About Us

Sobre Nosotros

Hypothesis is a NYC based gaming company that brings together artists, educators, mathematicians, scientists, software developers, and other visionaries and doers. Together, we create games that invite imaginative thinking about unsolved puzzles.

Hypothesis games are for people who aren’t afraid of a challenge. Playing our games is like entering a surrealist universe full of intellectual and philosophical questions. An important mission underlies our game design principles: to take information that has only been known to elite academic groups, and make it fun to explore for anyone who is curious. Because we are a small group of friends who come from a variety of different perspectives, we accomplish this more fluidly than is typically possible for rigid institutions.

We hope you have as much fun as we do!

Hypothesis es una empresa de juegos ubicada en New York. En esta empresa se reúnen artistas, científicos, desarrolladores de software, educadores, matemáticos, y otros visionarios y hacedores para crear juegos que animan la imaginación para pensar en rompecabezas no resueltas.

Los juegos de Hypothesis son para ellos que no tienen miedo de los retos. Jugar estos juegos es entrar en un universo surrealista lleno de preguntas intelectuales y filosóficas. Todos están diseñados con la misma meta importantísima: sacar información que antes sólo conocían grupos académicos de élite y presentarla de una manera divertida a todos los que tengan curiosidad por conocerla. Como un pequeño grupo de amigos con perspectivas muy distintas logramos nuestra meta con más fluidez que sea posible en las instituciones rígidas.

¡Esperamos que tengas tanta diversión como nosotros!


Some things folks have said about our director’s related work:

“Joe is able to see the world from the perspective of those with little to no mathematical comfort. He can break down the basics and present them in ways that struggling students can understand and use.”
— Alex Ott, Associate Dean, Bronx Community College

“It’s hard to make things like ... the fundamental theorem of algebra fun for a 14-year-old in the middle of his or her summer vacation, but Joe can and has. He is an exceptional educator and I cannot recommend him highly enough.”
— Joshu Fisher, Program Manager, Center for Talented Youth

“To say I enjoyed this program is an understatement. It was genuinely incredible. I feel like it taught me to think in a whole new and different way.”
— Caleb, student (11th grade) from Expedition given through Columbia University

“It’s definitely worth it. Even if you think you won’t be that interested the concepts might surprise you.”
— Student (9th grade) from Expedition given through BEAM

“We got to learn about concepts and ways of thinking that we wouldn’t learn anywhere else.”
— Yuki, student (grado 8) from Quinn’s Center for Talented Youth course


Algunas cosas que se han dicho del trabajo pertinente de nuestro director:

“Joe is able to see the world from the perspective of those with little to no mathematical comfort. He can break down the basics and present them in ways that struggling students can understand and use.”
— Alex Ott, Decano Asociado, Bronx Community College

“It’s hard to make things like ... the fundamental theorem of algebra fun for a 14-year-old in the middle of his or her summer vacation, but Joe can and has. He is an exceptional educator and I cannot recommend him highly enough.”
— Joshu Fisher, Administrador del Programa, Center for Talented Youth

“To say I enjoyed this program is an understatement. It was genuinely incredible. I feel like it taught me to think in a whole new and different way.”
— Caleb, estudiante (grado 11) de una Expedición lancado por Columbia University

“It’s definitely worth it. Even if you think you won’t be that interested the concepts might surprise you.”
— Estudiante (grado 9) de una Expedición lancado por BEAM

“We got to learn about concepts and ways of thinking that we wouldn’t learn anywhere else.”
— Yuki, estudiante (8th grade) de Quinn’s de un curso lancado por Center for Talented Youth

© 2020 Hypothesis LLC



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2021 September 5 — Solar Bound


For the past few weeks, I’ve been immersed in developing my prototype for Banisher, our board game that combines principles from magic and geometric group theory. Most recently, this entailed hand embroidering eleven diagrams in yellow and blue, a four-day endeavor during which my mind was filled with thoughts of what to say in this newsletter. Most of those things, I decided not to say because they were philosophical ramblings in defense of starting a business to accomplish non-commercial objectives, and I feel it’s more productive to focus on the new projects being created.

So, here I’ll do a quick follow-up about that UFO topic from last time and then share some recent developments of our projects. There’s a couple of queries at the end where you might help out if interested. As usual, feel free to respond (if you’re a subscriber receiving this via email) about those or anything else!

As far as the UFO stories in the news, I think that Simon from New Paltz put it best when he said “There is something stranger happening and right here with us (always has been?), and this nuts-and-bolts theory (that UFOs are physical beings/crafts from another planet) is either the only way that we can grasp it, or is being used by those in the know, or by the phenomenon itself, as a deceptive/manipulative way to frame the phenomenon / control the narrative / our perception of it.”

We get bombarded with so much information. It takes discipline to remember that we ourselves are responsible for what we think, especially about the unknown. This is where mathematical training helps. It makes our thinking more rigorous as we consider the information we have, be it logical, intuitive or perceptive. If after that, a phenomenon remains unknown, we can enjoy further study of and play with the mystery rather than falling for irresponsible interpretations (and attacking anyone who disagrees). In the field of pure math, open problems stay open until they are really truly solved; the big questions in life should be no different.

I had intended to focus on Gardens of Danu (our upcoming sci-fi video game) after my summer teaching work was over. My head was swimming with ideas about mythology and extraterrestrials, and Michael (the software developer on the project) had completed code ready to populate with dialogue trees with the NPCs. I made a new draft of my master document of backstory for the game, and wrote some of the dialogue for Silven, the Liralune of Earth’s moon Luna.

Then the excessive screen time caught up with me. After teaching online all summer and spending extra time writing on the laptop, my eyes rebelled with a spell of dryness.

So I switched to the only project that could be done by hand: Banisher. At that point, I had a set of instructions sufficient for remembering how to play (but not for teaching someone to play on their own), and a rough prototype made with foam board, model magic clay, glass pebbles and poker chips. That prototype had been sufficient to work out the game mechanics with my play testers (special shout outs to Victoria from Brooklyn and Brian from Danbury for their awesomely constructive criticism), but it did not convey the intended thematic/emotional effect. That part is very important for Banisher. It’s not intended as merely an eccentric strategy game with weird rules; it’s meant to tap into magical energy from my vision for it and conjure up similar feelings for other people using ancient techniques.

Something I’ve realized about making really weird content is that it’s important to get everything as close to right as you can before pitching it. People have a natural tendency to look for a pre-existing category to lump the idea into and if I don’t like that category, I shouldn’t expect people to read my mind and invent a new category just for me (at least, not without ample magical assistance!). When it comes to content “based on conceptual math”, the battle against indoctrinated negative categories is particularly uphill.

One of the principles of Banisher is a single set of rules that allow for playing on eleven specific diagrams. The diagrams are defined by a set of mathematical conditions but are topological (not geometric) objects, which means there’s some taste that goes into how to draw them. I’d been playing around with the form and aesthetics for these, trying a lot of things. Some of the ideas were informed by dreams. A particularly clear message from a dream occurred in the form of a voice saying “We are of brown, yellow and blue,” along with some new impressions on symbology. Later that day, I discovered a symbol that uniformized the configuration of all the diagrams and the moment I finished drawing it, the mail carrier knocked on my door to deliver a package of brown objects I’d ordered to experiment with as playing pieces. I painted the symbol on my prototype in yellow and blue and added the brown pieces, and had a deep sense of satisfaction with it. The development of Banisher has been rich with synchronous moments like this.

Now it goes a bit deeper, leading to something with which you might help.

My story for Banisher is set in a post-apocalyptic future where the game is a ritual for liberation from an evil deity. The idea is that this deity poses as a savior but in reality feeds sadistically upon our suffering. In the draft, I name that deity by a symbol (to be disclosed at a later time) and not a word. I’d made up this symbol based on my own impressions but then settled for something similar which could be more easily typeset. The closest match comes from an engraving that’s been used in archaic currency, which fits into my vision as the notion that my antagonist controls people by fixation on materialism.

Incidentally, I’d reconnected with an old friend through my teaching work who introduced me to the writings of Rudolph Steiner. Shortly thereafter, I noticed that the symbol I’d chosen occurs in reference to Ahriman, the entity which, according to Steiner, oppresses us by fomenting obsession with materialism. Since then, I’ve been broadening my understanding of Steiner and other elements of Western esotericism as context for my idea. Broadly speaking, I want to strike the right balance between originality (so the game taps a direct source of creativity) and basis in existing work (so that it’s respectful of and relevant to other peoples’ beliefs). The activity around theosophy and anthroposophy have been making the most sense for this lately.

