set”. This time we need a graph with the property that we can extract any arrow we want from it, by one graphic beta move. Here is the solution:

Indeed, in the next figure we see that we have three places, one for each arrow, which can be independently used for extraction of the arrow of choice.

In between these extremes, there are other possibilities.  In the next figure is a graph which packs the three arrows such that: there are three places where a graphic beta move can be performed, as in the case of the set graph, but once a beta move is performed, the symmetry is broken. The performed beta move does not free any arrow, but now we have the choice between the other two possible beta moves. Any such choice frees only one arrow, and the last possible beta move frees the remaining two arrows simultaneously.

Here is the figure:

The graph from the left hand side is not a list, nor a set, although it is as symmetric as a set graph.  There are $3 \cdot 2 = 6$ possible ways to unpack the graph. So this graph encodes all lists of two arrows out of the three arrows.

# We, researchers, just need a medium for social interaction, and some apps

… so that we can freely play the game of research. Because is a game, i.e. it is driven by curiosity, desire to learn, does not depend on goals and tasks, it is an extension of a child attitude, lost by the majority of adults. Let the vanity aside and just play and interact with other researchers, on equal foot. Let the creativity manifest freely.

Two    Three  Four examples:

Rap Genius is a very well-loved and well-used online tool for annotating rap songs.  Only, not so surprisingly, people are starting to use it to annotate other things.  Like scientific papers.

• Olivier Charbonneau writes

Actually, that’s an interesting take on mass data visualization – imagine creating an algorithm that could parse a dataset of bibliographic information into minecraft (for example) – what would that research “world” look like?

• Hermann Hesse’s   Das Glasperlenspiel (aka Magister Ludi)
• Timothy Gowers, some time ago, in this post, writes:

What I think could work is something like a cross between the arXiv, a social networking site, Amazon book reviews, and Mathoverflow.

_________

Context:

# Graphic lambda calculus used for quantum programming (Towards qubits III)

I want to make a bit more clear one of the goals of the research on graphic lambda calculus, which are reported on this blog.  I stress that this is one of the goals and that this is live research,  in the making, explained here in order to attract, or invite others to join, or use this exploration for their purposes.

More precisely, further I present several justifications for two series of posts

which have as common goal the application of graphic lambda calculus to some form of quantum programming (probably some version of a quantum lambda calculus). I use the informative linked wiki page on quantum programming  for citing. Please click on the links to go where the real information is.

Efforts are underway to develop functional programming languages for quantum computing. Examples include Selinger’s QPL,[1] and the Haskell-like language QML by Altenkirch and Grattage.[2][3] Higher-order quantum programming languages, based on lambda calculus, have been proposed by van Tonder,[4] Selinger and Valiron [5] and by Arrighi and Dowek.[6]

Simon Gay’s Quantum Programming Languages Survey has more information on the current state of research and a comprehensive bibliography of resources.

I hope that in some finite time I can prove that there is a “quantum lambda calculus” sector in graphic lambda calculus. Let me explain why.

Basically, leaving much detail aside, quantum computation needs a  mix of at least two ingredients:

• some algebraic structure, which contains objects like complex vector spaces, real projective spaces, unitary transformations, projections, etc,
• some logical structure overarching the algebraic one (purists may say that in principle a lambda calculus would do).

The algebraic structure is not needed entirely, i.e. the needed part is the web of relations between the various algebraic operations. For example, the vector space operations are needed and not the points of the vector space. Likewise, we need “linearity”, “unitarity” and not particular linear or unitary transformations. Enough is to know how linearity and unitarity interact with the algebraic operations.

In the same way, as concerns the logic part, we need (say, if we are interested in a quantum lambda calculus) an abstraction an an application operations (like in lambda calculus) which interact well with the algebraic structure. Right?

There is one more ingredient needed: some form of evaluation procedure. There we can see a difference between a quantum and a classical lambda calculus. A quantum lambda calculus is more geometrical, less commutative than a classical one. One has to take care of phases, of the order of evaluations more than in the classical one.

Graphic lambda calculus seems to be a welcoming host for all these demands. Indeed, let’s see.

