Category Archives: Mathematics

Physics of Data Flow

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Last week the Construction Specifications Institute (CSI) Northern Virginia Chapter (CSI NOVA) welcomed scientists from the NIST Fire Research Lab to give a talk about fire simulations and the new test facility.

NIST’s Fire Dynamics Simulator (FDS)

A couple simulations were of just the fires themselves rather than walls, furniture, elevator shafts and other elements that might influence where a fire would move next in a building. The NIST Fire Research lab studies both the effects and relationships of different building materials with fire, and the physics of fire by itself. The physics of fire by itself has some known properties, such as maximum temperatures, and the short SHORT flashover point. The space around a fire is not always needed for better understanding of what a fire is likely to do next.

National Fire Protection Association (2001) from NFPA 1710

Today we have a lot of data moving around the Internet. Behaviors and patterns in the physics of data flow may have properties like maximum temperatures or flashover points in fires.

Ebb and Flow of Box Office Receipts Over the Past 20 Years – at Flowing Data

However it seems like most of these studies only look at the data, rarely the space around. As if the way different areas of the Internet were built, or the composition of various user communities, could influence where data are likely to go next and whether they are likely to spread quickly or slowly smolder. Below is an image about the flow of physics data from CERN, but who is studying the physics of data flow? Or more importantly, structural details about spaces around data, or how more precise configurations might help push relevant information into specific areas that are most conducive to those particular ideas catching on, spreading, and growing… Until at some point, inevitably, even the most gigantic ideas, like fires, will eventually die out. We are still learning about the physics of fire today, the physics of data flow and a better understanding of the life cycle of ideas and information may take many MANY generations of study until the statistics and calculations are relatively accurate, or at least aligned with the unpredictable real world.


Taking Apart and Putting Back Together in a Repeatable Process

The greatest thing about relational databases is they store everything loose in some kind of homogeneous level playing field. It is only be establishing relationships between data that anyone is able to see anything in context. Without context, they are just data. In context they are messages, thoughts, ideas, studies, results, and work products.

If an idea is very complex sometimes it helps to break it down into component parts. Systematically taking it apart to understand what makes this idea tick.

DesignIT Studios

Starship ModelerWikicommons Watch Movement

Taking an idea apart can be very informative. Especially when various parts need to be updated and optimized, continually changing like software releases. If the watch above was wordpress, the Swift theme, and the internet each gear changes sooner or later but the whole watch still needs to work together if it is to continue functioning.  Putting things back together offers it’s own set of challenges.  There is an opportunity to purge elements that are no longer useful during this process. Like a hoarder moving everything out of their house onto the curb then back into the house, maybe some of those items are not worth saving after all. Or fixing a car engine, or someones medical condition, when it is unclear exactly what the problem is but simply by taking it apart and putting it back together, whatever was not working gets repaired.

IDSA Materials and Processes Section

Instructions are needed, parts need to be labeled. A sequence of reassembly is needed to ensure the reassembled whole still is the same. It can be difficult to see how the parts fit together when viewed too close.

Carol Padburg

Because everyone’s perception and experience is different, the exact same elements, in almost exactly the same combination may be understood a different way from different points of view. The receiving end may be “reading something into” what the sender intended. It may not be possible for two different people to consistently see the same things the same ways.

Put Back Together Pictures

However, this is not true for machines like computers or networks like the internet because machines have no prejudices, emotions, or previous experiences.  They simply process the information, break up whole ideas into packets, send them somewhere, another machine puts them back together. For this to be reliable everything on both ends needs to be a repeatable process. It would be so helpful to have a mold with the end result packed in with every packet to ensure consistency. MIT has just started a project to map controversies that may be useful to understand multiple interpretations of the same information.

MIT Mapping Controversies Project

This project is important today because we are surrounded by so many controversies, and so much data, it’s difficult to sort out which parts are actually valid, worth processing, keeping in the information houses where we store things. For example the Washington Post had an article today about the disconnect between science and the general public entitled “Not Blinded by Science, but Ideology” where global warming is a perfect example.

