38,000-year-old engravings confirm ancient origins of technique used by Seurat, Van Gogh | NYU News

"A newly discovered trove of 16 engraved and otherwise modified limestone blocks, created 38,000 years ago, confirms the ancient origins of the pointillist techniques later adopted by 19th and 20th century artists such as Georges Seurat, Vincent Van Gogh, Camille Pissarro, and Roy Lichtenstein." inform NYU News.

The 2014 excavations at Abri Cellier
Photo by M. Azéma

“We’re quite familiar with the techniques of these modern artists,” observes New York University anthropologist Randall White, who led the excavation in France’s Vézère Valley. “But now we can confirm this form of image-making was already being practiced by Europe’s earliest human culture, the Aurignacian.”

Pointillism, a painting technique in which small dots are used to create the illusion of a larger image, was developed in the 1880s. However, archaeologists have now found evidence of this technique thousands of years earlier — dating back more than 35,000 years.

The findings appear in the journal Quaternary International. 
http://dx.doi.org/10.1016/j.quaint.2017.02.001

Major discoveries by White and his colleagues–which include images of mammoths and horses–confirm that a form of pointillism was used by the Aurignacian, the earliest modern human culture in Europe. These add weight to previous isolated discoveries, such as a rhinoceros, from the Grotte Chauvet in France, formed by the application of dozens of dots, first painted on the palm of the hand, and then transferred to the cave wall.

Earlier this year, White’s team reported the uncovering of a 38,000-year-old pointillist image of an aurochs or wild cow–a finding that marks some of the earliest known graphic imagery found in Western Eurasia and offers insights into the nature of modern humans during this period. Now, in short order they have found another pointillist image–this time of a woolly mammoth–in a rock shelter of the same period known as Abri Cellier located near the previous find-site of Abri Blanchard.

Abri Cellier has long been on archeologists’ short-list of major art-bearing sites attributed to the European Aurignacian. Excavations in 1927 yielded 15 engraved and/or pierced limestone blocks that have served as a key point of reference for the study of Aurignacian art in the region...

Image and captions/photo credit may be downloaded here.
Read more... 

Source: NYU News

Bon Air Elementary demonstrates tech | Kokomo Tribune

Photo: Caele Pemberton

"The Kokomo School Corporation hosted a digital learning day, allowing parents and community members to tour Bon Air Elementary School to learn how students use technology to work through everyday projects." notes Caele Pemberton, covers education.

Photo: Kokomo Tribune

In one classroom, students worked on talking book reports. One student recorded herself talking about a Junie B. Jones book, which she could play for her teacher or classmates. Other students worked on a math app using their tablets.

In the music classroom, students used wires and robots to figure out how to play different nursery rhymes. One group used wires attached to a digital keypad to figure out how to play “Old MacDonald Had a Farm.” The wires were attached to globs of playdough, and when they touched each glob, it corresponded with a different piano key.

The students worked together, humming the tune over and over again to figure out which globs to press. After several tries, they were able to figure out the correct sequence of keys to press.
Read more... 

Source: Kokomo Tribune

Modern Band Workshop to Help Music Educators Get Kids Rocking | UKNow

Photo: Connie Sapienza

"The University of Kentucky School of Music will host a Modern Band Workshop that teaches methods for getting kids to perform, improvise and compose using popular styles that they know and love including rock 'n' roll, pop, reggae, hip-hop, and rhythm and blues." inform Connie Sapienza, Public Relations Intern at University of Kentucky.

"Modern Band" by Little Kids Rock 


The workshop will run 9 a.m. to 5 p.m. Saturday, March 25, at the College of Fine Arts Building room 22.

“Modern Band” is a new kind of school music program invented by Little Kids Rock, a national nonprofit organization that partners with public school districts to provide classrooms with musical instruments and resources. The organization offers classes that feature guitar, bass, keyboard, drums, vocals and technology at no cost to teachers or school districts. Through their programming, Little Kids Rock not only donates instruments and resources, but also builds lasting programs and children's enthusiasm towards music.