Graphic lambda calculus encodes algebraic structures in the barest way, by using only one gate: the emergent algebra gate $\bar{\varepsilon}$, with the parameter $\varepsilon$ in a commutative group. This $\varepsilon$ models “scale”, it is usually taken in $(0, \infty)$ or in $\mathbb{Z}$. However, phase is a kind of scale, i.e. the formalism works well with the choice of the commutative group of scales to be $\mathbb{C}^{*}$.   Any algebraic operation and any algebraic computation in complex vector spaces, or in real projective spaces, may be expressed into graphic lambda calculus by the intermediary of the emergent algebra gate. Moreover, even some of the differential calculus (needed but not mentioned previously) can be embedded into graphic lambda calculus, in a kind of constructive way. This is the “emergent algebra” point of view, introduced in arXiv:0907.1520 .

So, shortly said, in graphic lambda calculus we have the algebraic structure needed. It “emerges” from the $\bar{\varepsilon}$ gate, when we take the scale parameter to be in $\mathbb{C}^{*}$. With the barycentric move BAR from Towards qubits part I   we get the algebraic structures of vector spaces (see  how to get projective spaces in   part II, work in progress). More interesting, without the barycentric move we get Carnot groups, i.e. non-commutative vector spaces.

Question 1. What we obtain if in the formalism of quantum mechanics we renounce at complex vector spaces and we replace with their non-commutative version, the Carnot groups?

(This is the motivation for the series of posts Gromov-Hausdorff distances and the Heisenberg group part 0, part I, part II, part III  in this blog.)

For the logic part, we know that graphic lambda calculus has a sector which corresponds to untyped lambda calculus. In quantum programming it would be interesting to find a quantum version of the lambda calculus which interacts well with the algebraic structure. But in graphic lambda calculus are allowed interactions between the lambda calculus gates,  (or logical gates) of abstraction and application, and the algebraic gates. We don’t need more, that is what I shall try to convince you eventually. Indeed, probably obscured behind the lambda scale calculus  (which is a first, non-graphical version of the graphic lambda calculus), this was already explored in section 4 “Relative scaled calculus” of arXiv:1205.0139, where we see that to any scale parameter $\varepsilon$ is associated a relative lambda calculus. This was done in whole generality, but for the needs of a quantum lambda calculus  “linearity moves” like in the  “Towards geometric Plunnecke graphs” series could be applied selectively, i.e. only with respect to  the $(0, \infty)$ part of $\mathbb{C}^{*}$, thus obtaining a relative lambda calculus which is phase-dependent.

Question 2.  What would a relative scaled lambda calculus look like in graphic lambda calculus?

Finally, for the evaluation procedures which are adapted to quantum world, in this respect, for the moment, I have only results which indicate how to get usual evaluation procedures in graphic lambda calculus by destroying it’s geometrical nature (that’s what I call the “cartesian disease“, if you care), which are explained in some detail in   Packing and unpacking arrows in graphic lambda calculus    and Packing arrows (II) and the strand networks sector.

Question 3.  Design evaluation procedures in graphic lambda calculus which are geometrical, in the sense that, at least when applied to the yet vague quantum lambda sector of the graphic lambda calculus, they give evaluation procedures which are useful for quantum programming.

So, that’s it, I hope it helps a bit the understanding. You are welcome to join, to contradict me or to contribute constructively!

I don’t get it, therefore I ask, with the hope of your input. It looks that the Gamifying peer-review post has found some attentive ears, but the Game on the knowledge frontier not. It is very puzzling for me, because:

• the game on the frontier seems feasible in the immediate future,
• it has two ingredients – visual input instead of bonus points and peer-review as a “conquest” strategy – which have not been tried before and I consider them potentially very powerful,
• the game on the frontier idea is more than a proposal for peer-review.

My question is: why is the game on the frontier idea less attractive?

Looking forward for your open comments. Suggestions for improvement of such ideas are also especially welcomed.

_______________

UPDATE:  Olivier Charbonneau writes:

Actually, that’s an interesting take on mass data visualization – imagine creating an algorithm that could parse a dataset of bibliographic information into minecraft (for example) – what would that research “world” look like?