To avoid using information the wrong way, or putting together messages, thoughts, and ideas that may be different than original authors intended, especially while processing the data in emotionless machines – repeatable processes are needed.

BZen Consulting

Info-Sight Partners Actionability Index

Global Wonderware

Today the primary representation of how pieces of information are to be put back together need to work with SQL. Looking at the relationships is usually just miles and miles of code. However, there is a company at who makes Schemaball, a Schema Viewer for SQL Databases where the relationships themselves can be put under a microscope and examined across the whole database in one glance.

It’s curious why geometry proper is not used more often to direct the arc, layouts and relationships. Something like a mold could be useful to ensure the reassembly is 100 percent correct on the receiving end, to match exactly, what the sender intended.

But how would you store and encode that geometry?


Spending More Time with Better Information

In the book You Are Not a Gadget Jaron Lanier talks about the unrecognized value of ideas generated by individuals, and the unintended effects the internet is having on musicians, visual artists, writers and other professional creative people. One way he describes it is the the “digital flattening of expression into a global mush“. Another is the “adoration of fragments“.

From Jaron Lanier at the RSA uploaded to Flickr by PSD.

One of the best examples he uses is what MIDI did to music “squeezing all of musical expression through a limiting model of the actions of keys on a musical keyboard“. All of the nuances, individual interpretations and stellar performances are gone. Every performance is the same.

People are not spending enough time with better information because some parts of the internet design do not allow for multiple iterations without ditching the previous versions, or any way to see how an idea or the information surrounding it has evolved.  There is no variation of the same, there are only exact copies and links.  A new digital architecture is needed with provisions for continuity, and coming back to an idea again with a fresh perspective, to promote the slow building and appreciation of work that takes longer than a few minutes or hours to create or interpret. There is hope though, with organizations like the Long Now Foundation working on projects to foster long term thinking and responsibility. It is a monumentally large challenge to consider more efficient ways to process infinite data fields intersecting – in such a way that better data might rise up out of the fray.

From The Effects of Digital Crosstalk in Data Converters
by Maxim where Innovation is Delivered

For better data to be created in the first place, professional creative people need to be paid reasonable rates to be ABLE to spend more time making work that in turn lasts longer out in the world. Consider for example these beer taps, an actual designer was paid a reasonable rate to figure out a shape, they were free to use any typeface, the only design requirement was a universal hookup. That is all internet standards should be, universal screw threads that allow designs to be professionally created, manufactured, and distributed.

Dr. Dremo Donut Beer Tap from the Quest for the Holy Grain

It truly is a conceptual and mathematical problem to devise a system of standard access points that allow data to slowly evolve, and get better, in ways that enough people can become truly engaged in what hand crafters have made.

Some designs will last longer than others but there is no inherent functionality in the design of the internet currently to let digital cross talk start eliminating what should sticks around longer or pop up in searches faster because it is actually better or supported by people who have actually looked at some thing from all sides. The idea of what fits is underused because there is no geometry around data forcing some information to stick around certain areas or flow through and keep on going.

Processes need to be developed to start dealing with the pace ideas and information fly around.  Data flow needs to be treated more like music. Like many people have observed – the symbolic encoding can be very simple and the same everywhere – but more time and attention is needed for actually the shapes and architecture of what supports a digital idea or lets it exchange faster, slower, closer, further away.

Yale Research, Breakthroughs in the Water, the Science of Swimming

What would such an ideal exchange architecture look like? Where would the universal screw threads be and how can the visitor experience be directed through this information space like a museum design? Where are the long axial views? The hints of what might be around the corner? Where do you pause and consider individual works? There is a flatness to digital information, everything is in your face on the same plane. There needs to be a better way to get a longer perspective on what surrounds ideas and information. Where they came from, how they have evolved, and which parts need to stay connected so they can hold together and stand the test of time.