In my latest draft of the story, there’s a secret twelfth diagram which is necessary for completing the banishing ritual. I did this to encourage further exploration of the underlying math, but I did not have anything in particular in mind for the next diagram. Earlier this week, my research led me to the work of the Russian mystic George Gurdjieff. I learned that he taught his pupils to use a 9-sided star called the Enneagram, which he believed to encompass all understanding of the cosmos. The diagram has a similar look to the diagrams from Banisher, though does not follow the same mathematical principle.

There are two more direct synchronous mysteries stemming from Grudjieff’s Enneagram. The first is that a Dutch businessman named Per Striegler created a board game called Life Prison in which the game board is the Enneagram. Apparently it’s meant to teach a psychological profiling technique popular with certain corporations, but I can find no details on how the game is played. The second mystery relates to a book about Gurdjieff published by Solar Bound Press which, based on the description (I haven’t read it yet) may have details on Gurdjieff’s relevance to Banisher that had been eluding me. What makes this synchronous for me is that it was published in New Paltz, NY in 2002: the same year that I moved to New Paltz back when I was an experimental video artist (before my math career) exploring strange spiritual ideas. What makes this a mystery is that I never heard of the Solar Bound Press, and can find no information about them other than that they published this single book.

If chasing down things like that sounds insane to you, hey you’re entitled to your opinion! Regardless, I’d be very interested to know if anyone has or can find further info about the board game Life Prison or about the publishing company Solar Bound Press .

I’ll conclude with some shoutouts. I know we still have a long way to “success”, but real success (without quotation marks) is surviving while doing things that one believes in, and so far we’re successful! My collaborators have been crucial in making this possible. My mom, a retired Spanish teacher, has been helping with the Spanish website translation (any errors you find are very likely mine). Molly Miller (soon to be added to the site) has been helping with art and concepts for Banisher. The scariest new frontier for me in this endeavor has been asking people to help me when I want to pursue something strange, and I’m very glad I did. Also, Bridge to Enter Advanced Mathematics and Columbia SPS have been crucial in giving me work that’s relevant and helps pay the bills while our projects develop.

Oh, and Hypothesis has an Instagram account: @hypothesisnyc . There you’ll find cheeky comments on math and education and business, and some fun stuff about our creative process.

Have fun. Keep thinking. Stay curious.

2021 Mayo 23 — Extraterrestres en las Noticias

Cuando yo era niño mi papá era político. Vivíamos en un pueblo pequeño llamado Carmel en el estado de Nueva York donde el atributo más emocionante fue un lago donde podíamos nadar. Un día mi amigo Tom vio un platillo volante pero volveré a este asunto en un poco.

Mi papá era un Legislador del Condado en el Partido Democrático desde 1985 hasta 1993. Quiere decir que él fue implicado en escribir y aprobar las leyes que necesitaron la atención al nivel local en vez del nivel estatal o el nivel federal. Generalmente él apoyaba la regulación de las empresas por el gobierno. Por ejemplo, ¿cómo se protege el lago de la contaminación cuando se crece la población? Como niño no me interesaban mucho estas cosas; mi punto es que mi familia a menudo tenía la primicia interna sobre noticias políticas locales. Lo que me interesaba fue el hecho de que los reporteros nos informaron sobre eventos de que mi papá ya me había dicho. Yo revisaba las noticias para ver si los reporteros las habían informado correctamente. Frecuentemente no pasó. Los detalles que yo les había oído decir a los reporteros mi padre no incluyeron o simplemente los informaron incorrectamente. Como resultado de esta experiencia yo me volví escéptico de cualquier noticia de que no tenía conocimiento previo—algunas más que otras. (Para conocer las fuentes fiables le aconsejo que estudie las falacias lógicas más comunes: Es decir los argumentos que tienen el efecto de presentar algo como probado cuando verdaderamente no está). Como me hacía mayor llegué a comprender los modos en que los informes de noticia tuercen los datos para atender a grupos de interés especiales. Obviamente si no pueden mantener el interés del público no van a vender sus anuncios comerciales. Y la verdad es que algunas veces los anuncios no están limitados a las pausas comerciales designadas.

[A parte: Quiero separar lo que estoy diciendo aquí de la manipulación de hechos por Donald Trump cuando usa la expresión “noticias falsas”. Una ventaja de ser un LLC en lugar de ser una organización sin ánimo de lucro es que tengo la libertad de tomar partido político. Pues es totalmente legal cuando le digo: yo pienso que Donald Trump es narcisista y una vergüenza nacional. La falacia lógica es su modus operandi. Desafortunadamente los aficionados de él, como ellos que pertenecen a Q-Anon, han dado “mala fama” al escepticismo mediático y a la búsqueda de las verdades escondidas.]

Ahora alejar el zoom a las noticias sobre cosas que implican el estado entero, el país entero, el mundo entero…Si un periódico local puede estropear noticias sobre un lago de que se cuidan solamente miles de personas ¿qué pasa cuando la información es mucho más complicada e implica miles de millones de personas? Esto nos lleva a nuestro tema principal.

¿Cómo reaccionamos cuando las fuentes de noticia de la corriente principal como CNN, NBC y CBS reconocen la existencia de OVNIS? ¿Y qué pasa cuando lo hace también el Pentágono?

Hace mucho tiempo que sigo el fenómeno de OVNIS. Comencé en la época cuando mi amigo Tom me dijo que él vio un platillo volante encima de Lago Carmel. Tengo un conjunto de experiencias, datos de investigación y unas opiniones acerca de esto pero quiero dejarlos al lado por ahora.Tengamos en cuenta los informes de noticia de actualidad como punto de partida para pensar en este tema y acercarlo como matemáticos (es decir, lógicamente y con una imaginación abierta).

Hecho: Según las fuentes de noticia enlazadas arriba el Pentágono ha confirmado la existencia de aviones con la capacidad de maniobras que no se sabe ser posibles para los aviones hechos por el hombre y que no se puede identificar.

La confirmación de este fenómeno por el Pentágono no es nueva. Lo que es nuevo es que se presenta en plataformas convencionales. Como resultado tenemos algunas de muchas preguntas que surgen y algunas observaciones preliminares.

Básicamente ¿Dicen la verdad sobre lo que dijo el Pentágono las fuentes de noticia? Yo digo “Sí” porque las fuentes de noticia proporcionan referencias que se verifican y no tienen la fama de falsificar referencias. (Para no estar de acuerdo a este nivel nos lleva en el territorio de “noticias falsas” y yo tendría curiosidad saber por qué se sospecharía una falsificación tan completa de información.)

A continuación ¿dice el Pentágono la verdad sobre la existencia de estos aviones y las maniobras descritas? Para verificar esto tenemos el testimonio del personal de la Fuerza Aérea y la Marina incluido en los informes sobre el protocolo para verificar la existencia y la trayectoria de un objeto volador. Algunos reporteros especulan sobre las imágenes según cómo les aparecen a ellos pero este es un punto discutible. Por supuesto los efectos especiales son capaces de producir prácticamente cualquier imagen de video (incluyendo ellas que son granuladas y de baja resolución) pero lo que importa aquí es que el militar confía en personas formadas en la interpretación de los datos y su capacidad para hacerlo. Y estas personas dicen que los objetos son reales. Por eso yo acepto la respuesta aquí como otra “Sí”.

Próximo, preguntemos ¿sabe el Pentágono que las maniobras observadas son imposibles para aviones de fabricación humana? A esa cuestión es más difícil responder porque el militar lleva información confidencial y quizás el personal entrevistado no haya tenido la autorización saber esta información. Una declaración del Pentágono se pregunta por las cuestiones: ¿Quién es responsable por la divulgación? ¿Qué nivel de autorización tiene la persona? ¿Qué nivel de clasificación tiene la información? Con conocimiento limitado de estas cosas me resulta difícil contestar esta pregunta.

Finalmente, ¿son de origen extraterrestre las naves especiales? Por muy tentador que sea para saltar a una respuesta a esta pregunta tenemos muy poco para seguir adelante con la información dada en las referencias de que hablamos actualmente. Una vez que clasifiquemos los fenómenos como “no identificados” el resultado es ponerlos entre la inmensa mayoría de los fenómenos en la Tierra y en otros lugares.