# What group is this? (Parallel transport in spaces with dilations, II)

I continue from Parallel transport in spaces with dilations, I.   Recall that we have a set $X$ , which could be see as the complete directed graph $X^{2}$. By a construction using binary decorated trees, with leaves in $X$, we obtain first a set of finite trees $FinT(X)$, then we put an equivalence relation $\sim$ on this set, namely two finite trees $A$ and $B$ are close $A \sim B$ if $A \bullet B$ is a finite tree. The class of finite points $PoinT(X)$ is formed by the equivalence classes $[A]$ of finite trees $A$  with respect to the closeness relation $\sim$.

Notice that the equality relation is $\leftrightarrow$ , in this world.  This equality relation is generated by the “oriented Reidemeister moves”  R1a and R2a, which appear also as moves in graphic lambda calculus. (By the way, this construction can be made in graphic lambda calculus, which has the moves R1a and R2a. In this way we obtain a higher level of abstraction, because in the process we eliminate the set $X$. Graphic lambda calculus does not need variables. More about this at a future time.) If you are not comfortable with this equality relation than you can just factorize with it and replace it by equality.

It is clear that to any “point” $x \in X$ is associated a finite point $[x] \in PoinT(X)$. Immediate questions jump into the mind:

• (Q1)  Is the function $x \in X \mapsto [x] \in PoinT(X)$ injective? Otherwise said, can you prove that if $x \not = y$ then $x \bullet y$ is not a finite tree?
• (Q2)  What is the cardinality of $PoinT(X)$? Say, if $X$ is finite is then  $PoinT(X)$ infinite ?

Along with these questions, a third one is almost immediate. To any two finite trees $A$ and $B$ is associated the function $[AB] : [B] \rightarrow [A]$  defined by

$[AB](C) = A \circ (B \bullet C)$ .

The function is well defined: for any $C \in [B]$ we have $B \bullet C \in FinT(X)$, by definition. Therefore $[AB](C) \in [A]$, because $A \bullet \left( [AB](C) \right) \leftrightarrow B \bullet C$ .

Consider now the groupoid $ParaT(X)$ with the set of objects $PoinT(X)$ and the set of arrows generated by the arrows $[AB]$ from $[B]$ to $[A]$.  The third question is:

• (Q3)  What is the isotropy group of a finite point $[A]$   (in particular $[x]$ ) in this groupoid? Call this isotropy group $IsoT(X)$ and remark that because the groupoid $ParaT(X)$ is connected, it follows that the isotropy groupoid does not depend on the object (finite point), in particular is the same at any point $x \in X$ (seen of course as $[x] \in PoinT(X)$ ).

In a future post I shall explain the answers to these questions, which I think they are the following:

• Q1:  yes.
• Q2: infinite.
• Q3: a kind of free nilpotent group.

But feel free to contradict me, or to propose solutions. Of course, I shall cite any valuable contribution, even if it appears in a blog  (via +Graham Steel).

# MMORPGames at the knowledge frontier

I think we can use the social nature of the web in order to physically construct the knowledge boundary. (In 21st century “physical”  means into the web.)

Most interesting things happen at the boundary. Life on earth is concentrated at it’s surface, a thin boundary between the planet and the void. Most people live near a body of water. Researchers are citizens of the boundary between what is known and the unknown.  Contrary to the image of knowledge as the interior of a sphere, with an ever increasing interface (boundary) where active research is located, no, knowledge, old or new, is always on the boundary, evolving like life is, into deeply interconnected, fractal like niches.

All this for saying that we need an interesting boundary where we, researchers, can live, not impeded by physical or commercial constraints.  We need to build the knowledge boundary into the web, at least as much the real Earth was rebuilt into the google earth.

Game seems to be a way. Because game is both social and an instrument of exploration. We all love games, especially researchers. Despite the folklore describing nerds as socially inept, we were the first adopters of  Role Playing Games, later evolved into virtual worlds of the Massively Multiplayer Online Role Playing Games.  Why not make the knowledge frontier into  one of these virtual worlds?