DNA from Emergent Culture


Call for Mathematics and Design Papers

June 07 – 11, 2010
Buenos Aires, Argentina

Dra. Vera W. de Spinadel

Claudi Alsina
Drumi Bainov
Javier Barrallo Calonge
Ubiratan d´Ambrosio
Roberto Doberti
Rosa S. Enrich
Carlos Federico
Dirk Huylebrouck
Slavik Jablan
Amadeo Monreal
Janusz Rebielak
Adela Salvador Alcaide
Gunter Weiss

Centre  MAyDI  and Laboratory of Mathematics & Design, Faculty of Architecture, Design and Urban Planning, University of Buenos Aires, ARGENTINA
International Mathematics & Design Association

Susana Toscano
Marcela Franco
Néstor Díaz
Graciela Colagreco

Languages: Spanish and English.

Objective:  The objective of this conference is to convoke designers and scientists from different fields of knowledge, interested in the active interaction between Mathematics and Design. There exists an enormous wealth of experiences not only  in Architecture and Engineering but also in Graphic Design, Industrial Design, Textil Design, Light and Sound Design, Art Design, etc. It is important that the experts in some of these fields meet together to interchange their results and projects.

* Computer Design
* Mathematical modelling
* Visualization
* Multi-media
* Project Design
* Art and mathematics

Plenary Conferences:  These conferences will be delivered by well known invited researchers. They will dispose of one hour.

Scientific communications:  The scientific communications have to be the presentation of a finished investigation or in the state of conclusion. They can be presented orally or by means of a poster. For the presentation, the author will dispose of twenty minutes followed by ten minutes to answer questions from the audience.

The acceptance of the scientific communications will be a responsability of the Scientific International Committee and the Proceedings of the conference M&D-2010 will be published as a special issue of the Journal of Mathematics & Design.


Papers are invited on the topics outlined and other topics which fall within the general scope of the Conference. The deadline for the reception of the abstracts of the communications is July 31, 2009 .

Abstracts should be no longer than 300 words, contain a list of keywords and clearly state the methodology, purpose, results and conclusions of the final paper.

The answer about the acceptance will be sent  by  December 1, 2009.

CONTACT EMAILS  (Centre of Mathematics & Design) (International Mathematics & Design Association (Laboratory of Mathematics & Design)


Talking About Spirals

Context Driven Topologies are mathematical groups of ideas and information transmitted over computers and networks.  Their form and process are expressed using drawings and specifications.  Their purpose is to organize and drive network topologies to answer questions and derive meaning from data collections of any size, particularly in open source environments.  The purpose of answering questions and deriving meaning is to foster Collective Intelligence. Refer to Wikipedia Unassessed Systems for related work.

CItypes (131)

The default form envisioned for storage mode is a spiral.  Groups of ideas and information can be rearranged infinite ways while working with or distributing to and from precise locations. Locations can be physical, conceptual, or a combination of both.  Assuming constructing exchanges and working this way is possible, what shapes and topologies would be most effective?  What are their properties? What do they have in common? What would a computer and network language about these pathways, densities, colors, transparencies, forms, linkages and exchanges look like?


Its too complicated to wonder about ALL possible forms, the question can be simplified by just concentrating on spirals for an example. Therefore, a previous post Spiral Model is expanded to incorporate slides prepared by A&A Director Vera W. de Spinadel for a Postgraduate class on Form and Mathematics which focuses on logic and technique. Dr. de Spindel remarks “Of course this has a lot to do with the subject of Context Driven Topologies“. Lets see what this means to computers and networks, starting with :

spiral model

Spiral Model, Boehm, 1988, Original Creator: Conrad Nutschan

According to Wikipedia on November 22, 2006: The spiral model is a software development process combining elements of both design and prototyping-in-stages, in an effort to combine advantages of top-down and bottom-up concepts. What a perfect shape spirals are to portray complex evolving relationships. Just imagine the possibilities using spirals as a base structure.


A Equiangular Spiral and its Secants from the Visual Dictionary of Special Plane Curves

Now for Vera’s slides:











English captions to be completed at a later date – this slide says “Carrying out some modifications in the process of construction of this spiral, we are going to build other linked with the Numbers of the FNMPP. In the following figure details of the construction are shown.”



