 |
GUIDES:
Don, Carolyn, and Bob ACCESSORIES:
- Starter: ShockWave plug-in (easily available on the
web), NetAdventure Estimator Simulation (viewable in web browser)
- Super Challenge: ShockWave plug-in (easily available
on the web), NetAdventure Estimator Simulation (viewable in web browser)
- Mega Challenge: ShockWave plug-in (easily available on
the web), NetAdventure Estimator Simulation (viewable in web browser)
|
 |
A student who was asked for the age of the universe,
responded with "12,000,000,001 years old". The teacher was amazed at the implied
accuracy of the answer. "Are you sure we know it so accurately?" he was asked.
"Of course." came the response, "Last year you said that it was 12 billion
years old, so it is a year older now." Why is this silly?
The point, of course, is that many numbers in science are known only approximately.
When we say the universe is 12 billion years old, we are really saying that it is about 12
billion years old, but it might be more or less. Scientific communications should always
state the expected range, so it would be more accurate to say something like 12±2.3
billion, which means it is likely to be somewhere between 9.7 and 14.3 billion. If a range
is not stated, then you should assume that expected error would be half of the next digit.
Thus 12 billion would be 12±.5 billion, 12.0 billion would be 12.0±.05 billion, and so
on.
You can amaze your friends by learning how to estimate numbers quickly and accurately,
within reasonable ranges. This challenge will teach you some of the secrets to estimating
that many scientists use all the time.
Related Ideas:
- Try your hand at some truly fun estimation problems, called
Fermi Questions! These type of questions are
"... the estimation of rough but quantitative answers to unexpected questions
about many aspects of the natural world. The method was the common and frequently amusing
practice of Enrico Fermi, perhaps the most widely creative physicist of our times. Fermi
delighted to think up and at once to discuss and to answer questions which drew upon deep
understanding of the world, upon everyday experience, and upon the ability to make rough
approximations, inspired guesses, and statistical estimates from very little data."
[Philip Morrison, Letters to the Editor, Am. J. Phys., August 1963, v31n8 p626-627.]
So can you estimate the total number of hairs on your head?
Visit this great web site to learn how to improve your estimation skills at: http://aries.phys.yorku.ca/~rothery/fermi/fermi.faq.html
Practice your skills with the New Jersey Physics Olympics
Fermi Questions and answers at:
http://www.manchestertwp.org/physics/fermi.htm
Test your skills and join a monthly competition at: http://aries.phys.yorku.ca/~rothery/fermi/fermi.contest.html
- How may leaves are in this picture?
Before you announce your answer, are you digging deep enough to answer this question?
Did you:
Look at a small, representative section of the picture and then scale up by the ratio
of the size of your sample to the size of the picture?
You cannot see all the tree's leaves, so did you make an estimate of its total volume
and how that relates to the part of the tree you used to count leaves?
Count the leaves on several of what seem to be typical branches that are similar in
real life to those in the picture, and figure the average number of leaves per branch?
Count or estimate the total number of branches on a similar tree in your local area.
Multiply the number of branches by the average number of leaves per branch to find the
estimated number of leaves in the picture?
- Now try your hand at the NetAdventure Estimator Simulation! Click on Starter for the
easiest, Super for medium, and Mega for the hardest activity.
|