This workshop, organized by UK Assistant Professor of Music Education Martina Vasil, will help music education college students and music teachers learn how to teach popular music to children through primarily informal learning techniques.
Read more...

Source: UKNow (press release) and Little Kids Rock Channel (YouTube)

Five Steps to Seeing the Big Picture of Microlearning | e-Learning Leadership Blog

Photo: Linda Rening

"It doesn’t matter what assessment I do, because a common theme always emerges." says Linda Rening, Senior Instructional Designer.

On the Myers-Briggs Type Indicator® (MBTI®) personality inventory, I scored very highly in “N” (Intuition), which means that I see the big picture first and then the details. (That may seem like a good thing until I’m so busy walking through the forest that I don’t see the tree right in front of me.)

Similarly, on StrengthsFinder 2.0®, my number one strength is “Strategic,” which means I can pull together seemingly disparate pieces of information into a cohesive whole.

As I thought more deeply about those two things (perhaps pulling disparate pieces of information into a whole?), I realized that they are essential characteristics for Instructional Designers. I’m sure many of you reading this blog would score similarly on the assessments should you be moved to take them. 
Either naturally or because we’ve been trained to do it, Instructional Design always starts at the 40,000-foot level. We look at the entire landscape, and then begin to focus on the details within it.

That kind of big-picture thinking is probably what is needed for two of the hottest techniques out there right now: microlearning and serious learning games. Think about microlearning. Without a big picture plan, what is coming to be called “content curation,” we will simply have a hodge-podge of learning objects with no rhyme or reason as to how and when they are put to use. Learners need some guidance to finding the correct microlearning events when they need them, or else “just-in-time” quickly becomes “just-too-late.”

So where do we start? I think we should go up 40,000 feet and take a look at the big picture. Chances are that existing training materials, job aids, resources, and subject-matter experts for almost any topic already exist within your organization. So, how do you go about making sense of all of it? Here are some suggestions based on the work we’ve done with different organizations.
Read more...

Source: e-Learning Leadership Blog

We Can Double Teens' Learning | Education Week's blog > Rick Hess Straight Up

Photo: Rick Hess

This week, Rick is off talking about his forthcoming book, Letters to a Young Education Reformer. Letters won't be officially released until late April, but you can learn more about it here and order an advance copy here.
While Rick is away, we've got an illustrious line-up of guest stars. This week, Ed Jones, head of the Hackable High Schools initiative, will be guest-blogging.

---

Photo: Ed Jones

This week, Ed Jones, leads the Hackable High Schools initiative discusses how technological innovation in education can boost student learning and lead to systemic transformation.
 

Photo: GraphicStock.com

We can double what teens learn through school.

Some of you (most?) just rolled your eyes. I understand. Stagnant PISA scores, potential budget shortfalls, organizational challenges, an "incompetent" education secretary, all that. We'd be lucky to eek out a 10% gain, right?

Before I continue, I'd like to just say thanks so much, Rick, for this chance to spin some tales of unbundled learning and systemic transformation.

If you kept reading this far, you may be among the few who think the opportunity for learning growth is even more than 2x. Yet, let's stick with that; let's imagine it together, at least for this one week.

What would we do with such a gift? How might we make choices about all that new learning? By what means will we prioritize the new knowledge and skills they'll gain? How do we keep equity foremost in mind?

I mean in this exploration no slur on the work of today's educators. On the contrary, they've already performed near magic. While constrained by outdated systems, the larger picture shows they've even introduced significant amounts of new learning.

My niece is now Salutatorian in her rural district, just as I was. However, she will have packed in significantly more learning. Though not particularly a lover of math, she mastered AP Calculus as a junior, while I, with state awards in geometry, struggled with anti-differentiation and other concepts well on into my sophomore year in college.

What, and how, we teach has already greatly improved. We can count, too, the increased maturity in so many ways of a present-day teen vs one of a generation ago. While not all of that added maturity came via school, much did, and we have teachers to thank.
Read more...

