9's favourite resources .. 9 applauds A B
What should every 9 year old and up know about Tim Berners Lee? Vote whether you feel he is one of the 100 most trusted people all children should be taught about at school, as well as any other nominations you'd like us to rank

timbl invented the www

Without his crusading to keep the www an open space accessible by and for everyone, we who collaborate at mapmaking the world's most life critical social projects forecast the cross-cultural chances of sustaining future generations as far as century 22 to be very low.

We have no idea if timbl would rate the compound risks of global abuse (eg lost transparency) of power so highly but other mathematicians and engineers from Einstein to Buckminster Fuller have warned how transforming to a much more connected system (in which every vilage is interlinked with every other around the globe) is a chnage challenge without precedence. Humanity has made messes of much smaller challengers. The inconvenient truth of globlisation system is that if nature or other climactic events compound vicious spins, there comes a stage where the loss of sustainability is irreversible. My father, a leading economics journalist, wrote about this in 1984 (partly as an updated tribute to George Orwell) so it may be that I am biassed but I hate to see people under-estimate compound risks just because they only see the precipice of compound arithmetic after falling over it.

Here's some more from the values most

Q Why do you keep saying everything is so simple?
A Well, because it is basically.

No, honestly...

I want you to know that you too can make new programs which create new fun ways of using computers and using the Internet.

I want you to realize that, if you can imagine a computer doing something, you can program a computer to do that.

Unbounded opportunity... limited only by your imagination.

And a couple of laws of physics.

Of course, what happens with computers is that you have a basic simple idea and then you have to add things on to it for practical reasons. So real-world computer programs can end up with a lot of stuff in them. If they are good, they are still simple inside.

So do you think the Web is basically been a good idea or a bad one?
Some people point out that the Web can be used for all the wrong things. For downloading pictures of horrible, gruesome, violent or obscene things, or ways of making bombs which terrorists could use.

Other people say how their lives have been saved because they found out about the disease they had on the Web, and figured out how to cure it.

I think the main thing to remember is that any really powerful thing can be used for good or evil. Dynamite can be used to build tunnels or to make missiles. Engines can be put in ambulances or tanks. Nuclear power can be used for bombs or for electrical power.

So the what is made of the Web is up to us. You, me, and everyone else.

Here is my hope.

The Web is a tool for communicating.

With the Web, you can find out what other people mean. You can find out where they are coming from.

The Web can help people understand each other.

Think about most of the bad things that have happened between people in your life. Maybe most of them come down to one person not understanding another. Even wars.

Let's use the web to create neat new exciting things.

Let's use the Web to help people understand each other.

Q What did you do when you were a child?

A I grew up in south-west London. I wasn't very good at sports. When I was 11 I went to a school which was between two railway tracks, so I saw lots of trains and started train-spotting. I also had a model railway in my bedroom. It was a long thin layout with a 4-track station in the middle, and on each side pairs of tracks going off into tunnels to actually loop back to each other.

I made some electronic gadgets to control the trains. The I ended up getting more interested in electronics than trains. Later on, when I was in college I made computer out of an old television set. I bought the television from a repair shop down the road for £5 (about $7).

My mother and father were both working with the very early computers when they met. Later on, my mother taught maths in school. They taught me that maths is a lot of fun. (In England, mathematics is "maths", in the USA, "math").

When I went to Oxford University, I studied physics. I thought that science might be more practical than maths, halfway between math and electronics. In fact it turned out to be very special subject all of itself, and fascinating for all that.

Q Can you tell me more about your personal life?
A No, I don't want to - sorry. I like to keep work and personal life separate. What is on the web on this page and my home page is all there is. Please do not email me asking for more information for school projects, etc. Look -- if you had written a program like WorldWideWeb -- which you well might --- would you want everyone to know what you had for breakfast? No, you see? Ok. Thank you for your understanding.

Q But I am doing a project where we have to get "primary" sources, which means I have to A interview the subject. And I'm doing it on you. So I have to interview you.
I'm sorry, I don't have time to talk to everyone individually. Please use these web pages.

Q I'm interested in Math -- what exciting stuff is there we don't do at school?

A Some kids find solving math problems is fun, and like the power of having new techniques, and imaging new math concepts. If you are one of those, and you are wondering what bits of math might be fun to follow up on your own or with friends or friendly adults, here is an attempt to explain some paths which connect together. Some of it is easy, some hard, but honestly which is which for you depends on what your mind happens to grasp, and how well it is explained! These are some of the bits I found interesting. This is NOT an explanation - you will need books and people for that . It is just a sort of list of places you might want to go.

Vectors are fun. Vectors are quantities with direction, like not just how fast something goes but which direction it is going in. They can be written as three numbers instead of one. (The examples in this FAQ will only work is your browser supports MathML, which is rare. If your browser supports MathML, the following will be vertical, not horizonal.)

( 10 2 4 )

Vectors are fun partly because they are very visual. When you write equations using vectors, you define shapes in 3D, and how things move, and so on.