It looks doable, we almost have all we need. Keywords of research areas could be the countries, places. The physics of this world is ruled by forces with articles citation lists as force-carrying bosons.  Once the physics is done, we could populate this world and play a game of conquest and exploration. A massively multiplayer online game.  Peer-reviews of articles decide which units of places are wild and which ones are tamed. Claim your land (by peer-reviewing articles), it’s up for grabs.  Organize yourselves by interacting with others, delegating peer-reviews for better management of your kingdoms, collaborating for the exploration of new lands.

Instead of getting bonus points, as mathoverflow works, grab some piece of virtual land that you can see! Cultivate it, by linking your articles to it or by peer-reviewing other articles. See the boundaries of your small or big kingdom. Maybe you would like to trespass them, to go into a near place? You are welcome as a trader. You can establish trade with other near kingdoms by throwing bridges between the land, i.e. by writing interdisciplinary articles, with keywords of both lands. Others will follow (or not) and they will populate the new boundary land you created.

After some time, you may be living in complex, multiply-connected kingdom cities, because you are doing peer-reviewed research in an established, rich in knowledge field. On the fringes of such rich kingdoms a strange variety of creatures live. Some are crackpots, living in the wild territory, which grows wilder with the passage of time.  Others are explorers, living between your respectable realm and wild, but evolving into tamer territory.   From time to time some explorer (or some crackpot, sometimes is not easy to tell one from another) makes a break and suddenly a bright avenue connects two far kingdoms. By the tectonic plate movement of this world, ruled by citations, these kingdoms are now one near the other.  Claim new land! Trade new bridges! During this process some previously rich, lively, kingdoms might become derelict. Few people pass by, but there’s nothing lost: like happened in Rome, the marble of ancient temples was used later for building cathedrals.

If you are not a professional researcher, nevermind,  you may  visit this world and contribute. Or understand more, by seeing how complex, how alive research is, how everything is interwoven. Because an image speaks a thousand words, you can really walk around and make an idea of your own about the subject you are curious about.

Thinking more about peer-reviews, which are like property documents, as in real life some are good and some are disputable.  Some are like spells: “I feel that the article is not compelling enough …”. Some are frivolous nonsense: “I find it off-putting when an author  does not use quotation marks as I am used to”. Some are rock-solid: “there’s a gap in the proof” or “I have not been able to find the error in the proof, but here is a counter-example to the author’s theorem 1.2”.

So, how can it be done? We (for example by a common effort at github) could start from what is available, like keywords and citations freely available or easy to harvest, from tools like google scholar profiles, mathscinet, you name it.  The physics has to be written, the project could be initially hosted for almost nothing, we could ask for sponsors. We could join efforts with established international organisms which intend to pursue somehow similar projects. The more difficult part will be the tuning of interactions, so that the game starts to have more and more adopters.

After that, as I said, the knowledge frontier will be up for grabs. Many will love it and some will hate it.

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Context: The richness of knowledge comes from this web of interactions between human minds, across time and space. This knowledge is not reserved to the statistically few people doing research. We grow with it, during school, we live within, no matter what we do as adults, we talk about and we are curious about it. Even more, immensely more after knowledge has been liberated by the web.

In a short lapse of time (at the scale of history) it has become obvious that research itself needs to be liberated from outdated habits. Imagine a researcher, before the web.  She was a dual creature: physically placed somewhere on the physical earth, living in some moment in time, but  mentally interconnected with other researchers all over the world, anytime in the history. However, the physical place of living impeded or helped the researcher to reach further in the knowledge world, depending on the availability of virtual connections: books, other physically near researchers, local traditions. We can’t even speculate about how many curious minds did not accessed the knowledge web, due to the physical place and moment in time where they lived, or due to society customs. How many women, for example?

But now we have the web, and we use it, as researchers. It is, in some sense, a physical structure which could support the virtual knowledge web. The www appeared in the research world, we are the first citizens of it.  The most surprising effect of the web was not to allow everybody to access the knowledge boundary. Instead, the most powerful effect was to enhance the access of everybody to everybody else. The web has become social. Much less the research world.