Source: Education Week

Mobile-First? Don't Write Off The Tablet | EuroMail

Photo: Sean Hargrave

Sean Hargrave, MediaPost's London Editor argues, "Research shows tablets are as prominent in opening emails as the desktop. The two channels are very much alike, questioning our assumption that it's overwhelmingly a mobile-first market."

Photo: GraphicStock.com

We have all talked about a mobile-first world for a good couple of years. It has always seemed like an observation that splits the market into smartphones and desktop. There's a timely reminder today that this isn't totally accurate.

While the majority of emails in the UK and US are opened on smartphones (51% and 58%), the rest of the market is not desktop-only. There is our old friend, the tablet. 

It's quite a surprise that the latest Movable Ink research shows far more emails are being opened on tablets in the UK than in the US. In fact, a massive one in four emails are being opened on British tablets, compared to 15% in the US. 

If nothing else, then, the research works as a reminder that the power of the tablet should never be forgotten, particularly as it is a slightly bigger sector of the UK market than desktop -- 25% compared to 24%. So if we accept that as many opens happen on tablets as desktop, what does this mean for marketers?

The big difference between each email marketing channel is usually location. The desktop will typically be at work or in the study, perhaps on the laptop on a sofa, but this market is clearly being overtaken by the tablet. Or is it? Perhaps it's the same market? Just the device has changed. I agree with eConsultancy that although people often think about tablets as mobile devices, they're usually anything but. They're effectively slimmed-down laptops that are used on the sofa or dining room table, in the same way as a laptop used to be.
Read more... 

Recommended Reading

Follow on Twitter as @LaurieSullivan

Smartphones Cannibalize Web Site Visits From Other Devices by Laurie Sullivan.

Source: MediaPost Communications

Scientist speaks to ASU students and staff about how math can save species | The State Press

"“I have translated human’s hopes, dreams and fears into algebra,” Conservancy Scientist talks about using math to preserve more endangered species." summarizes Nathan J Fish, The State Press.
   

Hugh Possingham, chief scientist of The Nature Conservancy, speaks to an audience about how math can help save species in the Arizona Science Center in Phoenix, Arizon. 
 Photo: Nathan J Fish | The State Press

Saving one endangered species over another may come down to math. 
 
Hugh Possingham, chief scientist of The Nature Conservancy, spoke to ASU students and staff on

Monday at the Arizona Science Center in Phoenix about his experiences with mathematics and how efficiently allocated funds can be used to benefit nature conservancy.

“I have translated human’s hopes, dreams and fears into algebra,” said Possingham. “If you want to go do something, go save a plant … or you can make up a formula and save 250 species.”

Possingham said there is a finite amount of time, money and recourses that play a factor in choosing which endangered species receives needed funds.

“Everyone has allocation problems … you can never avoid prioritizing things,” he said.

Possingham said one of his systematic designs for conservation planning is to “build a compact and connected system of protected areas that equitably represent all habitats and species while annoying as few other people as possible.”

Possingham said prioritizing which species to focus on saving isn't necessarily a negative thing.

“When I talk about this people say, ‘oh, you’re letting species go, this is triage, you’re giving up on species.’ In a sense it’s not triage, all we can do as environmental scientists and mathematicians is give (governments) a list,” he said. “We don’t triage, we prioritize.”

Possingham said his philosophy is to use math to help conservation efforts of endangered species.

“In conservation, it’s relatively recent that we’ve started to use math. In some cases, people are still a little suspicious of math,” he said, “But let’s face it, who runs the planet? It’s mathematicians.”

“The most important aspect (of my work) is delivering better outcomes for less dollars. It’s all about efficiency and cost effectiveness,” he said.

As chief scientist of The Nature Conservancy, the world’s largest nongovernmental environmental organization, Possingham said he has worked all over the world using applied mathematics to economics to solve conservation problems.

Hugh Possingham - Decision science for marine conservation: planning and monitoring
 


Read more...