Hecho: Según las fuentes de noticia enlazadas arriba el Comité de Inteligencia del Pentágono les ha mandado que el Director de Inteligencia Nacional y el Secretario de Defensa le entreguen al Pentágono un informe sobre los avistamientos para el próximo mes (junio de 2021).

Es posible que ese informe no resuelva las ambigüedades que ya tenemos. Es posible que el informe plantee más preguntas que conteste. Lo que será importante es que guardemos nuestra capacidad para pensar en manera crítica sobre la información que el informe nos presenta. Quiere decir que se debe buscar interna coherencia lógica y “falacias lógicas”.

Otra cosa que se podría hacer es buscar información sobre OVNIS en el Internet. En el Internet se puede conocer a las personas que dicen una gran variedad de cosas y el desafío de pensar críticamente es más difícil. Una vez que se hace bueno en detectar falacias lógicas se puede dejar de lado muchas de las tonterías. Sin embargo no lo recomiendo como la primera práctica.

Una perspectiva en que he tenido muchísimo interés es la del Dr. Steven Greer de The Disclosure Project. En cuanto a todo me interesan mucho las impresiones de otras personas y en particular sobre ese proyecto. Mientras tanto sigo trabajando en algunos puntos de acceso juguetones a las teorías de la vida extraterrestre para nuestro juego de video Jardines de Danu. Por favor no dude en responder para compartir sus pensamientos si lo desea.

Diviértase. Siga Pensando. Manténgase curioso.

2021 May 23 — Aliens in the News

When I was a kid, my dad was a politician. We lived in a small town called Carmel in New York State where the most exciting attribute was a lake where you could go swimming. One day, my friend Tom saw a flying saucer over the lake, but I’ll come back to that topic in a bit.

My dad was a County Legislator on the Democratic Party line from 1985 to 1993. This means he was involved in writing and passing laws that required attention at the local level rather than state or federal, and generally supported government regulation of corporations. For example, how do you protect the lake from pollution amidst a growing population? These things weren’t very interesting to me as a kid; my point is that my family often had an inside scoop on local politics. What was interesting was when the local news reported on things my dad had already told me about. I would check the stories to see if they’d gotten them right and often, they hadn’t. Things I’d heard my dad say to reporters on the phone were misquoted. Details would be missing or just plain incorrect. Due to this, I was skeptical of any stories which I had no inside knowledge about — some more so than others. (To get a sense of what sources are reliable, I advise studying the common logical fallacies: arguments that can make it look like something has been proven when it really hasn’t.) As I got older, I came to understand how news reports twist facts to make things entertaining, or to cater to special interest groups. After all, if they can’t keep people watching then they can’t sell advertisements, and those advertisements are not always limited to the designated commercial breaks.

[Aside: I want to clearly disassociate what I’m saying here from Donald Trump’s manipulation of facts where he calls things “fake news”. A nice thing about being an LLC rather than a not-for-profit organization is that I’m free to take sides politically, thus it’s totally legal when I tell you: I think Donald Trump is a narcissist and a national embarrassment. Logical fallacy is his modus operandi. It’s unfortunate that fans of his such as the Q-Anon crowd have given a bad name to media skepticism and to the search for hidden truths.]

Now zoom out to news stories about things that involve the entire state, the entire country, the entire world... If a local newspaper can botch information about a lake that just a few thousand people care about, what happens when the information is far more complicated and involves billions of people? This takes us to our main topic:

How do we react when mainstream news sources like CNN, NBC, and CBS acknowledge the existence of UFO’s? What about when the Pentagon does, too?

I’ve been following the UFO phenomenon for a long time, starting around the time my friend Tom told me he saw a flying saucer over Lake Carmel. I have a set of experiences, investigative data, and opinions about this, but I want to leave those aside for now. Let’s take the recent news reports as a starting point for thought on the topic, and let’s approach it like mathematicians (that is, logically and with an open imagination).

Fact: according to the news sources linked above, the Pentagon has confirmed the existence of aircraft capable of maneuvers that are not known to be possible for man made aircraft, and which they are unable to identify.

The Pentagon’s confirmation of this is not new. What is new is that it’s showing up in mainstream platforms. Here are some of the many questions that this raises, and some preliminary observations.

Most basically, are the news sources telling the truth about what the Pentagon said? I say yes, since the news sources provide references that check out, and are not known to manufacture references. (To disagree at this level takes us into “fake news” territory, and I’d be curious to know why you’d suspect such a complete fabrication of information.)

Next, is the Pentagon telling the truth that these aircraft exist and maneuver as described? For this, we have the testimony of the Air Force and Navy personnel included in the reports about protocol for verifying a flying object’s existence and trajectory. Some reporters speculate on the footage based on what it looks like to them, but this is a moot point. Of course special effects are capable of producing virtually any video image (including grainy low resolution ones) but what matters here is that people who are trained in interpreting the video and radar data, and who’s ability to do so is relied upon by our military, are saying that the objects are real. Thus, I take the answer here to be another yes.

Then we ask, does the Pentagon know the observed maneuvers to be impossible for man made craft? That part is more difficult to answer because the military does manage confidential information, and the personnel interviewed may not have had clearance to know this. A statement from “the Pentagon” begs the question of who is responsible for the release, what level of clearance they have, and what level of classification the information is at. Looking into who is making the statements, with limited knowledge of these things, I find it hard to answer this question.

Finally, are the ships of extraterrestrial origin? As tempting as it may be to jump to this question, we have very little to go on based on the information given in the references currently being discussed. Once we classify phenomena as “unidentified”, all that does is put it among the vast majority of phenomena, on Earth and otherwise.

Fact: according to the news sources linked above, the Pentagon’s intelligence committee has ordered the director of national intelligence and the secretary of defense to deliver a report on the sightings by next month (2021 June).

It’s possible that this report won’t resolve the ambiguities we already have. It’s possible the report will raise more questions than it will answer. What will be important is that we maintain our ability to think critically about the information presented to us. That means looking out for internal logical consistency and looking out for logical fallacies.

Another thing one might do is go hunting for information about UFO’s on the internet. There you can find people saying a wide variety of things and the challenge of thinking about it critically is far greater. Once you’ve become good at spotting logical fallacies, you might find you can cut through a lot of the nonsense, but I wouldn’t recommend this as a first exercise.

One perspective I’ve been especially interested in is that of Dr. Steven Greer of The Disclosure Project. I’m very interested in other people’s impressions about all of this, and about that project in particular. In the meantime, I continue working on some playful access points to theories in extraterrestrial life for our video game Gardens of Danu. Please don’t hesitate to respond to share your thoughts if you so desire.

Have fun. Keep thinking. Stay curious.

2021 Abril 11 — Las Formas de los Números

Tracy‘s Response
La Respuesta de Tracy

En nuestro último boletín le presenté los siguientes retos:

  1. ¿Por qué cree que los símbolos 1,2,3,4,5,6,7,8,9 tienen las formas que tienen?
  2. Invente sus propios símbolos para el diez y el once que continúan el mismo patrón.

Yo recibí algunas preguntas y respuestas buenísimas sobre este tema. Tracy, de Wingdale, dio la respuesta siguiente al reto (B). Deje que la X represente el diez y el ∂ represente el once (comprenderá mejor más adelante). ¡Su respuesta a (A) es exactamente la misma respuesta que tengo yo a (A), la cual me hace pensar que hemos descubierto algo importante! No veo nada similar en ningún sitio en Internet, así que me encantaría ver más investigación de esta idea. Volveré a esa respuesta al fin de este boletín. Como la última vez, hágame el favor de responder a este correo con cualquier pregunta, comentario o idea pertinente que tenga.

¡Recuerde! Pensábamos en la base doce como una innovación importante para las primeras civilizaciones humanas. La idea es que la base doce lo hace más fácil para contar en tiempo geológico (porque está parecido a la duración de un ciclo lunar), y que el doce lo hace más fácil hacer aritmética mental (porque es divisible por muchos de los némeros menores). Notamos que este era el sistema utilizado por los sumerios, quienes tenían una manera de contar en la base doce usando las manos, quienes construyeron las primeras ciudades humanas de que conocemos (c 4500 BCE) y quienes inventaron la primera lengua escrita de que conocemos (c 3400 BCE). Yo sugerí que el avance desde la base diez hasta la base doce haya sido el salto crucial hacia adelante que les causó su impresionante capacidad para comunicar las matemáticas, y por eso, sus avances tecnológicos.

