Pathological Numerology

[wafflesex]

I like how dolphins breach with such vivacity

whales breach with grace

sharks breach with power

… then fucking manta rays be like

“there goes Billy fulfilling his dreams”

[onebookisallyouneed]

Question three. Tell us of an experience you have had that you think shows why you would be a good addition to the course?

[onebookisallyouneed]

Dozenal counting

Cara:

This is the system printed in one of the dozenal society's old mailouts - I get the impression they're pretty lucid about setting any system though, and there are others who suggest counting in dozens and grosses.

1-9 as in decimal

X (10) - dek

E (11) - el

10 (12) - do (pronounced like "doe" or "low"

100 - gro

1000 - mo

10,000 - do-mo

100,000 - gro-mo

1,000,000 - bi-mo

1,000,000,000 -tri-mo (etc)

Also: 

.1 - edo

.01 - egro

.001 - emo

.0001 - edo-mo

.00001 - egro-mo

.000001 - ebi-mo (etc)

What I haven't found yet is the names for the numbers between "10" and "100" - they seem to sometimes use a different symbol for 20 as well...

[onebookisallyouneed]

The fact is the world configures items by the dozen because it is a convenient number. Merchants have purveying ware by dozens and grosses for centuries... Some traditional systems are simply smart solutions that have functioned well for centuries because they are optimum.

[onebookisallyouneed]

The world will not likely "convert" to dozenal. Instead, duo-decimal numeration may continue to find use an an auxiliary number base. Duodecimal may find a future application, much like hexadecimal has in the configuration of bits into parcels that facilitate manipulation by human programmers.

[onebookisallyouneed]

The world would be run more efficiently if it were based on dozens rather than tens. Less time would be necessary in educating the young regarding arithmetic and mathematics would thereby be simpler.

[onebookisallyouneed]

1 2 3 4 5 6 7 8 9 X E 10: Advantages & Disadvantages of the dozenal system

Cara:

Advantages

In a decimal system, 10's divisors, 1, 2, 5 and 10, have regular multiplication patterns (i.e. all numbers ending in 0 or 5 are divisible by 5, all ending in 2, 4, 6, 8 or 0 are divisible by 2). Because 12 is divisible by more numbers, more sequences in a dozenal system are simple to learn and understand: 1 - all numbers (same) 2 - all numbers ending in 2, 4, 6, 8, x or 0 3 - all numbers ending in 3, 6, 9 or 0 4 - all numbers ending in  4, 8 or 0 6 - all numbers ending in 6 or 0 10 - all numbers ending in 0 For example, this would mean if we are shown a number ending in 0 like 30 in a duodecimal system we already know it's divisible by 1, 2, 3, 4, 6 and 10.

Even of those not direct divisible of "10", more of the patterns are simpler when learning multiplication tables: 1 - all numbers (same) 2 - all even (same) 3 - 3, 6, 9, 0 repeat (becomes simpler - vs 3, 6, 9, 2, 5, 8, 3...) 4 - 4, 8, 0, repeat (becomes simpler - vs 4, 8, 2, 6, 0, 4...) 5 - no simple pattern: 5, X, 3, 8, 1, 6, E, 4, 9, 2, 7, 0, 5... (becomes more complex - vs 5, 0, repeat) 6 - 6, 0, repeat (becomes simpler - vs 6, 2, 8, 4, 0, 6...) 7 - no simple pattern: 0, 7, 2, 9, 4, E, 6, 1, 8, 3, X, 5 (remains complicated - vs 7, 4, 1, 8, 5, 2, 9, 6, 3) 8 - 8, 4, 0, repeat (becomes simpler - vs 8, 6, 4, 2, 0, 8... 9 - 9, 6, 3, 0, repeat (becomes simpler - vs 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9...) X (10) -  X, 8, 6, 4, 2, 0, X... (becomes more complex - vs 0 only) E (11) - E, X, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, E... (remains same in sense of counting in ones - vs 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1...) 10 (12) - 0s only (becomes simpler - vs 2, 4, 6, 8, 0, 2...) Therefore in a dozenal system only the 5x and 7x tables will be difficult to learn, while almost all the others will become easy or easier. If you remember the simplicity of learning the 10x table vs that of 12 or 9, this could be key.