When you've done a bit of algebra, then simultaneous equations are good thing to play with. You don't have to do complicated ones, just look at "linear" equations where you have say 3 equations and 3 variables, say x, y and z.

x + y = 3 x - y = 1 3 y - z = 0

Because you've done vectors, you can visualize each equation as a plane in 3d, and the equations together define a point with a given x, y and z.

Once's you've got the hang of that, look at transformations where a set of linear equations define a new (x', y', z') in terms of any original point (x, y, z).

x + y = x ' x - y = y ' 3 y - z = z '

Two neat things. One is these transformations actually correspond to 3-d transformations such as squashing space or rotating it, or squishing it sideways. This is quite visual, and thinking of the 3-d transformation is sometimes a quick way of doing things with the equations.

Second neat thing: because you've used stacks of 3 numbers as vectors to represent points, you'll be happy representing the numbers in the equations in a 3x3 block called a matrix. This way you can write the transformation as a thing called matrix multiplication. You learn how to multiply matrices.

( x ' y ' z ' ) = ( 1 1 0 1 -1 0 0 3 -1 ) ( x y z )

or just

x' = M x

where the bold letters stand for vectors and matrices. Suddenly all kinds of things fall into place. To make a combined transformation, you just multiply two matrices together. You naturally start wondering about how to undo a transformation, which is finding the inverse transformation, which is finding the inverse of a matrix. And then you realize that this is just the same problem as solving the linear equations you had earlier. So any time you can see how to solve the equations, you can find the inverse matrix. Also, there is a way of working out the inverse of a 3x3 matrix, so you can always solve 3x3 equations (when a solution exists). It is this way everything fits together which makes math fun and powerful.

Another branch you might be interested in is calculus. This is about things changing and moving, to its very connected to physics, skiing, driving cars, flying planes, and so on. So it can also be fun to visualize. When you study calculus, you start off by thinking about how (say) the speed of a ball changes in a particular millisecond, and how its position changes. There is a lot of calculus where you know, say, how something's speed changes with time, and you want to figure out where it gets to. How fast a function changes is another function. Finding it is called differentiating the first function. The inverse is called integrating. Some people find learning and puzzling out how to differentiate and integrate all kinds of functions interesting.

But if you have done vectors and matrices then you can connect that to the ideas of calculus, and you have new powerful mental tools. You can now write equations about the force on something and its acceleration as vectors.

f = m a

says the force (a vector) on something is equal to the acceleration (how much its velocity is changing, another vector) times the mass of the thing. You can figure out how things like spaceships move in 3d space with time.

From there, you can think about values (like density, or pressure, or temperature) which have a single (non vector) value, but a different value in each place. You can think about how those values change with place. How does the pressure in a swimming pool change with depth? Why? Things which have values all over the place are called fields. Think of the pool being filled with little numbers showing the pressure at that place.

Then you can just put what you know about vectors together with what you know about fields, and think of values which are different in different places and times, and also have direction. They are vectors. Imagine a swimming pool full of little arrows, each arrow showing (by size and direction) how fast and which way the water is moving there. Imagine what happens when someone dives in. These are called vector fields. It turns out that when you do calculus with vector fields, you have really neat little results about how stuff swirls around, about how it squashes (or doesn't), and so on. When you connect how things change with position with how they change with time, then you can show waves happen. And just as it seems that the equations are getting complicated again, then suddenly get simple. It turns out that the differentiation in space can be written as a single "vector operator", called dell and written ? .

This makes all the equations writable in much less space (without even any x's and y's and z's).

One of the significant equations which you get from look the physics of all this is the wave equation, which tell you about sound waves in a swimming pool and even Maxwell's Equations which show that light waves follow from the properties of electricity and magnetism.

Another branch of this which connects to matrices is the eigenvector concept. For any transformation, it turns out there are some vectors which end up being stretched or shrunk but not changed in direction. These are called eigenvectors. It turns out that for lots of interesting problems, the eigenvectors are at right angles to each other, just like the x y and z axes. In fact, if you turn the problem around in your mind, and use the eigenvectors as the axes, then suddenly the problem becomes really simple. The complicated equations untangle and turn into a set of unconnected simple equations. Eigenvectors are finding out how complicated things (like a car suspension) behave. It also turns out that quantum mechanics says that the same equations are used to find out how atoms behave. Also, it turns out that when search engines like Google look at a mass of web links around a topic, the eigenvectors of the link matrix correspond to things the web pages are about, and finding them allows one to find the most relevant page for that topic. So eigenvectors are a really useful concept.

I guess I've used physics as the hook for most of this math, and that is one reason why it is interesting personally for me. If that doesn't interest you so much, then maybe the math of prime numbers will. Check out modulo arithmentic, Euler's theorem, and work your way to the RSA algorithm for public key cryptography. There are lots of other areas of math of course. And lots of books on each. And web sites, I'm sure. But there are some of my suggestions if you are looking for a map of things to look for. The main thing is, to have fun.


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