El Reto B: símbolos nuevos para el diez y el once

Nos interesan símbolos nuevos para el diez y el once para que podamos escribir y hacer cálculos en base doce. Algunos de Uds. preguntaron: “¿Por qué no necesitamos un símbolo nuevo para el doce?” ¡Buena pregunta! Básicamente la razón es la misma razón que explica por qué no tenemos un símbolo para el diez en base 10. Cuando escribimos 10 pensamos en “un diez y cero unos”. Suponga que estuviéramos trabajando en base doce ya tendríamos un lugar para el doce en vez de un lugar para el diez. Por ejemplo se escribirían los números nueve, diez, once, doce: 9, X, ∂, 10. Otro ejemplo: 23 significaría “dos doce más tres unos.”.

En cuanto a otra nota relacionada: &$191;por qué tenemos las palabras once y doce en vez de decir “un diez” y “dos diez”, como las escribimos? Apuesto a que esto proviene de una raíz lingüística en base doce que ya estaba profundamente arraigado antes de que el alfabetismo se extendiera y que esto está relacionado con la manera en que los números recibieron sus formas.

Aparece qué hay una organización totalmente dedicada a volver a la base doce. No la conocía cuando escribí el último boletín. Se llama The Dozenal Society. Un resultado interesante de ellos que leí es que las vidas extraordinariamente largas de algunas de las personas descritas en la Biblia podrían explicarse por pensar en bases alternativas (y no siempre las bases diez o doce) preferidas por los escritores originales. The Dozenal Society escogió un 2 y un 3 invertidos para representar el once y el doce, respectivamente. Sin embargo, no he visto ninguna literatura de la sociedad para explicar por qué los números tienen las formas que tienen. En realidad, me interesa más la cuestión sobre el origen de las formas que me interesa abogar por una reforma global a la base doce. Antes de poner a un lado el resultado de The Dozenal Society sólo sugiero que aprenda las bases alternativas para aumentar su flexibilidad con las matemáticas y se fije en la arbitrariedad de la base diez aparte de contar los dedos.

El Reto A: ¿Por qué los números 1, 2, 3, 4, 5, 6, 7, 8, 9 tienen el aspecto que tienen?

Para comenzar, tenemos una gran sugerencia de Amertah en San Diego: Usar un enfoque transcultural. ¿Cómo escribían estos números otras culturas antes? Remontémonos al comienzo — y, de veras, los albores de la lengua escrita no se acercan al comienzo. ¡Existen marcas de conteo encontradas en huesos remontándose a 35,000 BCE! Y hasta allí se encuentran diferentes técnicas para organizar las marcas. Al avanzar a una lengua más formal se ve una gran variación entre los sistemas sumerio, egipcio, chino y maya. El origen de nuestros símbolos actuales está atribuido a los matemáticos indios en los primeros cientos de años CE. En ellos se comparaban los sistemas de anotación que provinieron de fuentes diferentes y se buscaban puntos de acuerdo. Otro pedazo del rompecabezas, compartido por Victoria, de Brooklyn, es el papel de imprimir y de composición tipográfica en el proceso de estabilizarse las variaciones dibujadas a mano. Ella compartió un artículo extraordinario con video de “Radio France.” Este artículo también desacredita una interpretación falsa de las formas numéricas:

Es una actividad interesante buscar documentos sobre la manera en que las gentes diferentes en lugares distintos dibujaron los números a lo largo del tiempo. Se da cuenta de ciertas formas comunes que no tienen ninguna relación obvia con las cantidades que representan. Pues... ¿por qué esas formas?

Tracy y yo pensamos que provienen del lenguaje de signos en particular del sistema sumerio de conteo manual. Contaban hasta las doce con la mano derecha en la manera siguiente: (se puede encontrar dibujos de esto en Internet.) Para el número 1 toque con el pulgar el segmento más bajo del meñique. Para el 2 toque con el pulgar el próximo segmento arriba. Para el 3, toque con el pulgar la punta del meñique. Para el 4, 5, 6 haga la misma cosa en el dedo anular. Para el 7, 8, 9 lo mismo en el dedo corazón y para la X, ∂, lo mismo en el dedo índice. Ahora, mientras lo hace fíjese en las formas que hacen los dedos. En particular, piense en como podría orientar la mano si estuviera mostrando el número a otra persona. Las semejanzas para los números 4, 5, 6, 7 y 9 son convincentes. (Ampliar esto al diez es un poco delicado. Por esta razón nosotros optamos por la X reconocible pero ∂ sigue el patrón bien.)

Sigo ser curioso por el símbolo 8. Cuando estudiamos los datos transculturales el 8 parece ser uno de los números más consistentes pero no tiene ninguna relación obvia con la cantidad o con el símbolo manual. Tengo otras ideas sobre este fenómeno pero son más extrañas. ¡Me encantaría que me escribiera lo que piensa!

Diviértase. Siga pensando. Manténgase curioso.

2021 April 11 — The Shapes of the Numerals

Tracy‘s Response
Tracy‘s Response

In our last newsletter, I posed the following challenges:

  1. Why do you think the symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 look the way they do?
  2. Invent your own symbols for ten and eleven that extend the pattern.

I received some great questions and answers about this. Tracy from Wingdale gave the following answer to challenge (B). Let X represent ten and let ∂ represent eleven (you’ll see why later). Her answer to (A) happens to be exactly my answer to (A), which makes me think we may be on to something! I see nothing like it anywhere online, so would love to see more investigation of this. I’ll come back to that answer at the end of this letter. Like last time, please feel free to respond to this email with any relevant questions, comments or ideas.

Recall, we were thinking about base twelve as an important innovation for early human civilizations. The idea is that base twelve makes it easier to count geological time (being close to the length of a lunar cycle), and that twelve makes it easier to do mental arithmetic (being divisible by a lot of smaller numbers). We noted that this was the system used by the Sumerians, who had a way of counting in base twelve on their hands, who built the earliest known human cities (c 4500 BCE) and who invented the earliest known written language (c 3400 BCE). I suggested that moving from base ten to twelve may have been the crucial leap forward that led to their impressive ability to communicate mathematics, and hence their technological advances.

Challenge B: new symbols for ten and eleven

We were interested in new symbols for ten and eleven so that we can write and do computations in base twelve. Some of you asked: why don’t we need a new symbol for twelve? Good question! The reason is basically the same as why we don’t have a symbol for ten in base ten. When we write 10, we think of it as “one ten and zero ones ”. If instead we were working in base twelve, we’d have a twelves place instead of a tens place. For example, the numbers nine, ten, eleven, twelve would be written: 9, X, ∂, 10. For another example, 23 would mean “two twelves plus three ones”.

On a related note, why do we have the words eleven and twelve, rather than saying “oneteen” and “twoteen”, like how we write them? I bet that this is from a linguistic root in base twelve that was already deeply entrenched before literacy was widespread, and that this is related to how the numerals got their shapes.

It turns out there’s a whole organization devoted to switching back to base twelve, which I didn’t know about when writing the last newsletter, called The Dozenal Society. An interesting result I read from them is that some of the unusually long life spans of people described in the bible could be explained by accounting for alternative bases (and not always bases ten or twelve) that were preferred by the original writers. The Dozenal Society opted for an inverted 2 and 3 to represent eleven and twelve, respectively, but I didn’t see any literature from them on the topic of why the numbers look the way they do. I’m actually more interested in this question about the shapes’ origins than I am in advocating a global reform to base twelve. Before putting that topic aside, I’ll just suggest learning about alternative bases to build your flexibility with math, and to just be aware of the arbitrariness of base ten beyond counting fingers.

Challenge A: Why do 1, 2, 3, 4, 5, 6, 7, 8, 9 look the way they do?

To start us off, we have a great suggestion from Amertah in San Diego: take a cross-cultural approach. How were the numerals written by other cultures beforehand? Let’s take this all the way back — and the dawn of written language isn’t even close to the beginning. There’ve been tally marks found on bones dating back to 35,000 BCE! And even there, you find different techniques for organizing the marks. Moving up to more formal written language, one sees a lot of variation between the Sumerian, Egyptian, Chinese and Mayan systems. The origin for our current symbols is attributed to Indian mathematicians in the first few hundred years CE, where there was a lot of comparing of notational systems that came in from different sources and looking for common ground. Another piece of the puzzle, shared by Victoria from Brooklyn, is the role of printing and typesetting in stabilizing the hand drawn variations. She shared this great article and video from Radio France, which also debunks a fake interpretation of the numeral shapes:

It’s an interesting activity to look up records of how different people drew the numerals over time in different places. One notices certain common shapes that have no apparent relationship to the quantities they represent. So... why those shapes?

