Collaborative project - numbers

[TonyM]

Folks,

Join our Collaborative Project - Numbers

Recent collaborative discussions and illustrated some interesting methods and challenges for our community. Words and Numbers.

I thought I would initiate a couple to stimulate activity from the community, join in and contribute if you can otherwise lurkers are fine.

AIM: Develop and improve the ability for people to interrogate large number lists with TiddlyWiki. Allow each number to be annotated with relationships to other numbers.

Inspiration: Whatever your relationship to numbers, every number small or large has its own qualities, do you have a favorite number?, did you know the difference between 0 and one is either 1 or infinity?, Do you know about the beauty in the primes?, and that most of the common numbers 12 in a dozen, 24 hours a day, sixty seconds/minutes in a minute/hour and 360 degrees are all some of the most divisible numbers?

• Let us stick to the counting numbers - integers to start with.
• Let's have a way to annotate numbers with info we can share, manually, programmatically or by import 
• Learn more about numbers
• Build various number related algorithms in Tiddlywiki 
• Identify primes, Squares, special number sequences
• Find what sequences fit within other well known sequences

Large lists present possible performance issues, Numbers can stay in a single data tiddler, or generated in a list until you make a single tiddler once you wish to add information to a given number. Canned search strings that may interest people would also be fun, like reoccuring palindromes..

Where do we start?

• The best way to build a list of numbers and add annotations to each as desired
• How do we best generate them? Look them up?
• How do we annotate numbers (eg if a number has the field prime it is a prime number)
• What code would identify and flag which numbers are prime, can it restart without returning to 1 if you extend you number set further?
• Provide an easy to use way to list numbers with a shared nature, without necessarily re-computing
• How to we share new number annotations and relationships we can add to our own list in a non-destructive way

Lets get started Numberphiles.
A person who is a lover of numbers.

[TonyM]

• I just discovered the intuitive way to generate numbers is with the range operator, it appears this is limited to 9,999 But we do now have the add operator
• Perhaps if we do use a filter to list numbers we should first indicate the number that will be listed (count) so before you hit a button you can decide if you are happy for it to display a large number of items.

[@TiddlyTweeter]

Ciao TonyM

FYI I'm interested in the confluence of social (including historial) counting and calculation.

I find some of the widespread European decimal based (metric) systems poor compared to the other base systems still widely used in UK & USA for measures. 

For instance ...

• inch (12=1) foot (3=1) yard (220=1) furlong
• ounces (16=1) pound (14=1) stone
• nautical miles / knot
• Fahrenheit v Centigrade

Historically there emerged all sorts of mixed-bases for practical calculation, many still in use.

WHY so? is a very interesting question. But comes down to the fact the world is not divided into any particular system, rather the physical attributes of a social context fostered different bases of calculation matched to different ways of "carving it up" conceptually.

Being able to think in different bases is particularly useful. 

Since programmers can often think in other than base-10 (binary, octal & hexadecimal are obvious cases) it might be interesting for them too to play the social aspect, where "formal" calculation hits social praxis?

A good example is "a baker's dozen" (base-13). Its a case where needed utility built on from (base-12) maths. Another example is how nautical miles are related to longtitude & latitude.

This is somewhat different than looking within math itself as a self-referential world with interesting patterns to find & enjoy for their own sake. Also of great merit.

Just thoughts.

TT

[@TiddlyTweeter]

TonyM

Further to my last an obvious fact is that outside maths conversion "standards" -- where for instance base-12 counts "... A, B, 10 ..."---a lot of everyday usage is "dual based". For instance "10, 11, 12" inches. And 12 inches IS 1 foot.

This actually corresponds to how most people have counted through history where "the turn" is dual. And counting is in "cycles" that transfer (optionally) to a different base at the "turns". So 3 feet IS 1 yard, but remains 36 inches too etc. As such they are both "based" and "un-based". And you could say "2 foot & 12 inches" and still be understood that its 1 yard.

Just observations

TT

[TonyM]

TT

I have a bit of an obsession with Prime numbers, and wrote a program to list numbers and the number of divisors they had. It was quite illuminating.

My favourite number was the smallest number divisible by 1, 2 , 3, 4, 5, 6, 7, 8,, 9 and 10

I would like to annotate each number with things learned about each number. Thus I think a way to take a function and use it to annotate numbers would be helpful, for example compute the Squares and flag each number tiddler with a field square=squareroot (Previous square).

Overtime one could accrue a great resource. If done to a standard people could share there functions.

Tiddlywiki also provides various ways to display or graph tiddlers.

Regards

Tony