Of course spirals are seen in nature and architecture. Rough translation “Finally, in the country of the Architectural Design, fits to mention the interesting antecedent of the Spiral building, built by the Arq. Fumihiko Maki in Tokyo, Japan in 1985. Maki gue prizewinner with the Prize Pritzker in 1993 and in its Spiral building has utilized the geometry of the curve, that conjugates marvelously the concepts of fragment and unattainable center. The geometric figure is an evocation of the ones that are found in Kyoto, in the famous Temple of Ginkakuji (Silver Building) 1338-1573 and in the Temple of Kinkakuji (Building of Gold) 1398, reconstructed in 1955. Though these denominations of Gold and Silver have religious and historic meaning, they would be able to serve of example to design making use of so much, metallic spirals flat curves like helicoides metallic.”


The question Vera is looking for is geometrical interpretations of the members of the family of metallic means – which she discovered in 1997. She found a relationship of the golden mean with the pentagon and another of the silver mean with the octagon. And that was all, there were no more relationships with polygons. So, she began trying to construct metallic spirals, generalizing the well known golden spiral – and was successful! She introduced a family of metallic spirals and continues intensively working with the silver spiral. There will be more to see when she presents at the International Conference on Geometry and Graphics ICGG-2008 in Dresden Germany.


Other computer and network systems that may be interesting to study in terms of forms, dynamic properties, geometry and graphics to streamline information that have been highlighted in recent discussions include:

Artificial Neural Networks

Pattern Recognition

Single Instance Storage

But what is even more interesting is


Collective Intelligence


the Information Economy Meta Language IEML see the paper “Collective Intelligence Protocol Semantic Metadata Exchange Standard (CIP-SMES)” by Michel Bietzunski and Steven Newcomb 18 July 2007. A commentary on this paper and Chapter 3 of Topic Maps by the same authors, edited by Jack Park is here IEMLcomments









Matematica y Diseno


3rd International Mathematics & Design Workshop


The 3rd International Mathematics & Design Workshop will be held at the Faculty of Architecture and Urban Studies, La Plata University on 6th and 7th June, 2008. Every interested person is invited to send an abstract before the 5th May, for evaluation through the Scientific Committee.


Las matematicas el diseno de aviones

For each communication there will be 20 minutes and it is a necessary requisite that their content has not been previously presented or published elsewhere. There will be a distinction between:
1) new results obtained on the subject of the results presented at M&D-2007 in Blumenau, Brazil;
2) completely new subjects.
There will be also Plenary Lectures of 30 minutes, delivered by personal invitation and these lectures could be in Spanish or English. The Proceedings will be published as a special issue of the Journal of M&D.

nexus m&d

Please see the Nexus Journal and La Asociation Internacional de Matematica y Diseno


Discrete Continuity


Sticker Shock by SPEEDtv

See the sticker on the tire. It is a discrete rectangle. A fixed piece of information, it is not continuous.


Tire by Mayarishi

However, once the wheel goes in motion, the sticker can no longer be seen – the discrete shape appears to be a continuous blur.

Therefore, discrete elements put into dynamic motion only appear to be continuous. How can this be useful to take discrete instances of knowledge and make them continuous?
Continuity, even if only simulated, can benefit the digital age in many ways. For example, look at all the discrete papers published every day. Each one is a set of information like the sticker but what would happen if groups of paper were set in motion, to force continuity between them? What shape would serve this purpose best? A circle like the tire? Some shared, continuous knowledge would require far more complex geometry.


Notre Dame by Chi King

Please refer to this video Blaise Aguera y Arcas: Photosynth Demo wherein Flickr images are assembled to construct the Notre Dame Cathedral. The only way to do this is to know the geometry of the cathedral.

What is the geometry of knowledge? How can continuity be implied using shared geometry and many points of view more productively?


Perfect Geometry by Dancing Fishes

There is no way to address the topic without also thinking about slightly different versions of the same thing. Examples using music are below. The same notes and words are used but the songs and performances, even the performance requirements, are different. Each piece of music is discrete, the continuity is the fact they are the same song by different artists ~ in different times and places.