Tracy and I think it comes from sign language, particularly from the Sumerian hand-counting system. They would count to twelve on the right hand in the following way (you can also find pictures of this online). For 1, touch your thumb to the bottom segment of your pinky. For 2, touch your thumb to the next segment up. For 3, touch your thumb to the tip of your pinky. For 4, 5, 6, do the same thing on your ring finger. For 7, 8, 9, the same thing on your middle finger and for X, ∂, twelve, the same thing on your pointer finger. Now, as you do this, look at the shapes your fingers make. In particular, think about how you might orient your hand if you were showing the number to someone else. The similarities for 4, 5, 6, 7, and 9 are compelling. (Extending this to ten is a little awkward, so we opted for the recognizable X, but ∂ follows the pattern nicely.)

I remain curious about the symbol 8. When you look at cross-cultural records, it seems to be one of the more consistent ones, yet bears no obvious relationship to the quantity or to the hand symbol. I have other ideas about this but they are stranger. I’d love to hear from you about what you think!

Have fun. Keep thinking. Stay curious.

2021 February 22 — La Luna y los Manos

Existe una discrepancia entre la astronomía terrestre y los métodos primitivos de recuento. Ese dato fue el primero de varios que me dieron el motivo para entrar en una teoría sobre los antiguos extraterrestres, cosa que no haré aquí, pero si desea hacerlo por su cuenta tiene mi bendición. Yo voy a guardar la mía para otra ocasión. (Revelación completa: quizás no tenga nada que ver con mis ideas del argumento para Los jardines de Danu).

Aquí me he ceñido a los hechos históricos, y he tratado de ser claro sobre dónde me pongo creativo, pero por favor, compruébelos de todos modos; aunque no haya nada más, pueden ser divertidos para investigar.

La astronomía terrestre, en su forma más básica, tiene que ver con contar el número de días en un ciclo lunar (o “lunación”), y el número de lunaciones en un año. En la historia de la humanidad es el método más fundamental para contar el tiempo. Actualmente el internet nos dice que la lunación media es un poco más de 29 y medio días y qué hay un poco menos de 12 y media lunaciones al año. Si se redondea a n&uoacute;meros enteros (lo que hacemos) y se compensa con alguna corrección de errores (por ejemplo, el año bisiesto), esto sigue siendo un poco incómodo para un animal que cuenta con sus 10 dedos.

¿Sabía que 5 dedos cada mano ha sigo el número estandardizado evolutivo antes de que la gente era Homo Sapiens? ¡¿Sabía que si vuelve a nuestros orígenes evolutivos todas las especies de nuestra ascendencia tenían 5 cosas parecidas a dedos por cada mano (o algo parecido a una mano)?! Sigue este fenómeno hasta el período Devónico, hace más de 300.000.000 años. Supongo que el pensar en la base 10 está profundamente arraigado en nuestra neurología. Sin embargo el tiempo de la Tierra tiene una preferencia distinta.

Quizás la capacidad de adaptar nuestros números al cielo esté directamente relacionada con la formación de la civilización. Si desea dominar su medioambiente tiene que ser capaz de predecirlo. (Cuándo serán más claras las noches? ¿Cuándo hará calor o frío? ¿Cuándo subirá la marea, etc.?) Además hay otro beneficio, quizás más coincidente, por contar en 12. Evita el tema menos favorito de todos en la escuela primaria: las fracciones. Se puede dividir 12 por 1, 2, 3 y 4 sin tener que aprender una notación para esos abominables números no enteros. Quizás eso sea suficiente para la vida cotidiana y quizás guardemos nuestros métodos de división más robustos para trabajos más complicados. Mientras tanto, el 12 es amigable, incluso para los niños pequeños hasta que construyan mejor su sentido numérico. Ahora pensemos en el numero 10. El número 10 — el bufón — ni siquiera se puede dividir por 3 sin toparse con una expansión decimal infinita. Tal vez la adaptación de nuestra preferencia biológica por la base 10 a las bases astronómicas 12 y 30 fuera la clave para que tenga éxito Homo Sapiens.

Los hallazgos arqueológicos apoyan esta teoría. La primera civilización estuvo en la región de Sumer, en Mesopotamia, hace unos 6.000 años. Los sumerios tenían tenían como sistemas de contar las bases 12 y 60. El uso de 60 permite aún más divisibilidad que 30. El 60 funciona para los ciclos lunares si contamos los días y las noches como eventos distintos. En adición la evidencia sugiere que tenían un método eficaz para contar de esta manera en las manos.

(¡Investigue esto!) Algo que encuentro especialmente llamativo es que su método utiliza el pulgar opuesto como herramienta para contar con la mano, quizás un precursor del uso de un instrumento de escritura sobre papel. Aumentar el uso del pulgar de esta manera tiene implicaciones profundas. Pasa que los, sumerios también desarrollaron la primera lengua escrita.

Bien, ¿y qué pasa actualmente? Casi todo ha vuelto a la base 10. Dejamos que los ordenadores se encarguen de la mayoría (tal vez a de nosotros nos echamos las manos a la cabeza cuando se trata de las fracciones. Parece que el compartir se ha vuelto problemático ¡hasta un nivel metafísico! Pero fíjese en esto: ¿Que hora es? ¡Qué tamaño tiene un ángulo en un triángulo rectangular? ¡Esos sistemas de la base 12 y la base 60 se remontan a los orígenes de la palabra escrita! Creo que vale la pena pensar en el “¿por qué?”.

Diviértase. Siga pensando. Manténgase curioso.

2021 February 22 — The Moon & Our Hands

There is a discrepancy between Earthling astronomy and primitive counting methods. That was the first of several prompts to enter into an ancient aliens theory, which I will not be doing here, but if you wish to do so on your own, you have my blessing. I’ll save mine for another time. (Full disclosure, this doesn’t have nothing to do with my story ideas for Gardens of Danu.) Here, I’ve stuck to verifiable historical facts, and tried to be clear about where I’m getting creative, but please check me on them anyway — if nothing else, they’re fun things to look up.

Earthling astronomy at its most basic has to do with counting the number of days in a lunar cycle (or “lunation”), and the number of lunations in a year. That’s the most fundamental method of counting time in human history. Now, the internet tells us that the average lunation is a little over 29 and a half days, and that there are a little under 12 and a half lunations per year. If you round those off to whole numbers (which we do), and compensate with some error correction (e.g., leap year), this is still a tad inconvenient for an animal that counts on its 10 fingers.

Did you know that 5 fingers per hand has been the evolutionary standard number since before people were homo sapiens? Did you know that if you trace back our evolutionary origins, every species in our ancestry had 5 fingerlike things per hand-like thing, all the way back to the Devonian Period, over 300,000,000 years ago?! I assume that base 10 thinking is pretty deeply ingrained in our neurology. Yet, Earth time has a different preference.

Perhaps the ability to adapt our numbers to the sky is directly related to the forming of civilization. If you want to master your environment, you need to be able to predict it (When will the nights be lighter? When will it be warm or cold? When will the tide be high? etc). Then there’s another, perhaps more coincidental bonus for counting by 12’s. It avoids everyone’s least favorite topic from elementary school: fractions. You can divide 12 by 1, 2, 3, and 4 without ever having to learn a separate notation for those abominable non-whole numbers. Maybe that’s enough for everyday life, and maybe we save our more robust division methods for more complicated work. In the meantime, 12 is friendly, even to young children as they build their number sense. With 10 — the jerk! — you can’t even divide it by 3 before running into an infinite decimal expansion. Maybe adapting our biological preference for base 10 to the astronomical bases 12 and 30 were the key to getting it together as homo sapiens.

Archeological findings support this theory. The first civilization was in the Sumer region of Mesopotamia, about 6,000 years ago. The Sumerians had base 12 and 60 systems of counting. Using 60 gives even more divisibility than 30 does, and works for lunar cycles if we count days and nights as separate events. Not only that, but evidence suggests they had an efficient method for counting this way on their hands. (Look this up!) Something I find especially striking is that their method uses the opposable thumb as a tool for counting on the hand, perhaps a precursor for using a writing instrument on paper. Upgrading the thumb in this way has profound implications. It happens that the Sumerians also developed the earliest written language.

