Read Online 100 Essential Things You Didn't Know You Didn't Know by John D. Barrow - Free Book Online Page A
Authors: John D. Barrow
Ads: Link
figures of 7 for 40, an average of 5.71 runs per wicket taken. But Flintoff has the better (i.e. lower) bowling average in the first innings, 5.67 to 5.71.
In the second innings Flintoff is expensive at first, but then proves to be unplayable for the lower-order batsmen, taking 7 wickets for 110 runs, an average of 15.71 for the second innings. Warne then bowls at Flintoff’s team during the last innings of the match. He is not as successful as in the first innings but still takes 3 wickets for 48 runs, for an average of 16.0. So, Flintoff has the better average bowling performance in the second innings as well, this time by 15.71 to 16.0.
Who should win the bowling man-of–the-match prize for the best figures? Flintoff had the better average in the first innings and the better average in the second innings. Surely, there is only one winner? But the sponsor takes a different view and looks at the overall match figures. Over the two innings Flintoff took 10 wickets for 127 runs for an average of 12.7 runs per wicket. Warne, on the other hand, took 10 wickets for 88 runs and an average of 8.8. Warne clearly has the better average and wins the bowling award, despite Flintoff having a superior average in the first innings and in the second innings!
All sorts of similar examples spring to mind. Imagine two schools being rated by the average GCSE score per student. One school could have an average score higher than another school on every single subject when they are compared one by one, but then have a lower average score than the second school when all scores were averaged over together. The first school could correctly tell parents that it was superior to the other school in every subject, but the other school could (also legitimately) tell parents that its pupils scored more highly on the average than those at the first school.
There is truly something funny about averages.
Caveat emptor
.
26
The Origami of the Universe
Any universe simple enough to be understood is too simple to produce a mind able to understand it.
Barrow’s Uncertainty Principle
If you want to win bets against over over-confident teenagers then challenge them to fold a piece of A4 paper in half more than seven times. They’ll never do it. Doubling and halving are processes that go so much faster than we imagine. Let’s suppose that we take our sheet of A4 paper and slice it in half, again and again, using a laser beam so that we don’t get caught up with the problems of folding. After just 30 cuts we are down to 10 -8 centimetres, close to the size of a single atom of hydrogen. Carry on halving and after 47 cuts we are down to 10 -13 centimetres, the diameter of a single proton forming the nucleus of an atom of hydrogen. Keep on cutting and after 114 cuts we reach a remarkable size, about 10 -33 of a centimetre, unimaginable in our anthropocentric metric units, but not so hard to imagine when we think of it as cutting the paper in half just 114 times, a lot to be sure, but far from unimaginable. What is so remarkable about this scale is that for physicists it marks the scale at which the very notions of space and time start to dissolve. We have no theories of physics, no descriptions of space, time and matter that are able to tell us what happens to that fragment of paper when it is cut in half just 114 times. It is likely that space as we know it ceases to exist and is replaced by some form of chaotic quantum ‘foam’, where gravity plays a new role in fashioning the forms of energy that can exist. 4 It is the smallest length on which we can presently contemplate physical reality to ‘exist’. This tiny scale is the threshold that all the current contenders to be the new ‘theory of everything’ are pushing towards. Strings, M theory, non-commutative geometry, loop quantum gravity, twistors . . . all are seeking a new way of describing what really happens to our piece of paper when it is cut in half 114 times.
What happens if we
In the second innings Flintoff is expensive at first, but then proves to be unplayable for the lower-order batsmen, taking 7 wickets for 110 runs, an average of 15.71 for the second innings. Warne then bowls at Flintoff’s team during the last innings of the match. He is not as successful as in the first innings but still takes 3 wickets for 48 runs, for an average of 16.0. So, Flintoff has the better average bowling performance in the second innings as well, this time by 15.71 to 16.0.
Who should win the bowling man-of–the-match prize for the best figures? Flintoff had the better average in the first innings and the better average in the second innings. Surely, there is only one winner? But the sponsor takes a different view and looks at the overall match figures. Over the two innings Flintoff took 10 wickets for 127 runs for an average of 12.7 runs per wicket. Warne, on the other hand, took 10 wickets for 88 runs and an average of 8.8. Warne clearly has the better average and wins the bowling award, despite Flintoff having a superior average in the first innings and in the second innings!
All sorts of similar examples spring to mind. Imagine two schools being rated by the average GCSE score per student. One school could have an average score higher than another school on every single subject when they are compared one by one, but then have a lower average score than the second school when all scores were averaged over together. The first school could correctly tell parents that it was superior to the other school in every subject, but the other school could (also legitimately) tell parents that its pupils scored more highly on the average than those at the first school.
There is truly something funny about averages.
Caveat emptor
.
26
The Origami of the Universe
Any universe simple enough to be understood is too simple to produce a mind able to understand it.
Barrow’s Uncertainty Principle
If you want to win bets against over over-confident teenagers then challenge them to fold a piece of A4 paper in half more than seven times. They’ll never do it. Doubling and halving are processes that go so much faster than we imagine. Let’s suppose that we take our sheet of A4 paper and slice it in half, again and again, using a laser beam so that we don’t get caught up with the problems of folding. After just 30 cuts we are down to 10 -8 centimetres, close to the size of a single atom of hydrogen. Carry on halving and after 47 cuts we are down to 10 -13 centimetres, the diameter of a single proton forming the nucleus of an atom of hydrogen. Keep on cutting and after 114 cuts we reach a remarkable size, about 10 -33 of a centimetre, unimaginable in our anthropocentric metric units, but not so hard to imagine when we think of it as cutting the paper in half just 114 times, a lot to be sure, but far from unimaginable. What is so remarkable about this scale is that for physicists it marks the scale at which the very notions of space and time start to dissolve. We have no theories of physics, no descriptions of space, time and matter that are able to tell us what happens to that fragment of paper when it is cut in half just 114 times. It is likely that space as we know it ceases to exist and is replaced by some form of chaotic quantum ‘foam’, where gravity plays a new role in fashioning the forms of energy that can exist. 4 It is the smallest length on which we can presently contemplate physical reality to ‘exist’. This tiny scale is the threshold that all the current contenders to be the new ‘theory of everything’ are pushing towards. Strings, M theory, non-commutative geometry, loop quantum gravity, twistors . . . all are seeking a new way of describing what really happens to our piece of paper when it is cut in half 114 times.
What happens if we
Similar Books
![Taming Heather [Cariboo Lunewulf 1]](https://fs.dianahicksbooks.com/447568/thumbs/152x264/taming-heather-cariboo-lunewulf-1.jpg)