Going to California by Led Zeppelin and the String Quartet


Little Wing by Jimi Hendrix and Steve Ray Vaughn


I Will Survive by Gloria Gaynor and Cake



Unfold, Expand, Connect

Images about unfolding, expanding, and connecting


Heaven’s Orb from Rob’s Puzzle Page


PETER MAX boxed jigsaw puzzle at GASOLINE ALLEY ANTIQUES Antique Toys & Collectible


The Puzzling World of Polyhedral Dissections, by Stewart T. Coffin

This simple novelty (Fig. 126) is a practical example of a coordinate-motion puzzle in three dimensions. Each of the six identical puzzle pieces is made up of a right-triangular prism center block to which are attached a pair of rhomboid-prism end blocks. They assemble with no great mystery to form a hollow box, but if they are accurately made, some dexterity is required to get all six pieces aligned exactly right and mutually engaged. Once assembled, by holding on to opposite pieces, the puzzle can be made to expand almost to the point of collapse and then to shrink back together again. It is more of an amusement than a puzzle.


Mathematics of Movement

Movements such as democracy and trends in collective thinking must have some underlying mathematics that could be studied and perhaps improved to gently push information in more productive directions. But what would that look like?


Dynamic Painting by San Base, a Canadian artist born in Russia.


We Never Change Do We Melanie Weidner Listen for Joy


Abstract stripes lines of colour movement speed Dominic Harris from RefocusNow

Movement Path

Movement Phase from the MegaMek game


The Plates of a Movement by Peter Chong


Circles locate suspected underground water movement in the Ormond Beach area. Three different aerial photographs were used, along with an infrared one, to guesstimate these locations. Oxnard Coastal Wetlands


Movement 3 by Harp Spectrum


Form, Shape, Trace, Reckon, Calculate, Represent

The Institute for Figuring

To Figure: To form or shape, to trace, to reckon or calculate, to represent in a diagram or picture, to ornament or adorn with a design or pattern.

The Institute for Figuring does not yet have a physical space. Their location in the conceptual landscape is permanently located on the edge of this iconic fractal.mset_forweb.jpg

Institute for Figuring (IFF) Mandelbrot set location: (-0.7473198, i0.1084649) with detail (color inset.)


Crochet model of hyperbolic plane by Daina Taimina

In 1997 Cornell University mathematician Daina Taimina finally worked out how to make a physical model of hyperbolic space that allows us to feel, and to tactilely explore, the properties of this unique geometry. The method she used was crochet. See [105] Hyperbolic Space Crochet Models for more information.

[105] Hyperbolic Space

[111] It is one thing to know that something is possible, it is quite another to understand what it is. Like the blind man and the elephant, hyperbolic space appears in different guises depending on how we approach it. One way of visualizing this enigmatic space was discovered by the great French mathematician Henri Poincar?. In the Poincar? disc model the entire hyperbolic space is depicted inside a circle.

disc1 Poincare Disc Model of Hyperbolic Space

Image and text above from the website of the Institute For Figuring (


Brings to mind topological knots. Images below by Sofia Lambropoulou.


Escher mechanical trefoils


Ancient knots in Berlin museum


Mongolian knots on stamps


Complex Geometry

If attempting to draw the geometry of knowledge changing over time, curves and projection geometry make everything more complicated.

Computers prefer straight lines with nice even units but the geometry of knowledge seems more fluid. Important continuity must be shown and traced, some form of projection is nearly always be involved.

Domes, globes, spheres and spirals pose special problems. A example of dealing with a projections onto a curved dome is the Theatre of Pattern Formation made by James Crutchfield and David Dunn. A visual and auditory articulation of chaos theory designed for the LodeStar Astronomy Center in Santa Fe and planetariums everywhere. At a talk at CUNY December 2004, the authors explained their struggle with knitting together complex fractal imagery to present properly on a curved surface. Sample below:


In this and other examples, artists were able to help scientists see their own work a new way and vice versa.