More of the "natural fractions", i.e. those we use every day such as 1/2, 1/3 are simpler: 1/2   In decimal: 0.5  In duodecimal: 0.6 1/3   In decimal: 0.33333...  In duodecimal: 0.4 1/4   In decimal: 0.25  In duodecimal: 0.3 1/5   In decimal: 0.2   In duodecimal:  0.24972497... 1/6   In decimal: 0.16666...  In duodecimal: 0.2 Although 1/5 becomes more complicated, the advantages of being able to divide up by the others more easily is shown in how much simpler it is to divide up time using our base-12 time system than a decimal clock:

The dozenal society also claim prime numbers' arrangement becomes simpler - you can read their proof if you'd like, it washed over my own sleep-deprived mind.

Disadvantages

While 7 remains similarly complicated to divide, multiply, etc in the dozenal system as opposed to decimal, 5 in this system becomes equally complex, meaning we loose the usefulness 5 has in the decimal system:

"...this seems to imply that a human society using duodecimal will tend to be more "allergic" to factors of five, fifths, and their products than the current decimal civilization is to thirds, sixths, twelfths, etc... I think we would hardly ever encounter anything divided by five or ten in a dozenal civilization, just as sevenfold-ness is rare in decimal civilization. In this way, decimal perhaps makes us better arithmeticians, because we are forced to use transparent totatives" [i.e. we use thirds even though they don't fit so easily into a decimal system]

E (11) also becomes a little more complicated - although as this is a larger number with fewer comparative uses (how often do you need 1/11th of something?) 

[onebookisallyouneed]

The costs of not being able to count

Cara:

An estimated 15 million adults have skills at or below that expected of an 11 year old - 6.8 million at or below that of a 9 year old.

In 2007, 30,022 children left primary school with "very poor" numeracy skills - about 5.8% of the population.

Of all children who require extra support due to being labelled as "special educational needs", the largest group is those with poor numeracy and/or literacy skills

These children are more likely to be truant, and a report in 2001 found that more than half of permanently excluded pupils were in the lowest 2% of population for numeracy skills

Adults with poor numeracy skills are much more likely to be unemployed (e.g. four out of ten "economically inactive" women have poor numeracy skills), while those with numeracy skills above that expected of an 11 year old earn on average 26% more than those with skills below this.

Adults with these poor skills are also more likely to be depressed

There is also a strong link between poor numeracy skills and crime, even when comparing children from similar backgrounds.

Overall the every child counts trust estimates that poor numeracy skills cost the economy £2.4 billion a year, giving the program a £12-£19 return on every pound invested.

[onebookisallyouneed]

MIKE:

This is the original copy of the newsletter that the duodecimal society published in 1960, however, notice how the document says *1174 because they did it by dozenal calculations. This is important because we can reference this actual image when we talk in the film about societies in modern day that still operate under this archaic/radical numeracy. 

[onebookisallyouneed]

Cara: Nationwide programme designed to "catch up" students who struggle with basic numbers and maths - could be good for interviews showing how children are taught to count

[onebookisallyouneed]

Cara: 

Few things from the Babylonian system of counting that Sam posted a link to and that Cathy kept going on about. 

The Babylonians counted in 60s (well, sort of- look at the picture, they kind of used a base-ten structure as well), using two symbols to count. But with no "place holder" i.e. zero some may have been open to be misunderstood

They originally divided the day up into our days, hours, minutes and seconds (24, 60, 60, 60) - we know from experience that these divide up easily (blocks of half hours, blocks of quarters, blocks of fifths, blocks of sixths...) - the fact we still use it shows the advantages of a base-60 system

[onebookisallyouneed]

Maths in China vs Maths in the USA

Cara: 

Cross-country mathematical tests of young students repeatedly show children in countries such as Japan and South Korea (no mention of Welsh kids) out-performing those in English-speaking countries such as the USA. While some of the causes may be put down to differences in culture and schooling systems, many also suggest language is a factor. The authors of the article point to fact that American-born students who also speak Chinese out-perform their monolingual peers.

Some examples are:

Words for shapes - chinese term for triangle is 三角形 (san jiao xing) literally translates as "three corner shape" (triangle means similar in latin, but unless you've time travelled from Rome, how will a four year old know that!?)

