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This seems like an extension of Colin McNamara's post a while back, which Eric Waldstein is quietly referencing by copying the two of us: https://www.yammer.com/bhpteachercommunity/#/Threads/show?threadId=493899391

I'm also reminded of some of the simple examples that Warren Weaver and John Robinson Pierce presented shortly after the publication of Claude Shannnon's seminal work "The Mathematical Theory of Communication" which, because it underpins ALL of the modern day communications revolution (digital communication, computers, satellites, cell phones, etc.) since the 1940's, is often cited (along with religious texts like the Bible, the Koran, etc.) as one of humanity's most influential written works. [http://worrydream.com/refs/Shannon%20-%20A%20Mathematical%20Theory%20of%20Communication.pdf]

Shannon had previously taken George Boole's new "algebra" from the late 1800's (now known as Boolean Algebra, which underpins most of modern logic) and applied it to electronic circuits. Though somewhat technical most advanced high school algebra students should be able to read and understand most of Claude Shannon's MIT master's thesis, which itself is often cited as one of the most influential theses ever written. [http://www.cs.virginia.edu/~robins/Shannon_MS_Thesis.pdf]

In any case, Pierce in particular does some simple exercises relating to language in his book "An Introduction to Information Theory: Symbols, Signals and Noise" [http://www.amazon.com/gp/product/0486240614/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0486240614&linkCode=as2&tag=bighistory-20&linkId=ITZN6S4HHWRWDZZB] Amongst a bevy of interesting topics, he has a chapter on "Language and Meaning" as well as examples of the built in redundancy of languages and "error correcting" which mathematically allows us to have crossword puzzles as word games.

This also to some extent, underpins our ability to look at the following paragraph and understand what it says. All the letters have been jumbled (mixed). Only the first and last letter of ecah word is in the right place:

I cnduo't bvleiee taht I culod aulaclty uesdtannrd waht I was rdnaieg. Unisg the icndeblire pweor of the hmuan mnid, aocdcrnig to rseecrah at Cmabrigde Uinervtisy, it dseno't mttaer in waht oderr the lterets in a wrod are, the olny irpoamtnt tihng is taht the frsit and lsat ltteer be in the rhgit pclae. The rset can be a taotl mses and you can sitll raed it whoutit a pboerlm. Tihs is bucseae the huamn mnid deos not raed ervey ltteer by istlef, but the wrod as a wlohe. Aaznmig, huh? Yaeh and I awlyas tghhuot slelinpg was ipmorantt! See if yuor fdreins can raed tihs too.

Pierce's book, while it does have some small amount of math, should be generally readable by most high school students. He also provides a simple model of language in his chapter "A Mathematical Model" which many may find interesting, or be able to pull some interesting examples out of. This particular book is also an excellent example of the intertwining of the ideas of physics, mathematics, engineering, psychology, thermodynamics as well as the ideas of emergence, convergence, and allows for the increased complexity and collective learning that underpins the philosophy of Big History.

 

I've also just run across a cultural related vocabulary-based speech "generator" with a relatively small vocabulary that could also particularly be used for an exercise similar to Chris Scaturo's. https://www.crumbles.co/?crumble=big+history+is+awesome&dictionary=standard&fb_action_ids=10100827035645785&fb_action_types=og.shares

It takes its vocabulary list and allows the user to pick and choose from the short list of words to create their own sentences. These sentences are then "played" by way of short video clips from relatively popular movies/television shows that are strung together in a near natural way. Meant in some ways as a possible internet meme generator, some may find it an interesting/entertaining tool for such an exercise. They have other alternate "vocabularies", for example a Homer Simpson version in which all of the vocabulary is comprised of video clips taken from Homer Simpson scenes of the cartoon "The Simpsons."

(Do skim through the vocabulary as some may find a few words racier than some classrooms may tolerate.)

 

Shannon Reid, It's a bit more involved depending on your background, but over the summer, you might also take advantage of free MOOC's like edX's "The Chemistry of Life" [https://courses.edx.org/courses/course-v1:KyotoUx+001x+2T2015/] which might give you some additional ideas as well as to give you more insight as to how all the material of Big History ties together.