Due to old habits,  we loose the pace. We are still chained by physical demands. Being dual creatures, we have to support our physical living. For example, we are forced by outdated customs to accept the hiding behind paywalls of the results of our research.  The more younger we are, the more is the pressure to “sell” what we do, or to pervert the direction of our work in order to increase our chances of success in the physical world. In order to get access to physical means, like career advancements and grant money.

Old customs die hard. Some time ago a peasant’s child with a brilliant mind had to renounce learning because he needed to  help his family, his sister was seen as a burden, not even in principle considered for eventual higher education. Now young brilliant minds, bored or constrained by the local research overlord or local fashion, rather go doing something rewarding for their minds  outside academia, than slicing a tasteless salami into the atoms of publishable units, as their  masters (used to) advice them.

# Parallel transport in spaces with dilations, I

I intended to call this series of posts “What group is this?”, but I switched to this more precise, albeit more bland name. In this first post of the series I take again, in more generality, the construction explained in the post   Towards geometric Plünnecke graphs.

The construction starts in the same way, almost. After I give this first part of the construction, an interpretation in term sof groupoids is provided.  We consider only the moves  R1a and R2a, like in the post “A roadmap to computing with space“:

(The names “R1a”, “R2a” come from the names of oriented Reidemeister moves, see arXiv:0908.3127  by M. Polyak.)
Definition 1. The moves R1a, R2a  act on the set of binary trees  $T(X)$ with nodes decorated with two colours (black and white) and leaves decorated with elements of a set of “variable names”  $X$ which has at least two elements.  I shall denote by  $A, B, C$ … such trees and by  $x, y, z, u, v, w$ … elements of  $X$.

The edges of the trees are oriented upward. We admit  $X$ to be a subset of  $T(X)$, thinking about  $x \in X$ as an edge pointing upwards which is also a leaf decorated with $x$.

The moves are local, i.e. they can be used for any portion of a tree from  $T(X)$ which looks like one of the patterns from the moves, with the understanding that the rest of the respective tree is left unchanged.

We denote by $A \leftrightarrow B$ the fact that the $A$ can be transformed into $B$ by a finite sequence of moves.
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Definition 2. The class of finite trees   $FinT(X) \subset T(X)$ is the smallest subset of  $T(X)$ with the  properties:

•   $X \subset FinT(X)$,
• if $A, B \in FinT(X)$ then  $A \circ B \in FinT(X)$  , where $A \circ B$ is the tree

• if $A, B, C \in FinT(X)$ then  $Sum(A,B,C) \in FinT(X)$ and $Dif(A,B,C) \in FinT(X)$, where  $Sum(A,B,C)$ is the tree

and $Dif(A,B,C)$ is the tree

• if $A \in FinT(X)$ and we can pass from  $A$ to  $B$ (i.e. $A \leftrightarrow B$ )  by one of the moves then  $B \in FinT(X)$.

_________________

Definition 3. Two graphs   $A, B \in FinT(X)$  are close, denoted by  $A \sim B$, if there is   $C \in FinT(X)$ such that  $B$ can be moved into   $A \circ C$.

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Notice that $A \leftrightarrow B$ then $A \sim B$.
Proposition 1. The closeness relation is an equivalence.

Proof.  I start with the remark that $A \sim B$ if and only if $A \bullet B \in FinT(X)$, where $A \bullet B$ is the tree

Indeed, $A \sim B$ if there is $C \in FinT(X)$ such that $B \leftrightarrow A \circ C$. Then

which proves that $A \bullet B \in FinT(X)$.  Then  $A \sim A$ for any $A \in FinT(X)$, because $A \leftrightarrow A \bullet A$, therefore $A \bullet A \in FinT(X)$. Suppose now that  $A \sim B$. Then $A \bullet B \in FinT(X)$. Notice that $B \bullet A \leftrightarrow Dif(A, A \bullet B, A)$, by the following sequence of moves:

But $Dif(A, A \bullet B, A) \in FinT(X)$, from the hypothesis. Therefore $B \bullet A \in FinT(X)$, which is equivalent with $B \sim A$.