Both languages have unique numbers up to ten (i.e. if you know "four" in both there is no way to figure out word/symbol for "five") but after this in chinese the system is simple, e.g. seventeen is "ten seven" and thirty-seven is "three ten seven". Meanwhile, we have all the crap with the teens, plus: "...the English system reverses place value... for 2-digit number names less than 100. Thus, '13' is pronounced "thirteen" rather than "one-ty three" or even "teen-thir"" 

The Chinese system puts focus on there being a base-ten structure since kids are constantly counting in tens, while English system with unique names for each decade ("twenty", "forty") means young learners struggle to see structure of numbers, which also appeared to affect ability in arithmetic 

When learning 'ordinals' (i.e. 3rd, 51st), English students struggle further as there is no clear system, while the Chinese just add prefix "di"

The authors also suggest slightly older workers who speak Chinese are able to do mental arithmetic faster as the words for numbers are shorter than in English (think how long it takes to say "three thousand five hundred and fifty two", you'd have already forgotten the question...

Surveys and tests done by the writers seem to back up this theory. While two-year olds in both countries tested struggled at the same level when learning the first ten numbers, Chinese-speaking students dramatically overtook those who spoke English as they went on to larger numbers, quickly picking up the numbers to 100 at a stage when many english-speakers are still struggling with difficult teens. 

While once learned by both, this may be less of a problem, the authors argue that getting over these extra barriers makes a "stumbling block" for many students as well as delaying them from moving onto more complex ideas.

May, then, make a good argument for a re-haul of English counting system.

Source: Miller, K. F., Kelly, M., Zhou, X. (2004) 'Learning Mathematics in China and the United States: Cross-Cultural Insights into the Nature and Course of Pre-School Mathematical Development'. In Campbell, J. I. D. (Ed.) Handbook of Mathematical Cognition pp. 163-178. Hove: Psycology Press.

[onebookisallyouneed]

MIKE: this is the "ladybird picnic" song that (SAM) posted earlier in the facebook group, which features counting to 12 as the primary block of digits. It's important because it's a classic, and therefore instantly recognisable to an audience, which will help them to subconsciously connect with a more foreign concept. 

[onebookisallyouneed]

Cara:

Video about the Piraha tribe (TURN CAPTIONS ON UNLESS YOU SPEAK GERMAN), who count only one/roughly one (kind of how "a couple" means around two); two, and many. There's an article about the piraha tribe here which covers most of this, but couple of intresting points:

The tribe DO use their fingers to count - but this was "highly inaccurate"; even for small numbers.

When given tests to measure their ability to count, "participants responded with relatively good accuracy with up to two or three items, but performance deteriorated considerably beyond that to 8 or 10 items" - i.e., they had less sense for numbers they had no words for

The writer of the article sums up that: "The piraha's impoverished counting system limits their ability to enumerate exact quantities when set sizes exceeded two or three items... [the experiment allows] us to ask whether humans who are not exposed to a number system can represent exact quantities for medium-sized sets of four or five. The answer appears to be negative"

There's a few articles about tribes like this and most mention some theory by Benjamin Lee Warf, might be worth looking into. 

Source: Gordon, P. (2004) 'Numerical Cognition Without Words: Evidence From Amazonia' Science 306 pp 496-499

[onebookisallyouneed]

Sheik: Hey guys :D I had a flip through Alex's Adventures in Numberland thanks to Amazon's nifty 'Look Inside!' feature, and halfway through remembered this video, and thought you guys might like to see it :D Vihart is a mathemartist who explains mathematical/geometrical concepts in very playful and visual ways (also http://www.youtube.com/watch?v=VIVIegSt81k).  

[onebookisallyouneed]

MIKE: Hey guys, so this is our blog and you can put ANYTHING down on here, it's basically our virtual scrapbook. Sound clips, videos, picture, treatments (ideas), blocking diagrams, screenshots from other films etc etc etc. it can be stuff you've found online or you can upload your own stuff, I know this might seem obvious but I just really want to get a wide variety of material, that when we come to having meetings, we can converse about. Also if you are posting something like a photo/sound/video, then also write in the caption part explaining WHY your blogging it. It doesn't have to be long or complex, just to give the rest of us some idea of the context that your contribution should be viewed with.  make sure that your profile has a picture of you so we know who posts what OR alternatively, if your infamous within your online social circles :P, you can just post whatever it is and put your name at the beginning at the beggining of your description underneath (like what i've done above), so that we can all see who posted that particular thing :)