What can be done today between artists and scientist to create and establish the complex data structures we need today? What is the geometry like? Is it more suited to networks than individual computers working in isolation? Where are curves and projections necessary in such projections?



In architectural construction documents, elements may appear many times in the drawings but are only specified in one location in the project manual. To assure consistency and to know where to look for information, the American Institute of Architects (AIA) and Engineers Joint Contract Document Committee (EJCDC) established a Uniform Location of Subject Matter published in AIA Document A521/EJCDC 1910-16. Uniform subject matter locations for contracting and building the semantic world needs to be defined also.

What would be the most functional layout to show a full spectrum of information use in semantic space?
Curves and waves on axis like this diagram explaining Remote Sensing of the Global Environment by David J. Schneider in the Department of Geological Engineering and Sciences at Michigan Technological University

But how to accommodate and show various digital materials being transmitted, for example images, text, video, sound recordings etc. It may be better to establish a lay out similar to the electromagnetic spectrum as shown by the Division of Chemistry Education at Purdue University.

What about the pace information is exchanged? Perhaps quantum mechanics diagrams like this one by Alyssa A. Goodman at the Harvard-Smithsonian Center for Astrophysics would work.



Number Systems of the World


Number Systems of the World

I translate words included in number words to English, and I use ‘+’ and ‘?’ for implicit additions and multiplications. For instance, I explain the French words vingt et un (21) and quatre-vingt-dix-neuf (99) as “20 and 1” and “4 ? 20 + 10 + 9” respectively.

Please let me know if you find a mistake. A list of numbers in your language is welcome.

Some pages use the character set UTF-8. Latest web browsers automatically choose a proper character set.

