Hi Lisa and everyone, let's try and address these, I think it would be very helpful for revising the introduction to the handbook.
Haven't fully decided on my three votes yet, but here comes my current personal no. 1:
This picture from Dave Radcliffe is a digraph (directed graph) illustrating the function f(n) = n^2 + 2 mod 1000. More precisely, the little red dots in the picture represent the numbers 0 up to 999, in some order, and the grey arrows show what happens if you take one of these numbers, square it, add 2, and then take the last three digits of the result.
For example, if one starts with the number 125, squaring it gives 15625, and adding 2 gives 15627. Taking the last three digits leaves us with 627. We represent this in the picture by joining the dot numbered 125 to the dot numbered 627 with a grey line whose arrow points towards 627.
There are a lot of other numbers that map to 627 under this function. Any numbers n that leave a remainder of 25 when divided by 50 (i.e., any n with n = 25 mod 50) will have the same property. There are twenty such numbers in the range 0 to 999: 25, 75, 125, and so on, all the way up to 975. Each number n in this list satisfies n^2 + 2 = 627 mod 1000.
What this means is that point corresponding to 627 in this list is one of the five points with twenty incoming arrows, shown near the top of the picture. Another number with twenty incoming arrows is 102: any number n that ends with the digits 10 or 90 (i.e., n = ±10 mod 100) has the property that n^2 + 2 ends in the digits 102. The other three such numbers are 402 (which corresponds to n = ±20 mod 100), 902 (which corresponds to n = ±30 mod 100), and 602 (which corresponds to n = ±40 mod 100).
There are two other striking points in the picture that have even more incoming arrows: forty, in fact. The forty numbers of the form ±5 mod 100 all map to 27, and the forty numbers of the form ±15 mod 50 all map to 227.
Although this may be recreational mathematics, the resulting graph provides an illustration of some other mathematical phenomena, as well as being aesthetically pleasing. One of these is that, if one ignores the directions of the arrows, the graph features a huge connected component that contains most of the vertices. In network theory, this sort of thing is called a giant component. One would expect to see something like this in a model of the connections between individuals in an established social network.
Another feature of the graph is that it has no self-loops; in other words, no arrow connects a point to itself. The reason for this is that the congruence n = n^2 + 2 mod 1000 has no solutions in integers; this in turn follows from the easier observation that n = n^2 + 2 mod 5 has no solutions. In contrast, the function g(n) = n^2 mod 1000 would not have had this property, because g(0) = 0.
This picture was recently posted on Twitter by Dave Radcliffe (@daveinstpaul). I think that he is also the creator of the picture.
Another aesthetically pleasing mathematical object that is generated by repeated squaring and adding is the famous Mandelbrot set: http://en.wikipedia.org/wiki/Mandelbrot_set
Wikipedia on giant components: http://en.wikipedia.org/wiki/Giant_component
There is a graph with a countably infinite set of vertices called the random graph. If its parameters are tuned appropriately, this graph also features a giant component. Here's a post by me from two years ago about the random graph: https://plus.google.com/101584889282878921052/posts/34guwy4ftWX
I have Scrivener on my PC upstairs. The problem is that I have a broken leg which makes getting upstairs to said PC problematic. So, I've been stuck doing everything in Google Docs on my Chromebook.
Recently I became aware of a new Google App called Google Draw. One of the options in Google Draw allows you to create a textbox. You can leave the textbox transparent or paint it a different color. The nice thing about these text boxes is that they are drag and drop. So, you can set them up and organize or reorganize them how you like.
There are many other things Google Draw allows you to do. You can add images and may even be able to use it for some basic mind-mapping. I've only just begun to play with it, but it looks like a good work around if you use index cards and don't have access to Scrivener.
Here's a link to Google Draw:
17 February 2014
Notes on Hangouts - Every 2 weeks is too much. Once a month.
More content, interviews, guests and news.
More interesting and useful.