Okay, so what about today? Nearly everything has gone back to base 10. We let computers handle most (perhaps too many) computations, and most of us throw our hands in the air when it comes to fractions. It seems like sharing has become problematic, on a metaphysical level! But check this out. What time is it? How big is an angle in a regular triangle? Those base 12 and 60 systems trace all the way back to the origins of the written word! I think it’s worth thinking about why.

Subscribers were Invited to Participate in the Following Challenge

I say we bring back base 12. Who’s down? We’ll need two things: a new symbol for ten, and a new symbol for eleven.

To make this more interesting, let’s try to make our new symbols consistent with the symbols we already have for the digits 1 through 9. The hardest part, perhaps, is figuring out why the heck the symbols for 1 through 9 look the way they do in the first place! Actually, nobody knows the answer to this for sure, so use your imagination. I have my own idea, which I’ve never even told anyone publicly. Maybe I’ll tell you next time.

So, to participate, send me your own invented symbols for the numbers ten and eleven. Bonus challenge: give me your reason why you think the symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 look the way they do, and explain why your new symbols continue the pattern. (If sending an image attachment, please keep the file size small.)

Have fun. Keep thinking. Stay curious.

Developing Projects


A Hypothesis Expedition is a multi-part virtual course developed and taught by Dr Joe Quinn. We focus on philosophical questions that stir the imagination and evoke critical thinking about ultimate reality. Students are introduced in an accessible way to math not typically seen in school. Usually these run through institutions such as BEAM and Columbia but other avenues are possible. Contact hello [at] hypothesisnyc.org if interested.

Gardens of Danu

A video game that takes place on the moons of our solar system, where players’ learning is compared to artificial intelligence as they interact with a race of playful but passive-agressive aliens called The Liralunes — a collaboration with software developer Michael Adams, featuring dolls by Tracy Pecarina of 2Ts in a Pod, and music by Dylan Sparrow. Join the mailing list to receive announcements about online playtesting events to be scheduled for 2021.


A picture book in which two characters test the boundaries of logic in an attempt to “Think about nothing”, aimed at imaginative readers, ages 8 to ∞ — a collaboration with Dennis Ryan.


A dark magic-themed tabletop board game featuring an original game mechanic based on concepts from geometric group theory. This is a long-term pet project of Hypothesis Director Joe Quinn, which he is play testing in confidence with small groups of friends. It will be scaled up and released publicly once it’s ready. Details will be posted here when available.

Proyectos en Desarrollo


Una Expedición de Hypothesis es un curso virtual escrito y enseñado por Dr Joe Quinn. Enfocamos en preguntas filosóficas que dan alas a la imaginación y se hacen reflexionar criticamente en la realidad última. Estudiantes tienen la oportunidad de ver temas de matemáticas, de manera accesible, que típicamenta no se ve en las escuelas. Lanzan por instituciones como BEAM y Columbia pero vías independientes también son posibles. Contáctanos a hello [at] hypothesisnyc.org si te interesas.

Jardines de Danu

Un videojuego que tiene lugar en las lunas de nuestro Sistema Solar, en donde el aprendizaje de los jugadores se compara con la inteligencia artificial mientras que interactúan con una raza de alienígenas lúcidos y pasivo-agresivos se llaman Los Liralunes — una colaboración con Michael Adams, que presenta las muñecas de Tracy Ryan de 2Ts in a Pod, y la música de Dylan Sparrow. Únete a nuestra lista de correo para noticias sobre pruebas del juego en línea, que tendrán lugar en 2021.


Un libro de ilustraciones en el que dos personajes prueban los límites de la lógica en el intento de "Pensar en nada," dirigido a lectores de 8 a ∞ años con mucha imaginación — una colaboración con Dennis Ryan


Un juego de mesa tenebroso sobre mágica, que incorpora un conjunto de mecanismos originales creados usando la teoría geométrica de grupos. Este es un proyecto de largo plazo del Director de Hypothesis, Joe Quinn, que está probando en privado con grupos pequeños de amigos. Será dado a conocer públicamente cuando sea listo, y los detalles se publicarán aquí.


A Hypothesis Voyage is a virtual play testing session, conducted live over video chat. These involve interactive digital content, and sometimes common household materials. They give you a glimpse of our games in development, and your feedback helps us continue making them awesome. Sessions are held in both English and Spanish.

Forms to sign up for Voyages will appear on this page. To get notified when we’re booking a new Voyage, sign our mailing list. The intended ages, prerequisites, etc, vary by session and are specified in the invitations.

Past Voyages

Note: in the entries below, the language is fixed to agree with the language of the session.


Un Viaje de Hypothesis es una prueba de juego virtual, hecho por videocharlas. Estos incluyen contenido interactivo digital, y a veces usan materiales comunes en la casa. Te permiten echar un visto a nuestros juegos en desarrollo, y tu comentario nos ayuda seguir haciendo contenido genial. Las sesiones se llevan a cabo en inglés y en español.

Viajes Anteriores

Nota: el texto sobre Viajes específicos está fijado para corresponder con el idioma de la sesión descrita.

2020.11.6 — Viernes Sin Cargo: Maker vs Breaker (esp)

Con participantes de México, exploramos la historia del teorema de cuatro colores. Entonces, enfocamos en un juego desarrollado para hacer más accesible los principios involucrados, y que tiene sus propios problemas no resueltos.

2020.10.10, at Ohio State University BAMM — Pipes and Pentagrams (eng)

For middle and high school students. Division is probably the least popular topic in grade school. Topology can be pretty hard too. But put them together and you get an awesome all-ages game that gets us thinking about one of the most important theorems in graph theory. This also resulted in some awesome post-session worksheets created in collaboration with BAMM.

2020.10.2 — Free Fridays: Maker vs Breaker (eng)

In a fun evening with fellow educators from Italy and the US, we explored the story of The Four Color Theorem, and how we use that as a source for games that teach math as a developing process. We shared methods for online engagement and how we are all rising to the challenge of online teaching, including methods that work better online than they do in the classroom.

2020.9.11, at Ohio State University BAMM — When the Maker Wins (eng)

For faculty and graduate students of the math department. We discussed the roll of artificial intelligence in mathematics, and Thurston’s notion of what constitutes a proof, focusing on the example of the Four Color Theorem. We explored a game invented in the late 80s in order to study that theorem, and played it against each other on our interactive boards via Google Docs. Finally we talked about some open problems related to the game.

2020.9.4 — Viernes Sin Cargo: El Problema de Futurama (esp)

Con una audencia de edades mezcladas de los EEUU, Francia y México. Conductor Doctor Roldan compartió unas diapositivas nuevas y chidos para introducir el problema. Doctor Quinn mangó tableros interactivos por Google Docs. Había varias soluciones e ideas interesantes sobre el problema y pensamos en visitarla de nuevo en el futuro.

2020.8.7 — Free Fridays: The Futurama Problem (eng)

Conductor Doctor Quinn came into this Voyage ready with brand new interactive virtual game boards and more (soon to be regular staples of our Voyages). But the weather was not on our side! Power outages across the northeastern US prevented many from joining, and thus we embarked with just one brave pilot, Luis, who solved The Futurama Problem all on his own!

2020.6.5 — Viernes Sin Cargo: Paradromia (esp)

Viaje de Hypothesis número cuatro, y el primero en español. Gracias a nuestros amigos de Matemorfosis y de Music Math, había mucho interés de México — ¡tuvimos 46 solicitantes para solo 16 asientos! Los pilotos exploraron patrones aritméticos en anules paradrómicas, y también algo de topología, y nos divertimos mucho.

2020.5.2 — Free Fridays: Heads, Tails, Tricks (eng)

The third Hypothesis Voyage was piloted by Juniper and Toby, and new pilots Mason and Kartik. Our pilots solved a coin tossing paradox, then pushed into some tougher territory where the problem got a little too hard for us. Nonetheless, we learned a lot about using trees to analyze games and probabilities, which apply to a broad range of scenarios.

2020.4.24 — Free Fridays: Paradromia (eng)

The second Hypothesis Voyage featured two pilots: Juniper and Toby, and was extremely successful. They conducted paper cutting experiments to study arithmetic patterns in paradromic rings. This lead us unexpectedly into some knot theory and some really fun visual thinking. According to their dad, our pilots continued their experiments for the next week, decorating the house with Möbius strips and other paradromic rings.

