Duodecimal finger counting

This is a second attempt to explain how to count in base twelve on your fingers.  The former attempt was said to be confusing because it was too "three dimensional".  I don't understand this criticism, so i've redone the video in the possibly vain hope that it's clearer.

The point is this.  We have ten digits on our hands and as a result we use ten symbols for our numbers:  0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.  As a result, we have a number system with at least two drawbacks which make arithmetic harder and lead people to feel that maths as such is more difficult than it really needs to be.  Both of these arise from the awkwardness of the number ten.

Ten divides into two and five, and of course itself and one, and nothing else.  This means that the number of regular patterns in the multiplication table in numbers written using this system is rather limited.  There are the repeating pattern in the five times' table, the even numbers of the twos, the downward counting of the nines, the repetition of the elevens and the adding a zero of the tens.  That's it.

The second problem is associated with decimal fractions.  Just up to ten, the fractions associated with the following numbers can never be exact:  3, 6, 7, 9, 11 and an infinite number of further numbers.  Each of these is recurring:
1/3=0.33333...
1/6=0.166666...
1/7=0.142857142857...
1/9=0.1111111....
1/11=0.09090909...

This makes things difficult unnecessarily.

One suggestion is to use hexadecimal - base sixteen.  This has much to recommend it but i have personally chosen the duodecimal base instead.  Moreover, i would advocate the universal use of the duodecimal system where possible.  This is the system which uses twelve symbols instead of ten, and as a result most recurring decimals and hard-to-discern or absent patterns are eliminated from arithmetic.  Twelve divides into two, three, four and six as well as itself and one.  This gives each of those times tables a pattern.  It also gives eight and nine times tables a pattern because they are multiples of factors.  Eleven has a pattern akin to nine in the decimal system and even thirteen has a pattern.  All that's needed is to use two extra symbols, and for typographical ease i use A and B, though there are other choices.

Another advantage is the absence of recurring "duodecimals".  In this system, 2, 3, 4 and 6 have no recurring digits.  Hence fractions are also easier.

One objection frequently made to this is that we tend to have fewer than a dozen digits on our hands.  This is not a problem because what we do have on our hands is a dozen finger bones.  This video shows how to count using those finger bones, and it is in fact possible to count to 144 using this system, and to do various forms of arithmetic using easy finger manipulations - addition is demonstrated here, but other arithmetic operations are also easier.

Moreover, i believe the decimal number system should be abandoned for weights and measures and money, for the same reason, and replaced with duodecimal.

As it stands, we have a disabling numerical notation that teaches the lie that arithmetic and maths are hard and to be hated and feared.  Get rid of decimal and that fear and hatred will go away.  Do it now.

The Village That Raised Our Children

More splurging today i'm afraid, due to starting this post on the mini-tablet, which rather unhelpfully just saved this locally and i'm now copying.  At least that means this had a first draft for once.

Yesterday i briefly mentioned my slight unease at continuing to see myself as part of the home ed community now that the children are both at college, because now i no longer home educate in the commonly understood sense, although of course i still home educate because everyone does and it isn't even home education and so on, blah blah, you know the spiel.  One possible danger of course is that i could lose touch, to the extent that i was ever in touch in the first place, with approaches apt to appeal to children.  There are, however, a couple of reasons why that might not be so.

One of these is that i may only ever have been in limited touch with the needs of children anyway, and in fact due to my moderate but not total commitment to autonomous education, this could be said to be unnecessary in any case, though a varied life wherein one is able and willing to include children is probably important.  Against this might be set the fact that many children with this way of life spend so little time actually at home as opposed to hanging out or sleeping over at other children's homes or doing other stuff with them that their inclusion in the lives of other children and adults might make this less important.  We have a village which raises children in this community, both physically and virtually present, and we are not just families doing things in isolation unless it either suits us to do so, we are unlucky or we have been artificially isolated by a hostile social climate as engendered by, for example, local authorities scaring people into hiding or insufficient publicity regarding the reality of this approach to parenting.

One of the failures of school is that it severs the connection between adults and children and segregates them.  Part of that severance involves teachers being in loco parentis while being relatively unable to establish a natural rapport with the children, often through no fault of their own.  Now, i of course do offer science, maths and other workshops for children who are not mine, and this is potentially questionable.  It can lead to problems and is in danger of drifting towards schooling, something against which i strive.  However, it differs in various ways from teaching.  I am not waylaid by red tape and bureaucracy, by syllabi or curricula or by fear of bullying from the children.  However, i see this as being part of the village.  I must remain vigilant not to become "teachery", which is a risk in this situation.

One way in which i'm now trying to sidestep this issue is by attempting to participate in education in other ways.  To this end, i am embarking on a concerted effort to make a series of educational YouTube videos.  This project is still in its early stages and i am still learning how to put good videos together, and it is of course "no substitute for hands on" but they will improve and i also plan to link them, for people who are interested, to topic areas in the National Curriculum - it is a fact that some people do pay attention to that and i don't judge them for that although i had little interest in it myself.  For those who are interested, here are the links to the two i've made so far which have not been deleted, both about soap making:

https://www.youtube.com/watch?v=HEUmX7UpZ9w&list=UUa-j3lgC_ThPt9Ggov0yIyA&index=2&feature=plcp

and the second, which is more about the science (and how cheaply soap can be made!):

https://www.youtube.com/watch?v=a1QAgdZ01lo&feature=BFa&list=UUa-j3lgC_ThPt9Ggov0yIyA

The other way in which i'm pursuing education, of course, is through writing books.  I have plans for a number of these.  So far, i've published one:  'You Could've Thought Of That', whose children's edition will soon be available from lulu.com (where the adult edition is already available here:  http://www.lulu.com/shop/mark-a-ure/you-couldve-thought-of-that-a-compendium-of-ideas-which-havent-been-thought-of-yet/paperback/product-20266026.html).  The second one is of course 'Here Be Dragons', a bestiary and atlas which aims both to entertain and inform.  Also, of course i plan to continue the science and maths sessions, and if possible start new ones on other subjects such as classical languages and philosophy if the interest is there, for as long as at least one child wants me to do so.

So what am i saying?  I suppose that you can all rest assured that i will try to make sure i stay in touch with the needs of children, and that i hope you still see me as part of your village