Finally, suppose that $A \sim B$, $B \sim C$. Then $B \sim A$ by the previous reasoning. Then there are $A', C' \in FinT(X)$ such that $A \leftrightarrow B \circ A'$ and $C \leftrightarrow B \circ C'$. It follows that $A \bullet C \leftrightarrow Dif(B, A', C')$, therefore $A \bullet C \in FinT(X)$, which proves that $A \sim C$.

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Definition 4. The class of finite points  of $T(X)$ is  $PoinT(X)$  is the set of equivalence classes w.r.t  $\sim$.

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Same construction, with groupoids.  We may see $\leftrightarrow$ as being an equivalence relation. Let  $T_{0}(X)$  be the set of equivalence classes w.r.t $\leftrightarrow$. We can define on  $T_{0}(X)$ the operations $(A,B) \mapsto A \circ B$ and $(A,B) \mapsto A \bullet B$  (because the moves R1a, R2a are local). Then  $(T_{0}(X), \circ, \bullet)$ is the free left idempotent right quasigroup generated by the set $X$.

Idempotent right quasigroups are the focus of the article arXiv:0907.1520, where emergent algebras are introduced as deformations of such objects. An idempotent right quasigroup $(M, \circ, \bullet)$ is a non-empty set endowed with two operations, such that

•   (idempotence) $x \circ x = x \bullet x = x$ for any $x \in M$,
•   (right quasigroup) $x \bullet (x \circ y) = x \circ (x \bullet y) = y$ for any $x, y \in M$

Let $T_{0}(X)^{2}$ be the trivial (pair) groupoid over $T_{0}(X)$. This is the groupoid with objects which are elements of  $T_{0}(X)$ and arrows of the form  $(A,B) \in T_{0}(X) \times T_{0}(X)$. Equivalently, we see $T_{0}(X)^{2}$ to be the set of it’s arrows, we identify objects with their identity arrows (in this case we identify $A \in Ob T_{0}(X)^{2}$ with it’s identity arrow $(A,A) \in T_{0}(X)^{2}$). Seen like this, the trivial groupoid  $T_{0}(X)^{2}$ is just the set  $T_{0}(X) \times T_{0}(X)$, with the partially defined operation (composition of arrows)

$(A,B) (B,C) = (A,C)$

and with the unary inverse operation

$(A,B)^{-1} = (B,A)$ .

Remark that the function  $F: T_{0}(X)^{2} \rightarrow T_{0}(X)^{2}$  defined by  $F(B,A) = (A \circ B, A)$  is a bijection of the set of arrows and moreover

•   it preserves the objects $F(A,A) = (A,A)$,
• the inverse has the expression  $F^{-1}(B,A) = (A \bullet B, A)$.

Define the groupoid  $F \sharp T_{0}(X)^{2}$ by declaring $F$ to be an isomorphism of groupoids. This means  $F \sharp T_{0}(X)^{2}$ to be  the set of arrows  $T_{0}(X)\times T_{0}(X)$, with the partially defined composition of arrows given by

$(B,A) * (D,C) = F^{-1} \left( F(B,A) F(D,C)) \right)$
for any pair of arrows $(B,A), (D,C)$ such that $F(B,A)$ can be composed in  $T_{0}(X)^{2}$ with $F(D,C)$, and unary inverse operation given by

$(B,A)^{-1,*} = F^{-1} \left( \left( F(B,A) \right)^{-1} \right)$  .

The groupoid  $F \sharp T_{0}(X)^{2}$ has then the composition operation

$(B, C \circ D) * (D,C) = (Sum(C,D,B), C)$ ,

the unary inverse operation

$(B,A)^{-1,*} = (Dif(A,B,A), A \circ B)$

and the set of objects $Ob(F \sharp T_{0}(X)^{2}) = T_{0}(X)$ .

Consider the set  $X^{2} = X \times X$, seen as a subset of arrows of the groupoid   $F \sharp T_{0}(X)^{2}$ .

The class of finite trees $FinT(X)$ appears in the following way. First define  $Fin_{0}T(X)$ to be the set of equivalence classes w.r.t  $\leftrightarrow$ of elements in $FinT(X)$.