2020.4.3 — Free Fridays: Square Deal (eng)

First Hypothesis Voyage ever! Thanks to pilots Ben, Johnny, Juniper and Toby for getting this space ship off the ground. They solved a card game (meaning, figured out how to win the game no matter what the opponent does), then learned how to use the same principle to perform an impressive magic trick. Thanks to parents Jason and Curtis for the great feedback and for helping to make this happen!

Past Projects

2021 July-August; Expedition

Developed and taught the course Geometric Topology: A Tool for Modeling the Universe for Columbia University’s Online Summer Programs for High School Students.

2021 June-July — Expedition

Taught the course Thinking and Problem Solving: A New Look at Mathematics for Columbia University’s Online Summer Programs for High School Students.

2021 February-April — Curriculum development

Taught online courses and developed new activities to foster growth mindsets in the Entry Points program of Bridge to Enter Advanced Mathematics.

2021 February-May — Expedition

Conceived, wrote, and taught the online Saturday enrichment course Infinity for BEAM Next.

2020 September-December — Expedition

Conceived, wrote, and taught the online Saturday enrichment course The Shape of the Universe for BEAM Next.

2020 July-August — Expedition

Developed and taught the new course Geometric Topology: A Tool for Modeling the Universe for Columbia University’s Online Summer Programs for High School Students.

2020 June-July — Expedition

Taught the course Thinking and Problem Solving: A New Look at Mathematics for Columbia University’s Online Summer Programs for High School Students.

2020 May — Expedition

Conceived and wrote the new course Geometric Topology: A Tool for Modeling the Universe for Columbia University’s Online Summer Programs for High School Students.

2020 April — Curriculum development

Developed the Math for Pirates course on logical reasoning for Bridge to Enter Advanced Mathematics.

Hypothesis filed its articles of organization with the State of New York on April 1, 2020.

Proyectos Anteriores

2021 julio-agosto — Expedición

Desarollar y enseñar el curso nuevo Geometric Topology: A Tool for Modeling the Universe de la Universidad de Columbia, Programa en Línea del Verano para Estudiantes de la Preparatoria.

2021 june-julio — Expedición

Enseñar el curso Thinking and Problem Solving: A New Look at Mathematics de la Universidad de Columbia, Programa en Línea del Verano para Estudiantes de la Preparatoria.

2021 febrero-abril — Desarrollo del plan de estudios

Enseñar clases en linea y desarollar actividades para el programa Entry Points de Bridge to Enter Advanced Mathematics.

2021 februaro-mayo — Expedición

Concebir, escribir, y enseñar el curso de enriquemiento Infinity para BEAM Next de Bridge to Enter Advanced Mathematics.

2020 septiembre-diciembre — Expedición

Concebir, escribir, y enseñar el curso de enriquemiento The Shape of the Universe para BEAM Next de Bridge to Enter Advanced Mathematics.

2020 julio-agosto — Expedición

Desarollar y enseñar el curso nuevo Geometric Topology: A Tool for Modeling the Universe de la Universidad de Columbia, Programa en Línea del Verano para Estudiantes de la Preparatoria.

2020 junio-julio — Expedición

Enseñar el curso Thinking and Problem Solving: A New Look at Mathematics de la Universidad de Columbia, Programa en Línea del Verano para Estudiantes de la Preparatoria.

2020 May — Expedición

Concebir y escribir el curso nuevo Geometric Topology: A Tool for Modeling the Universe de la Universidad de Columbia, Programa en Línea del Verano para Estudiantes de la Preparatoria.

2020 abril — Desarrollo del plan de estudios

Escribir un conjunto de propuestas didácticas para BEAM.

Hypothesis depositó sus artículos de organización en el estado de Nueva York en 1 de abril, 2020.


Dennis Ryan

Visual Artist

Dennis has a unique vision and ability to communicate emotion through exquisite control of a wide variety of media. He works in creative and decorative painting as well as fine art. Samples of his work and info for contracting his unparalleled craftsmanship can be found at his website (dennis-ryan.com). Dennis holds a BA in painting from SUNY New Paltz, and has worked with architects, designers and decorators, specializing in watercolor, photoshop, faux finishes, color design, Tromp l’ceil, gilding, ornamental painting, murals, and more.

Dylan Sparrow


Dylan is a NYC based visual artist, musician and writer with an enthralling style that is at once nostalgic and futuristic. His newest digital book, The Dujodians, was released in late 2020 through Tsundoku Books via his website (www.dylansparrow.com) and explores the pathology of conservatism. His hobbies are street hiking, making mixtapes, and playing Quarth. Dylan holds a BA in Illustration from the School of Visual Arts and an MA in Teaching of Writing from LIU Brooklyn.

Érika Roldán Roa

Mathematician, Co-Founder of Hypothesis *

Érika works in the fields of stochastic topology, topological and geometric data analysis, extremal combinatorics, and recreational mathematics. She accompanies her research with gamification and visualization technology, with a passion for bringing people of all ages and backgrounds into the fray. She recently founded BAMM at Ohio State University, and co-founded Matemorfosis and Music-Math. Like Hypothesis, these projects promote and increase public awareness and enjoyment of mathematics and its applications. Within Hypothesis, she volunteers developing and implementing content. Érika holds a Ph.D. in probability and statistics from CIMAT Guanajuato, and has held various teaching and research positions, working for Universidad Juarez del Estado de Durango, ICERM (Brown University), CIMAT Guanajuato, and Ohio State University. She is currently a Marie Skłodowska-Curie Fellow under the EuroTechPostdoc program hosted by the Technical University of Munich and the École Polytechnique Fédérale de Lausanne. She receives funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 754462.

Joe Quinn

Director & Co-Founder of Hypothesis *

Before studying mathematics, Joe was an experimental video and performance artist working in surrealism and anticommercialism. He studied math at Hunter College and earned a PhD in topology from the Graduate Center, CUNY (2016), followed by a research postdoc at the Universidad Nacional Autónoma de México (UNAM) yielding publications on non-Euclidean 3-manifolds. Alongside his pure math pursuits, his interests moved toward innocative math education, teaching and developing curricula for Johns Hopkins Center for Talented Youth, Bronx Community College, Matemorfosis CIMAT, and the National Museum of Mathematics (from which he was fired for his advocacy of more inclusive practices). He continues to teach and write for Bridge to Enter Advanced Mathematics and Columbia University alongside his work for Hypothesis.

Kat Byrne

Artist / Poet

Kat has been writing poetry, drawing, and sculpting since she was a kid. Her poetry has been published by Slope. Kat’s creations are like warm spoonfuls of honey that can cure even the illest of conditions. She holds a BA in Creative Writing from SUNY Purchase, and works as a Barista and Auditor for Oslo Coffee.

Katrina Colletti

Data Analyst

Katrina is a brilliant and detail oriented creator who spends her time pursuing interests such as teaching, scientific research, animal care and rescue, making math fun for the general public, data science for social good, and advocating that everyone looks like a scientist. Most of her science research pursuits have centered around theoretical and experimental high energy physics. Katrina holds an MS in Physics from Texas A&M University. During her time there she was part of the SuperCDMS Collaboration, an experiment aiming to discover and understand the particle nature of dark matter.

Marcel Alexander

Marketing Coordinator

Marcel is known by many for his charismatic, generous and bright approach to life and to the popularization of science. He has been studying innovative marketing techniques since he was a high school student, working in everything from door-to-door sales to online marketing strategies. In his free time, he enjoys sci fi, hanging out with his friends, and composing music. Marcel holds a BA in Classical Composition from Purchase College, and studied orchestration under the tutelage of Richard Milan Simons in Westchester County, NY.

Michael Adams

Software Engineer

Michael is a software engineer based in New York City with a striking skill and passion for outreach mathematics. Before turning to coding, he served for three years in the Peace Corps teaching math in a rural primary school in South Africa. While there, he also helped set up a science centre in the village before spending a year as the Mathematics Program Coordinator at the Unizulu Science Centre in Richards Bay. When he’s not coding or math-ing, he enjoys biking, rock climbing and reading. Michael holds a BA in Mathematics from Bucknell University.

Sylvia Miles


Sylvia is a long time lover of and successful advocate for math and education. As a teacher, she taught math to all ages, from first grade through college calculus. She currently works as a CPA in sunny Southern California, where you can find her hiking or playing math games with her nephew. Sylvia holds a BS in Mathematical and Computational Sciences from Stanford University, and an MEd in Secondary Education and Teaching from UCLA.