Source: The State Press  

Top 3 gadgets for music lovers of 2017 | ABC2 News

Photo: GraphicStock.com

If you've ever wanted to learn an instrument, but thought it would be too time consuming, hard or expensive to learn then this is the story for you. There are new products that will teach you those skills without having to pay a tutor. Donna Ruko has the top three you should check out.

Watch the Video

1.  The ONE Smart Piano 
This piano is so smart that it teaches you without sheet music. You just need and iPad and it shows you what notes to hit. Their app has thousands of songs and games to choose from to make learning fun. There's even a grand piano version with 88 keys and foot pedals. Pick one up for around $300.
Introducing The ONE Smart Piano that teaches you to play
 
Read more...

Source: ABC2 News and The ONE Smart Piano Channel (YouTube)

How music benefits children | The Conversation UK

Photo: Dawn Rose

"Turns out learning a musical instrument really could benefit your child, in more ways than you might think." according to Dawn Rose, Researcher in the Psychology of Music and Dance, University of Hertfordshire. 

Photo: GraphicStock.com

Popular ideas, such as the “Mozart effect” – the idea that listening to classical music improves intelligence – has encouraged the belief that “music makes you smarter”.
This interest in the relationship between musical aptitude on ability and intelligence has been around for some time. But despite these beliefs being pretty widespread, there is still no conclusive evidence to actually prove that listening to certain types of music really can improve your intelligence.

In 1974, music researchers Desmond Sergeant and Gillian Thatcher said that:

All highly intelligent people are not necessarily musical, but all highly musical people are apparently highly intelligent.

And “apparently” is the key word here, because the evidence regarding musical listening in itself is mixed. Research has shown that listening to music shows an improvement in certain kinds of mental tasks. But these are specifically short-term improvements involving “spatial-temporal reasoning” skills – puzzle solving type tasks.

Listening vs playing 
But while listening to music is all well and good, what about actually playing it? Research that focuses on how or if playing a musical instrument can impact on intelligence, often looks at how learning in one area can lead to improvements in other areas – an idea known as “transfer effects”.

This is the idea that learning to play the violin, or the drums, could help children to do better in their spellings or a science project. And this is in part the reason why some parents naturally encourage their children to learn an instrument – because of a belief that it will in some way make them more intelligent.

While some studies have shown how musical training can shape brain development. And that improvements in small motor skills and general intelligence have been linked to musical training. A recent review suggests that actual evidence supporting this idea of “transfer effects” is limited at present.

But despite these finds, there is still a wealth of evidence suggesting musical learning is beneficial. And with this in mind, drawing from my experience as a professional musician (drummer), music teacher and performing artist, I decided to investigate the effects of individual musical instrument learning on aspects of cognitive and behavioural development.

I also looked at the impact on “socio-emotional” development, which includes the child’s experience, expression, and management of emotions, as well as the ability to establish positive and rewarding relationships with others. 

All the children who took part in the study had typical school group music lessons, but half of them had also chosen to learn an instrument individually for the first time that year.

The results showed that children who had started individual music lessons developed a better awareness of their “aim” and “force” in relation to their own motor skills as well as improving their “fluid intelligence” – which is the ability to solve new problems, use logic in new situations, and identify patterns.

This suggests that musical instrument learning encourages the development of a physical sense of self in relation to the how we use objects in the world around us, as well as developing a specific kind of intelligence that is used in problem solving. 
Read more...

Source: The Conversation UK

Luther Burbank Center for the Arts on how children benefit from music and theater | North Bay Business Journal

"Did you or someone you love play music or perform in theater as a child?" continues North Bay Business Journal.

Photo: Will Bucquoy

If so, you know first hand about how music and the performing arts enrich the lives of children. It helps with their education and builds self-esteem.

However, some students, schools and families don’t have the means to participate in high-quality arts programs. For students and teachers in this situation, there are programs in the community that are here to help.