Rank Language Language Family, Subfamily Native speakers
population Spoken Area
1 Huli
(new) Trans-New Guinea, Main Section 70,000 Papua New Guinea
2 Ndom
(new) Trans-New Guinea, Kolopom 450 Frederik Hendrik Island
(near New Guinea)
3 Nimbia Afro-Asiatic, Chadic ? Nigeria
4 Hindi Indo-European, Indo-Iranian 182,000,000 Northern India
5 Tzotzil Mayan, Cholan-Tzeltalan 265,000 Mexico
6 Ainu (language isolate) 15 Hokkaid? (Japan)
7 Alamblak Sepik-Ramu, Sepik 1,500 Papua New Guinea
8 Nahuatl Uto-Aztecan, Southern Uto-Aztecan 1,377,000 Mexico
9 Malagasy Austronesian, Malayo-Polynesian 10,156,900 Madagascar
10 Yoruba Niger-Congo, Atlantic-Congo 20,000,000 Nigeria, Benin
11 Welsh (Traditional)
(new) Indo-European, Celtic 580,000 Wales (U.K.)
12 Breton Indo-European, Celtic 500,000 Brittany (France)
13 Manx Indo-European, Celtic 0 Isle of Man (U.K., extinct)
14 Scots Gaelic Indo-European, Celtic 94,000 Scotland (U.K.)
15 Georgian South Caucasian, Georgian 4,103,000 Georgia
16 Danish Indo-European, Germanic 5,292,000 Denmark
17 Javanese Austronesian, Malayo-Polynesian 75,500,800 Java (Indonesia)
18 Latin Indo-European, Italic 0 Italy (extinct)
19 French Indo-European, Italic 72,000,000 France
20 Zulu Niger-Congo, Atlantic-Congo 9,142,000 South Africa
21 Basque Basque 580,000 Basque (France, Spain)
22 Arabic Afro-Asiatic, Semitic 0 West Asia, North Africa (ancient)
23 Ganda Niger-Congo, Atlantic-Congo 3,025,440 Uganda
24 Maltese Afro-Asiatic, Semitic 370,000 Malta
25 Assyrian Afro-Asiatic, Semitic 217,000 Iraq
26 Kurmanji Indo-European, Indo-Iranian 7,000,000 Turkey
27 Dutch Indo-European, Germanic 20,000,000 Netherlands
28 German Indo-European, Germanic 98,000,000 Germany
29 Swahili Niger-Congo, Atlantic-Congo 5,000,000 Kenya, Tanzania
30 Ojibwa Algic, Algonquian 50,000 Canada, U.S.
31 Italian Indo-European, Italic 37,000,000 Italy
32 Spanish Indo-European, Italic 332,000,000 Spain, Latin America
33 Swiss French Indo-European, Italic 1,272,000 Switzerland
34 Tigrinya Afro-Asiatic, Semitic 6,060,000 Eritrea, Ethiopia
35 Turkish Altaic, Turkic 59,000,000 Turkey
36 Balkan Romani Indo-European, Indo-Iranian 1,000,000 Former Yugoslavia
37 Hungarian Uralic, Finno-Ugric 14,500,000 Hungary
38 Tagalog Austronesian, Malayo-Polynesian 17,000,000 Philippines
39 Polari (unclassified) 0 U.K.
40 Scots Indo-European, Germanic 100,000 Scotland (U.K.)
41 English Indo-European, Germanic 322,000,000 U.S., U.K., etc.
42 Norwegian Indo-European, Germanic 5,000,000 Norway
43 Swedish Indo-European, Germanic 9,000,000 Sweden
44 Sukuma Niger-Congo, Atlantic-Congo 5,000,000 Tanzania
45 Hawaiian Austronesian, Malayo-Polynesian 1,000 Hawaii
46 Finnish Uralic, Finno-Ugric 6,000,000 Finland
47 Estonian Uralic, Finno-Ugric 1,100,000 Estonia
48 Romanian Indo-European, Italic 1,500,000 Romania
49 Ancient Japanese Japanese 0 Japan (ancient)
50 Kiribati Austronesian, Malayo-Polynesian 67,000 Kiribati
51 Wolof Niger-Congo, Atlantic-Congo 3,215,000 Senegal, Gambia
52 Croatian Indo-European, Slavic 21,000,000 Croatia
53 Seneca Iroquoian, Northern Iroquoian 200 U.S.
54 Indonesian Austronesian, Malayo-Polynesian 17,050,000 Indonesia
55 Mandinka Niger-Congo, Mande 914,500 Senegal, Gambia
56 Wu Chinese Sino-Tibetan, Chinese 77,175,000 Shanghai (China)
57 Tok Pisin Creole, English-based 50,000 Papua New Guinea
58 Vietnamese Austro-Asiatic, Mon-Khmer 66,897,000 Viet Nam
59 Igbo Niger-Congo, Atlantic-Congo 17,000,000 Nigeria
60 Thai Daic, Tai 21,000,000 Thailand
61 Welsh (Modern)
(new) Indo-European, Celtic 580,000 Wales (U.K.)
62 Aymara Aymaran 2,200,000 Bolivia, Peru
63 Cuzco Quechua Quechuan, Quechua II 1,500,000 Peru
64 Chinook Wawa Pidgin, Amerindian 100 Canada, U.S.
65 Mandarin Sino-Tibetan, Chinese 885,000,000 Northern China
66 Japanese Japanese, Japanese 125,000,000 Japan
67 Cantonese Sino-Tibetan, Chinese 66,000,000 Guangdong (China)
68 Esperanto (artificial) 200 France etc.
69 Tongan Austronesian, Malayo-Polynesian 123,000 Tonga


Numeral Systems of the World’s Languages – an excellent site of a comprehensive list of number systems
Numbers from 1 to 10 in Over 4000 Languages
Numerals in Indo-European Dialects

Surprisingly enough, it’s proven that Chinese-speaking children are better at counting numbers than English-speaking counterparts because of their language. Bilingual children are better at counting when they think in Chinese than in English. The irregularity of the English number system makes it harder for children to count numbers properly.

English words may hinder math skills development
Counting Ability in Bilingual Children
Visualization and Explicit Number Naming as a Foundation for Children’s Early Work in Mathematics
The Mathematical Brain

Copyright(C) TAKASUGI Shinji (