Soliciting idea -
Make inclusing and wide reaching
Jono in LA at Scale - This weekend
Southern Californa Linux Expo
Global Learning XPRIZE - $15 m open source
Read, write and
54 million have no education access
250 m without basic literacy skills
Collaborate on common components - those should be open source
Talking about this work at open source conferences.
Android Builder Summit
XPRIZE built on Android platform.
Lot of discussions about this prize and think tanks.
Matchmaking drive - easy for people to find a team, skills
Global Learning Design Drive
Voice recognition is likely feature - how would you design that?
Usually in a small venue. A theme set. Competition for using particular pieces of technology.
Explore ways to do this for Global Learning XPRIZE components.
This is an open source software XPRIZE.
Big project. Big piece of software.
Things you would need - such as speech recognition.
No open source platform out there. Proprietary ones.
Storytelling systems. Power management.
Whether you are designer, project manager, you can help.
Reason is to help kids read. So they can open up the world of knowledge, business.
Get people together to solve that problem.
Collaborate and work together.
How we engage developers.
Contributor licence, github getting set up.
Things to help teams.
Lots of small projects which form foundation.
If you are developer and want to play role, come to forum and post message.
We can learn from you and get your experience to drive this forward.
On ground floor. This is brand new.
Not aware of others coming together like this before.
People are fundamentally good. And have a talent to share.
Problems are solved with small groups of people.
Say you want to cure cancer. Perhaps only a few scientists are working on this, using closed data.
New approach is to use open genomic data.
With more eyeballs, all bugs are shallow.
Lots of people looking at problem help get to solutions quicker.
When we can connect skills and expertise to problems, we can get to solutions quicker.
How to connect people to problems?
We don't really know the solution here.
Jono has worked with hundreds and hundreds of people in the software world.
How do we get people actively involved?
Q: Jack Ring
What is the interest in an Android app that can formulate audio output?The emphasis on speech recognition by machine ignores speech recognition by learner, the primary mode of kid learning.
Not of discussion yet.
Festival does text to speech.
Would be valuable to have a discussion about this.
XPRIZE Think Tank
Organize local XPRIZE groups near them
For example, Chicago.
Hear about group. Meet people.
Presentation, guidance. Discussion on how to solve problems.
Compare to TEDx.
Think Tanks about real local communities. Discussion between events.
Oriented toward practical solutions to the world.
"Wouldn't it be great ..." conversations don't help.
Think Tanks about actually doing it.
Make a practical difference.
Process to on-board Think Tanks.
Visit like-minded people in other cities.
How to grow communities in other parts of XPRIZE as well:
Forum currently on Think Tanks and Global Learning
Bring in Oceans, Space
Idea is to have lots of sub-groups.
XPRIZE Alumni community
VP of Prize Operations
Using Discourse forum software.
Phonibet song to teach phonemes challenge
Open source has become the dominant way to build software
Reason: everybody has an opportunity to feed into it.
What other areas could we build engagement.
Collaborative - anyone with skill, talent or time - can make a really practical difference to the world.
Instead of watching TV, make a difference.
British Sugar produces a diverse range of sustainable products, from sugar to electricity and animal feed to biofuel. Each year, next to its Wissington sugar factory in the UK, the company grows over 80 million tomatoes, using waste combustion gases and heat from the factory’s combined heat and power plant (CHP) at its Cornerways Nursery. Carbon dioxide from the CHP plant is pumped into the enormous glasshouse, encouraging plants to grow at twice the normal rate. The glasshouse is also home to over 5,000 bees which pollinate the plants naturally. The glasshouse is the size of ten large football pitches, so the rainwater from such a large roof is used as the main source of irrigation for the tomato plants.
- Goldsmiths College2013 - presentResearcher in Computational Creativity
- PlanetMath.orgBoard Member, present
- Knowledge Media InstituteResearch Assistant, 2013 - 2014
- The Open University2010 - 2014
- New College of FloridaMathematics, 1998 - 2002
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