If that course is too involved given your background, you might also find some interesting/useful similar material from The Great Courses via The Learning Company. (For after all, wasn't it Bill Gates listening to Dr. Christian's Big History series via the Great Courses that set what we're all doing in motion?) Keep in mind that you can often find DVDs, CDs, and materials in their series for free at your local library, or you can take advantage of free trial offers on platforms like audible [This one should give you two free audiobooks: http://www.amazon.com/gp/product/B00NB86OYE/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B00NB86OYE&linkCode=as2&tag=bighistory-20&linkId=LWQXKALDLO24JNYN]. I find it easy and entertaining to listen to material like this while jogging or on my morning commute.

 

This is a brilliant exercise!

I have to imagine that once the conceptualization of language and some basic grammar existed word generation was a much more common thing than it is now. It's only been since the time of Noah Webster that humans have been actively standardizing things like spelling. If we can use Papua New Guinea as a model of pre-agrarian society and consider that almost 12% of extant languages on the Earth are spoken in an area about the size of Texas (and with about 1/5th the population of Texas too), then modern societies are actually severely limiting language (creation, growth, diversity, creativity, etc.) [cross reference: http://www.scmp.com/infographics/article/1810040/infographic-world-languages]

Consider that the current extinction of languages is about one every 14 weeks, which puts us on a course to loose about half of the 7,100 languages on the planet right now before the end of the century. Collective learning has potentially been growing at the expense of a shrinking body of diverse language.

To help put this exercise into perspective, we can look at the corpus of extant written Latin (a technically dead language): It is a truly impressive fact that, simply by knowing that if one can memorize and master about 250 words in Latin, it will allow them to read and understand 50% of most written Latin. Further, knowledge of 1,500 Latin words will put one at the 80% level of vocabulary mastery for most texts. Mastering even a very small list of vocabulary allows one to read a large variety of texts very comfortably. These numbers become even smaller when considering ancient Greek texts. [cross reference: http://boffosocko.com/2014/07/05/latin-pedagogy-and-the-digital-humanities/ and http://dcc.dickinson.edu/vocab/vocabulary-lists]

Another interesting measurement is the vocabulary of a modern 2 year old who typically has a 50-75 word vocabulary while a 4 year old has 250-500 words, which is about the level of the exercise.

As a contrast, consider the message in this TED Youth Talk from last year by Erin McKean, which students should be able to relate to: https://www.ted.com/talks/erin_mckean_go_ahead_make_up_new_words

 

For those looking for an interesting summer read(s), I've recently picked up the two volume treatise on political history by noted political scientist Francis Fukuyama with the titles:

*The Origins of Political Order: From Prehuman Times to the French Revolution (Farrar, Straus and Giroux, 2011) [http://www.amazon.com/gp/product/B00457X7VI/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B00457X7VI&linkCode=as2&tag=bighistory-20&linkId=6J5DI7DWGOZGDWFN] and

*Political Order and Political Decay: From the Industrial Revolution to the Globalization of Democracy (Farrar, Straus and Giroux, 2014) [http://www.amazon.com/gp/product/B00IQOFS7M/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B00IQOFS7M&linkCode=as2&tag=bighistory-20&linkId=AVDVZ7OWOLZIBEQS]

The introduction of the first reads almost as if it were being submitted as a major work of big history scholarship as Fukuyama hits on almost every major theme and concept behind big history. Though it only covers human political formation from roughly the early Holocene onward (threshold 6 forward to the present day), it's got a very interesting thesis to help explain the difficulties and complexities of modern-day politics. I'm sure many here may appreciate it if they hadn't heard of these two volumes already.

 

Mathematics and Category Theory for Big History?! @davidgchristian @bighistory @BigHistoryInst

5 min read

The more I read of the introductory chapter of Category Theory for the Sciences by David Spivak, the more I'm sure there is a firm and solid foundation for potentially making mathematics a major pillar of Big History.  

The structural scheme for category theory within mathematics sounds almost like that of the structure of Big History as a whole. If nothing else it screams convergence while making very complex structures much simpler. (Big History in reverse perhaps?)

Cover of Complexity Theory for Scientists

I can't wait to delve further in. Spivak's text, though very mathematical in nature seems to have all the basic set theory (at a high school level), and the introduction indicates that he expects readers to have some facility with linear algebra, but there are no other highly daunting prerequisites.

A few excerpts:

This book extols the virtues of a new branch of mathematics, category theory, which was invented for powerful communication of ideas between different fields and subfields within mathematics. By powerful communication of ideas I mean something precise. Different branches of mathematics can be formalized into categories. These categories can then be connected by functors. And the sense in which these functors provide powerful communication of ideas is that facts and theorems proven in one category can be transferred through a connecting functor to yield proofs of analogous theorems in another category. A functor is like a conductor of mathematical truth.