Remark that $\left( Fin_{0} T(X)\right)^{2}$ is a sub-groupoid of $F \sharp T_{0}(X)^{2}$, which moreover it contains $X^{2}$ and is closed w.r.t. the application of $F$, seen this time as a function (which is not a morphism) from $F \sharp T_{0}(X)^{2}$ to itself. In fact $Fin_{0} T(X)$ is the smallest subset of $T_{0}(X)$ with this property. Let’s give to the groupoid $\left( Fin_{0} T(X)\right)^{2}$ the name   $\langle X^{2} \rangle$, seen as a sub-groupoid of  $F \sharp T_{0}(X)^{2}$ .

Moreover  $F\left( \langle X^{2} \rangle \right)$ is a sub-groupoid of the trivial groupoid  $T_{0}(X)^{2}$, with set of objects  $Fin_{0}T(X)$. But sub-groupoids of the trivial groupoid are the same thing as equivalence relations. In this particular case $(A,B) \in F\left( \langle X^{2} \rangle \right)$ if and only if  $A, B \in Fin_{0}T(X)$ and $A \sim B$.

Next time you’ll see some groups (which are associated to parallel transport in dilation structures) which are in some sense universal, but I don’t know (yet) what structure they have. “What group is this?” I shall ask next time.

________

Do you remark at which stage of this construction the map becomes the territory, thus creating points out of abstract nonsense?

To get a sense of this, replace the set of arrows $X^{2}$ with a graph with nodes in $X$.

# An account of personal motivations concerning research and publication

Motivated by a g+ mention of two posts of mine, I think I need to explain a little bit the purpose of such posts, also by putting them in the context of my experience. (I don’t know how to avoid this appeal to experience, because it is not at all an authority argument. Authority arguments, I believe, are outside of the research realm, they should be ignored in totality.)

Despite my attraction to physics and painting, I was turned to become a mathematician by a very special kind of professor. When I was little there was the habit of taking private preparatory classes for increasing the chances of admission in a good college. So, at some point, although I claimed not to need such classes, one day when I came back home after a soccer game I met a strange old guy, who was speaking in an extremely lively and polite way with my parents. I was wearing my school uniform which was full of dust gathered in the schoolyard and I was not at all in the mood to speak with old, strange persons. He explained to my parents that he is going to give me one problem to solve, for him to decide whether to accept me or not as a student. He gave me an inequality to prove, then I spent a half hour in my room and found a solution, which I wrote. I gave the solution to the professor, he looked at it and started: “Marius, a normal kid would solve this inequality like that  (he explained it to me). A clever kid would prove the inequality like this (a shorter, more elegant solution). A genius kid would do like this (one line proof). Now, your proof is none of the above, so I take you.”  It was an amazing experience to learn, especially geometry, from him. At some point he announced my parents that he is willing to do the classes with no pay, with the condition that he could come at any time (with a half hour notice). We did mathematics at strange hours for me, like midnight or 5 in the morning, or whenever he wanted.  Especially when geometry was concerned, he was never letting  me write anything until I could explain with words the idea of the solution, then I could start writing the proof. An amazing professor, a math artist, in the dark of a communist country. I have never met anybody as fascinating since.

If someone would had come to tell me that doing research exclusively means to dig one narrow area in order   to write as big as possible a NUMBER of articles  in ISI journals, then I would have thought that’s a disgusting perversion of a lovely quest. Then I would have switched to painting, because at least in that field (as old, no, older than mathematics)  creativity won against vanity since a long time.

I was young then and I wanted to do research in as many areas as I see fit. There was no internet at the time, therefore I was filling notebooks with my work. Most of it it’s  just lost, mostly because of not having anybody around to share my thoughts with, to learn from and to grow into a real researcher in  a welcoming environment (with one exception, the undergraduate experience was a disappointment). I was not willing in fact to show what I do because it was much more rewarding to find out some more about some subject than to loose time to explain it to somebody, moreover now I know to trust my intuition which was telling me that there was no point to waste time for this.