IMPACT OF ART AND MUSIC

Before we discuss the programs offered, here are just a few of the things we know about the positive impacts of art and music in the classroom. Music, performing arts and visual arts can:

• Contribute to higher test scores. Researchers are now linking involvement in the arts to better child development and higher student achievement.
• Help build self-esteem. Participation in the arts allows them to grow their self-confidence, developing poise and learning to overcome anxieties.
• Help children understand the multicultural world.
• Help teach self-reliance and collaboration with others in order to reach a goal.

Art in the classroom is of huge importance in a child’s life, and Luther Burbank Center for the Arts is here for the North Bay community to provide all of the resources a school could need to achieve this.

The center’s Education Through the Arts programs are committed to offering teachers and students a variety of programs that support Common Core standards using the arts. The LBC uses the arts to teach core subject matter and enhance understanding and learning. It provides learning experiences that lead to greater academic achievement and the development of self-assurance, creativity and communication skills.

Education Through the Arts provides accessibility for all children, with more than half the students coming from low-to-moderate income families. This program serves Sonoma, Mendocino, Lake, Marin and Napa counties.

Studies show the arts encourage creativity, build community, and improve test scores. LBC’s distinguished education programs serve each and every grade level, while tying into curriculum and meeting Common Core Standards.

Source: North Bay Business Journal

Listening to or learning to play music improves thinking skills | Tyler Morning Telegraph

Photo: Patrice Dunagin

Patrice Dunagin, Texas A&M AgriLife Extension Service says, "Music is powerful. It can change the way we feel. It can even change the way we think. Babies are born with billions of brain cells. In the first three years, brain cells connect with other brain cells. These connections form pathways in the brain. Children who grow up listening to music have strong music pathways."
 

Photo: FreeDigitalPhotos.net

Some of these pathways can change the way we think. Listening to classical music can improve some thinking skills for a short time. Learning to play music improves those thinking skills for even longer.

Music gets our brains ready for certain kinds of thinking. Adults who listen to classical music solve some problems faster, like putting together puzzles. Listening to classical music gets certain brain cells “turned on” and ready to work. This makes it easier to work a puzzle quickly. But our brain pathways do not stay “turned on” for very long - only about an hour.

Learning to play music also helps “turn on” some brain pathways. Children who take music lessons for at least six months can work puzzles more quickly. Music lessons help the brain 
cells make new connections. This helps the brain work better.

Classical music is not the same as other kinds of music. It is more complex. Even three-month-old babies can tell the difference between classical music and other kinds. Classical music helps the brain work faster and think well. It helps the brain solve problems quickly. But other types of music are not bad. Music makes us feel good. And that can make learning easier. 

Read more... 

Source: Tyler Morning Telegraph

Mathematics supports a new way to classify viruses based on structure | Science Daily and The Okinawa Institute of Science and Technology

Photo: The Okinawa Institute of Science and Technology

"Professor Robert Sinclair at the Okinawa Institute of Science and Technology Graduate University (OIST) and Professor Dennis Bamford and Dr. Janne Ravantti from the University of Helsinki have found new evidence to support a classification system for viruses based on viral structure." reports ScienceDaily.

Professor Robert Sinclair,
head of OIST’s Mathematical Biology Unit,
holds a model of a Zika virus.

(from left)
Professor Dennis Bamford and
Dr. Janne Ravantti of the
University of Helsinki

The team developed a new highly-sensitive computational prototype tool, and used it to detect similarities in the genetic code of viruses with similar outer structures, that conventional tools have failed to detect, suggesting that they share a common ancestor. This is not what would have been expected if similarities in the structure of viruses were due to similar environmental pressures -- a phenomenon known as convergence.

The results, published in the Journal of Virology, suggest that viral structure could provide a means of categorizing viruses with their close relatives -- a potentially superior approach to current classification systems. Application of this new structure-based classification system could make it easier to identify and treat newly emerging viruses that cannot easily be classified with existing classification systems.

Viruses are notoriously difficult to classify due to their enormous diversity, high rates of change and tendency to exchange genetic material. They challenge the very concept of a clear distinction between the living and the dead, with many characteristics resembling those of living things, but lacking the ability to reproduce themselves, without the help of a host cell. As such, they do not fit neatly into the established biological classification system for cellular organisms.