Tracy Pecarina

Visual Artist

Tracy is known by many for the beautiful original paintings, drawings, and dolls she creates as presents for her friends’ birthdays. She now forms one half of the mother-daughter art and woven wares team 2 Ts in a Pod (www.2tsinapod.com), based in Pawling, New York. Therein, she works with repurposed and up-cycled yarns and fabrics to create one-of-a-kind dolls, each with their own unique names, stories, and personalities, all looking to find their rightful adoptive homes. Tracy holds a BA in Communications from SUNY New Paltz.

* Hypothesis is a single-member LLC owned and directed by Joe Quinn, founded by Érika Roldán Roa and Joe Quinn, and which works alongside various like-minded artists, contractors, and volunteers.


Dennis Ryan

Artista Visual

Dennis tiene una visión única y la capacidad de comunicar emociones por su control exquisito de una amplia variedad de medios. El trabaja en la pintura decorativa y creativa, y en bellas artes. Muestras de sus obras y información sobre contratar a su artesanía magnífica se puede encontrar a su sitio web (dennis-ryan.com). Dennis tiene una licenciatura en pintura de SUNY New Paltz y ha trabajado con arquitectos, diseñadores y decoradores, especializado en acabados falsos, diseño de colores, Tromp l’ceil, dorados, pintura ornamental, murales y más.

Dylan Sparrow


Dylan es un artista visual, músico, y escritor con base en NYC, con un estilo cautivador que es al mismo tiempo nostálgico y futuristo. Su libro digital más reciente, The Dujodians, se publicaró en 2020 a través de Tsundoku Books por su sitio web (www.dylansparrow.com) y explora la patología de conservatismo. Sus pasatiempos son senderismo urbano, hacer mixtapes, y jugar a Quarth. Dylan tiene un licenciatura en Ilustración de School of Visual Arts y una maestría en Enseñanza de la Escritura de LIU Brooklyn.

Érika Roldán Roa

Matemática, Cofundadora de Hypothesis *

Érika trabaja en el área de topología estocástica, análisis topológico y geométrico de datos, combinatoria extrema y matemáticas recreativas. Acompaña su investigación con tecnología de visualización y ludificación, con la pasión de hacer accesible el gozo de las matemáticas a personas de todas las edades y orígenes. Recientemente fundó BAMM en Ohio State University y también ha sido cofundadora de Matemorfosis y Music-Math. Al igual que Hypothesis, estos proyectos también tienen como objetivo el promover para todo el público el conocimiento de las matemáticas y sus aplicaciones. Actualmente, en Hypothesis, es voluntaria en el desarrollo de contenidos. Érika tiene un Doctorado en probabilidad y estadística del CIMAT Guanajuato y h a ocupado varios puestos de enseñanza e investigación: en la Universidad Juárez del Estado de Durango, ICERM (Brown University), CIMAT Guanajuato y Ohio State University. Actualmente tiene un Fellowship de Marie Skłodowska-Curie en el marco del programa EuroTechPostdoc en la Universidad Técnica de Munich y la École Polytechnique Fédérale de Lausanne. Recibe financiación del programa de investigación e innovación Horizonte 2020 de la Unión Europea en el marco del acuerdo de subvención Marie Skłodowska-Curie N° 754462.

Joe Quinn

Director & Cofundador de Hypothesis *

Antes de estudiar las matemáticas, Joe fue artista experimental de video y performance trabajando con surrealismo y contracomercialismo. Él estudió las matemáticas en Hunter College y obtuvo un doctorado en topología del Graduate Center, CUNY (2016), seguido por puesto como Investigador Postdoctoral en la Universidad Nacional Autónoma de México (UNAM) con publicaciones en el campo de 3-variedades no euclideanos. Mientras que seguir sus actividades en matemáticas puras, se interesó más en la divulgación. Ha enseñado y desarollado cursos extracurriculares al Centro para Jóvenes Talentosos de Johns Hopkin, Bronx Community College, Matemorfosis CIMAT, y al Museo Nacional de Matemáticas (de donde fue despedido por abogó por prácticas más inclusivas allí). Actualmente él enseña y escribe para Bridge to Enter Advanced Mathematics y eColumbia University paralelmente a su trabajo con Hypothesis.

Kat Byrne

Artista / Poetisa


Katrina Colletti

Analista de Datos

Katrina es una creadora brillante y detallista quien pasa su tiempo realizando aficiones como enseñar, investigación científica, rescatar y cuidar animales, mejorar el aspecto público de las matemáticas, ciencia de datos para al bienestar social, y abocar que cada quien se ve como científico. La mayoría de sus investigaciones científicas han tenido que ver con la física de altas energías, tanto teórica como experimental. Katrina tiene una maestría en las físicas de la Universidad de Texas A&M. Mientras que estaba allí, ella fue parte de la Colaboración SuperCDMS, un experimento con el propósito de descubrir y entender la naturaleza particulada de la material oscura.

Marcel Alexander

Coordinador de Mercadeo

Marcel es bien conocido por su enfoque carismático, generoso y lúcido a la vida y a la divulgación de las sciencias. Él ha estudiado maneras innovadoras de mercadotecnia desde la preparatoria, trabajando en todo desde venta a domicilio hasta estrategías de venter en linea. En su tiempo libre, disfrute la ciencia ficción, gastar tiempo con sus amigos, y componer música. Marcel tiene licenciatura en Componer Clásico de Purchase College, y estudió orquestación bajo de la tutela de Richard Milton Simons en Westchester County, NY.

Michael Adams

Educador y Ingeniero de Software

Michael es ingeniero de software afincado en Nueva York con impresionante capaz y pasión por divulgación de las matemáticas. Antes de interesarse en la codificación, sirvió por tres años en el Cuerpo de Paz como maestro de las matemáticas en una escuela primaria en Sudáfrica. Mientras que estaba allí, él ayudó a montar un centre de las ciencias en la aldea antes de dedicar un año como Coordinador del Programa de Matemáticas del Centro de las Ciencias de Unizulu, en Richards Bay. Cuando no está escribiendo código o explorando las matemáticas, le gusta andar en bicicleta, escalar rocas, y leer. Michael tiene una licenciatura en matemáticas de la Universidad de Bucknell.

Sylvia Miles


Sylvia es una amante de y promotor exitosa de las matemáticas y la educación. Como profesora, ella enseñaba las matemáticas a gente de todas las edades, desde primer grado hasta calculo de nivel universidad. Actualmente, ella trabaja como Contable Pública en el sur de California, donde se la puede encontrar haciendo senderismo o jugando juegos matemáticos con su sobrino. Sylvia tiene una licenciatura en Ciencias Matemáticas y Computacionales de la Universidad de Stanford, y una maestría en Educación Secundaria de UCLA.

Tracy Ryan

Artista Visual

Tracy es conocida de muchas personas por sus dibujos, pinturas, y muñecas hermosas y originales, cuales que ella hace como regalos para los cumpleaños de sus amigos. Ahora, como la mitad del equipo de madre e hija se llama 2 Ts in a Pod (www.2tsinapod.com), que vende arte y tejidos, y que tiene su sede en Pawling, New York. Así, ella trabaja con hilos y tejidos readaptados y upcycled para crear muñecas, cada una con su único forma, nombre, historia, y personalidad, y cada uno esperando su hogar adoptivo legítimo. Tracy tiene una licenciatura en comunicación de SUNY New Paltz.

* Hypothesis es una LLC de un solo miembro, propiedad de y dirigido por Joe Quinn, fundado de Érika Roldán Roa y Joe Quinn, que trabaja junto a varios artistas, contratadores, y voluntarios afínes.


We welcome and greatly appreciate any donations. With your help, we strive to provide affordable access to our content for as many people as possible.


Agradecemos y apreciamos mucho cualquier donación. Con su ayuda, nos esforzamos por proporcionar acceso económico a nuestro contenido a tantas personas como sea posible.

Past Donations

2021 February 11 — $100 USD

2020 December 8 — $700 USD

2020 October 28 — $100 USD — “Looking forward to seeing your initiative grow. It’s needed.”

Donaciones Anteriores

2021 febrero 11 — $100 USD

2020 diciembre 8 — $700 USD

2020 octubre 28 — $100 USD — “Looking forward to seeing your initiative grow. It’s needed.”