We build scientific understanding by developing models, and category theory is the study of basic conceptual building blocks and how they cleanly fit together to make such models. Certain structures and conceptual frameworks show up again and again in our understanding of reality. No one would dispute that vector spaces are ubiquitous throughout the sciences. But so are hierarchies, symmetries, actions of agents on objects, data models, global behavior emerging as the aggregate of local behavior, self-similarity, and the effect of methodological context.

Hierarchies are partial orders, symmetries are group elements, data models are categories, agent actions are monoid actions, local-to-global principles are sheaves, self-similarity is modeled by operads, context can be modeled by monads.

The paradigm shift brought on by Einstein’s theory of relativity led to a widespread realization that there is no single perspective from which to view the world. There is no background framework that we need to find; there are infinitely many different frameworks and perspectives, and the real power lies in being able to translate between them. It is in this historical context that category theory got its start.

However, in 1957 Alexander Grothendieck used category theory to build new mathematical machinery (new cohomology theories) that granted unprecedented insight into the behavior of algebraic equations. Since that time, categories have been built specifically to zoom in on particular features of mathematical subjects and study them with a level of acuity that is unavailable elsewhere.

Bill Lawvere saw category theory as a new foundation for all mathematical thought. Mathematicians had been searching for foundations in the nineteenth century and were reasonably satisfied with set theory as the foundation. But Lawvere showed that the category of sets is simply one category with certain nice properties, not necessarily the center of the mathematical universe. He explained how whole algebraic theories can be viewed as examples of a single system. He and others went on to show that higherorder logic was beautifully captured in the setting of category theory... 

In 1980, Joachim Lambek showed that the types and programs used in computer science form a specific kind of category. This provided a new semantics for talking about programs, allowing people to investigate how programs combine and compose to create other programs, without caring about the specifics of implementation. Eugenio Moggi brought the category-theoretic notion of monads into computer science to encapsulate ideas that up to that point were considered outside the realm of such theory.

It is difficult to explain the clarity and beauty brought to category theory by people like Daniel Kan and Andr´e Joyal. They have each repeatedly extracted the essence of a whole mathematical subject to reveal and formalize a stunningly simple yet extremely powerful pattern of thinking, revolutionizing how mathematics is done.

All this time, however, category theory was consistently seen by much of the mathematical community as ridiculously abstract. But in the twenty-first century it has finally come to find healthy respect within the larger community of pure mathematics. It is the language of choice for graduate-level algebra and topology courses, and in my opinion will continue to establish itself as the basic framework in which to think about and express mathematical ideas.

As mentioned, category theory has branched out into certain areas of science as well. Baez and Dolan [6] have shown its value in making sense of quantum physics, it is well established in computer science, and it has found proponents in several other fields as well. 

But to my mind, we are at the very beginning of its venture into scientific methodology. Category theory was invented as a bridge, and it will continue to serve in that role.

 

@TheEconomist on Gangnam Style and Productivity
http://www.economist.com/blogs/graphicdetail/2014/06/daily-chart-1?fsrc=scn%2Ftw%2Fte%2Fbl%2Fed%2Fthehiddencostofgangnamstyle

Often giving students a good idea of the size and scope of historical events can be difficult.

The Economist has a lovely graphic today that equates the number of man hours used ("wasted"?) in watching the music video Gangnam Style on YouTube to the man hours required to build various historical structures like Stonehenge, the Great Pyramid, or Burj Khalifa. Hopefully for many, it will put into high relief something from their daily lives in comparison with societies and cultures far distant in time from their own while also exercising some critical reasoning skills.

The Economist usually has some interesting daily charts that can be interesting to take apart and ask additional questions about. For instance on this one, how might man hours translate into direct cost across each of these disparate time periods? What does this say about the freedoms different societies either enjoyed or didn't? What might this indicate about the "next" potential threshold we reach? Are we possibly not getting to it as quickly as we otherwise might because of base entertainment?

On a smaller time scale, what is the equivalent if an individual student gave up something in their life (texting, video games, television) and instead spent it on something else (studying, for example)? How could one calculate the amount of time it takes to get a Ph.D., for example, and convert that into video gaming time? If one then gave up videogaming, how many Ph.D.s could one earn?