The next important moment in my life as a researcher was the contact with the www, which happened in 1994 at Ecole Polytechnique from Paris, when I was doing a master. I was not interested in the courses, because I already had (a bit better, due to the mentioned exception) ones back home, but, OMG, the www! At that point, after having only one article published (The topological substratum of the derivative) — can you imagine? — which was written at a typewriter, with horrific handmade underlines and other physical constraints of the epoch — so I decided that’s have to be the future of doing research and I completely lost interest into the contrived way of communicating research by articles.

I had to write articles, and I did, only that very frequently I had problems concerning their publication, because I hold the opinion that an interesting article should combine at least three fields and it should open more questions than those solved. Foolish, really, you may say. But most of all I am still amazed how much time it took me to start to express my viewpoints publicly, through the net.

Which I am finally doing now, in this blog.

In this context, I use the personal experience as a tool in order to stress the obvious belief that www is changing the (research) world much more, much faster, than the printing press. I don’t complain about the mean reviewers, but I offer examples which support claims as: the future of peer-review is one which is technical (correct or not?), is open to anybody to contribute constructively, not based on unscientific opinions and authority arguments,  separated from “publication” (whatever this means today) and perpetually subjected to change and improvement with the passage of time.

More on open peer-review in this blog here.

# Gamifying peer-review?

Fact is: there are lots of articles on arXiv and only about a third published traditionally (according to their statistics). Contrary to biology and medical science, where researchers are way more advanced in new publishing models (like PLoS and PeerJ, the second being almost green in flavour), in math and physics we don’t have any other option than  arXiv, which is great, the greatest in fact, the oldest, but … but only if it had a functional peer-review system attached. Then it would be perfect!

It is hard though to come with a model of peer-review for the arXiv. Or for any other green OA publication system, I take the arXiv as example only because I am most fond of. It is hard because there has to be a way to motivate the researchers to do the peer-reviews. For free. This is the main type of psychological argument against having green OA with peer-review. It is a true argument, even if peer-review is made for free in the traditional publishing model.  The difference is that the traditional publishing model is working since the 1960’s and it is now ingrained in the people minds, while any new model of peer-review, for the arXiv or any other green OA publication system, has first to win a significant portion of researchers.

Such a new model does not have to be perfect, only better than the traditional one. For me, a peer-review which is technical, open, pre- and post- “publication” would be perfect. PLoS and PeerJ already have (almost) such a peer-review. Meanwhile, us physicists and mathematicians sit on the greatest database of research articles, greener than green and older than the internet and we have still not found a mean to do the damn peer-review, because nobody has found yet a viral enough solution, despite many proposals and despite brilliant minds.

So, why not gamify the peer-review process? Researchers  like to play as much as children do, it’s part of the mindframe requested for being able to do research. Researchers are driven also by vanity, because they’re smart and highly competitive humans which value playful ideas more than money.

I am thinking about Google Scholar  profiles. I am thinking about vanity surfing. How to add peer-review as a game-like rewarding activity? For building peer communities? Otherwise? Any ideas?

UPDATE:  … suppose that instead of earning points for making comments, asking questions, etc, suppose that based on the google scholar record and on the keywords your articles have, you are automatically assigned a part, one or several research areas (or keywords, whatever). Automatically, you “own” those, or a part, like having shares in a company. But in order to continue to own them, you have to do something concerning peer-reviewing other articles in the area (or from other areas if you are an expansionist Bonaparte). Otherwise your shares slowly decay. Of course, if you have a stem article with loads of citations then you own a big domain and probably you are not willing to loose so much time to manage it. Then, you may delegate others to do this. In this way bonds are created, the others may delegate as well, until the peer-review management process is sustainable. Communities may appear. Say also that the domain you own is like a little country and citations you got from other “countries” are like wealth transfer: if the other country (domain) who cites you is more wealthy then the value of the citation increases. As you see, until now, with the exception of “delegation” everything could be done automatically. From time to time, if you want to increase the wealth of your domain, or to gain shares in it, then you have to do a peer-review for an article where you are competent, according to keywords and citations.

Something like this could be tried and it could be even funny.