Existing classification systems are imperfect and often lead to very similar viruses being categorized as entirely different entities. These systems are also unable to account for the fact that viruses are constantly changing.

If scientists could identify something that viruses are unable to change, it could provide a basis for a more meaningful approach to classification and enable the scientific community to tackle emerging viruses, such as HIV, SARS coronavirus and Zika virus, more easily.

Previously observed similarities between the protein shell, or 'capsid', of viruses -- that encloses and protects the genetic material -- provide a basis for a classification system based on capsid structure, as previously proposed by Prof. Bamford. The few ways in which viruses package themselves are very similar, even between viruses that are likely to have had their common relative more than a billion years ago. Whether this conservation is due to convergence or common descent has been disputed.

For a classification system based on virus capsid structure to be meaningful, the amino acids that provide the building blocks of the capsid proteins should be similar in related viruses. A seeming lack of sufficient amino acid sequence similarity picked up by conventional sequence analysis tools previously undermined capsid structure as a viable way to classify viruses.

Using ideas from mathematics and computer science, Professor Sinclair from OIST's Mathematical Biology Unit worked with scientists at the University of Helsinki to reinvestigate whether the structure-based classification for viral capsids is in fact supported by previously undetected sequence similarity.
 
"The conventional tools for detecting sequence similarity are very fast but they can miss things," says Professor Sinclair. "We used a more classical approach that takes longer but is much more sensitive."
Read more...

Additional resources
Journal Reference:

1. Robert M. Sinclair, Janne J. Ravantti, Dennis H. Bamford. Nucleic and amino acid sequences support structure-based viral classification. Journal of Virology, 2017; JVI.02275-16 DOI: 10.1128/JVI.02275-16 

Mathematics Supports a New Way to Classify Viruses Based on Structure - The Okinawa Institute of Science and Technology
New research supports a structure-based classification system for viruses which could help in the identification and treatment of emerging viruses.

Source: ScienceDaily and The Okinawa Institute of Science and Technology

‘Citizen science’ is the way to encourage critical thinking | Irish Times

Photo: Aoibhinn Ni Shuilleabhain

"Meaningful dialogue about the nature and importance of science and research has already begun." summarizes Aoibhinn Ní Shúilleabháin, assistant professor in the UCD school of mathematics and statistics.

Gorongosa National Park in Mozambique: members of the public use webcams to detail the wildlife captured throughout the park.
Photo: Getty Images

In an age where information is readily available at one’s fingertips, it can be difficult to interpret what material is trustworthy and what facts may be distorted. Peer-reviewed research, and the quality thereof, has become increasingly important and a healthy criticality is required in reading news about research and statistics related to our everyday lives. It is one of the aims of the EU to increase the scientific literacy of citizens in order to support each person in making informed decisions about changes in, for example, society, politics, environment and education. Our new Junior Cycle science curriculum has paralleled this goal in aiming to support students “to make informed decisions about many of the local, national and global challenges and opportunities they will be presented with”.

An important part of scientific literacy is a familiarity with the nature of science – appreciating how scientists work and how scientific ideas are modified over time. In finding out what constituted the smallest building blocks of nature, JJ Thomson had proposed the pudding model of the atom and it was not until 1911 that Rutherford established that the atom was, in fact, mostly empty space. From the 17th century, Newton’s laws of gravity were upheld as fundamental laws of nature until Einstein’s theory of relativity demonstrated their limitations. Contrary to commonly-held views on science, science is not a pre-ordained structure of ready-made facts but rather a collective body of knowledge which is constantly being refined and reviewed. One way of developing an understanding of the nature of science is through participation in “citizen science”.

Read more...

Source: Irish Times

Wichita State hosting ‘Math Circle’ sessions for fifth- through eighth-graders | Wichita Eagle

Follow on Twitter as @SuzanneTobias

"Wichita State University is offering free math, statistics and physics lectures for fifth- through eighth-graders most Sundays through April. Each “Math Circle” lecture, discussion or activity is led by a WSU professor. They are 2 to 3 p.m. Sundays through April 30 in 372 Jabara Hall." inform Suzanne Perez Tobias, Education reporter for The Wichita Eagle and @kansasdotcom.

Photo: Brian Corn

WSU’s Math Circle gives students the chance to meet with math professionals in an informal setting to work on interesting problems or topics in mathematics, university officials said. The goal is to get students excited and passionate about math.

For more information or to register, visit www.wichita.edu/MathCircle or e-mail mathcircle@math.wichita.edu.

Source: Wichita Eagle

“God’s Number”: The Origins of One | Ancient Origins

Photo: Luis Teia

"According to Plotinus (Greek philosopher of the 3rd century AC), ‘One’ is the ultimate reality and source of all existence (Yael, 2006). Philo of Alexandria (Jewish-Egyptian philosopher born during the 1st century BC) regarded the number one as God's number, and the basis for all numbers ("De Allegoriis Legum," ii.12 [i.66])." inform Luis Teia, author of the book " X3+Y3=Z3: The Proof " - a book that presents the mathematical and geometrical proof of the Pythagoras' theorem in 3D. He is a passionate scientist, mathematician, writer and free-thinker. 

Mathematical symbols - Representational image only (public domain)

Like all truths, the fundamental nature of One is recurrent in time. An example is the evolution of the written sign 1. As the picture below shows, it started with a horizontal line used by the Indians, and mutated and evolved until it recurred again as a line, this time vertical. The quest for the meaning of One is ongoing still today. For example, in the beginning of last century, the mystic mathematical genius Ramanujan believed that all units emerge from a product between zero and infinity (Saymal and Ravi, 2016). And in this matter, who are we to question the man who knew infinity.

The Beginning
The more one wonders about something, the more one tends to question the foundations of knowledge. Our limitation is first and foremost our foundations. How did the ancients define One? How does a child acquire the concept of unity? These questions are not dissimilar. The concept of one or unit emerges from repetition. Without a recurring pattern, there could be no unit. If the universe was never repetitive, patterns would not exist, and neither would our ability to categorize and analyse our surroundings. There is an underlying universal gear that drives all creation. From reality, an entity emerges when our brain acknowledges both the existence of a pattern, and its disappearance. For example, the pattern of an apple repeats itself in the next apple. Conversely, it disappears in the space surrounding the apples. That is to say, our mind creates an invisible border that delimits an inside (the pattern, the apple, which typically is red or green with a round type of shape, and a little branch exiting from the top) from an outside (the “not” pattern, “not” apple which is for instance the tree, or the ground where the apple fell). This notion of separation between what “is” gave birth to the number 1, and the interaction of different “1”s gave birth to geometry and mathematics.

Life of Fermat 
Fermat was a rogue philosopher and mathematician of the 17^th century. His interest was not in publishing articles, as indeed, he published none. It was his son that made his work known after he passed away. His interest was to discover the unknown. And to that end, he was quite successful. His famous Last Theorem was first discovered in the margin of his copy of an edition of Diophantus, and included the statement that the margin was too small to include the proof (Singh, 2002). No written account was found of this proof. The apparent simplicity of the proof (as suggested by Fermat’s statement) eluded mathematicians for centuries, including great names in mathematics such as Gauss. His sole interest in integers makes one wonder how deep did he go to search for answers. Did he go deep enough to question the meaning of an integer? Did he search for its meaning only with mathematics, or did he expand into geometry? Alas, did a mathematical-geometrical perspective of the meaning of an integer provided him with the tools to solve his (Fermat) last theorem?

Photo: Pierre de Fermat (public domain)

The answer to all things is at the beginning, after all, an entire tree always starts with a tiny seed of knowledge. An example of this is the ternary tree of primitive Pythagorean triples that Dr. Teia showed to be a tree born from the triple (3,4,5) and growing always with the same fundamental movement (Teia, 2016).
Read more...

Source: Ancient Origins