2001: A Space Odyssey
Arthur Clarke's science fiction novel 2001: A Space Odyssey mentions a black stone stele. People measured it with an ordinary ruler and found that its three-sided ratio was 1:4:9. Measured with more precise instruments, it is still 1:4:9. Human beings have exhausted all their wisdom and tried their best to measure the ratio with the highest precision, and it is still a terrible precision of 1:4:9.
Isn't it just a stone, that scary? Yes, there really is.
If this is true, it means that our human civilization is not on the same level as the civilization that made this stele. It may be similar to how we chase beasts in leaf hides and wield sticks (or we may be chased by beasts), and that civilization has built the atomic bomb.
No matter which physical quantity is measured, there will always be a difference between the measured value and the true value, which is the error. It's a death-defying fact of obsessive-compulsive disorder, but, why?
▲ Do you have obsessive-compulsive disorder?
The first reason: people!
The observer's sensory discrimination ability is limited (bad eyes, hand whimpering, unresponsiveness, etc.), as well as different technical proficiency, which will produce errors in the alignment, leveling and aiming of the instrument. For example, when measuring time with a stop meter, we cannot guarantee that the end of the event and the time the stop meter are pressed are absolutely simultaneous. Like this big brother:
Hands on it...
The second reason: measuring instruments!
The index value of the measuring instrument cannot be infinitely small. And due to various factors, the instrument itself also has a certain error. For example, if you take two rulers (borrow one from the front desk, remember to pay back) and stick their 0 tick marks closely, you will be surprised to find that the tick marks representing 20 cm are slightly staggered.
▲ The scales of the two scale rulers are sometimes not aligned
The third reason: the method of measurement!
For example, if you use a scale ruler to measure the diameter of a coin D, you cannot guarantee that the diameter is measured when you directly measure it, and the measurement of the perimeter L is calculated using the formula, and the selection of the π value will also lead to the error of the final result.
▲Measure the circumference of the coin
[Tearful] Xiaoming: So sad, I can't even measure the real value
[Cool] Daming: Xiaoming, do you know my specific height?
[what] Bob: I don't know, how tall?
[Cool] Daming: 182.8973547cm
[Little applause] Bob: ... I get it, sometimes it doesn't have to be too precise
[Cool] Daming: People's pursuit of precision is endless, but different life and production needs have different requirements for accuracy, such as height, accurate to cm, and then accurate is meaningless
[Make a grimace] Xiaoming: Teacher, do you say your height again?
[Gaze] Daming: 182.... Forgot
Although the error cannot be eliminated, we can reduce the error. The method is very simple, such as the use of sophisticated measuring tools.
▲Use of precision measuring tools
Another example: improving measurement methods.
▲ Improve the measurement method
The skill of the finale is definitely at the end: averaging multiple measurements.
[what] Bob: The results of my four measurements of the length of the same object are 18.43cm, 18.45cm, 18.23cm, 18.46cm.
[Nose picking] Daming: The data 18.23cm is obviously blind, and the wrong data is directly discarded. The remaining three sets of data are averaged.
[what] Bob: The result is 18.44666.... In addition to the whole thing?
[Cool] Daming: Can you eliminate the number of digits after the decimal point and the data in the question! So the result is 18.45cm.
Although the "error" is very similar to the "error" name, it is not the same thing at all. Mistakes can be avoided, such as in the exercises in the previous part, looking for errors:
▲Find the error
Summary of knowledge points (picture version, can be saved)
Epilogue:
1. If we can make/measure something with an accuracy of 0.1 μm, and the other party is already accurate to 0.1 nm, then the other party is at least already dealing with atoms, and we will indeed be crushed.
2. "Space Odyssey" series and "Three-body" series, recommended for science fiction enthusiasts to read.
3. In "Three-Body 2: Dark Forest", Liu Cixin paid tribute to "A Space Odyssey" and described the black stone slab -
More than two centuries ago, Arthur Clark described in his novel 2001: A Space Odyssey a black obelisk left on the moon by an alien super-civilization. ...... Clark writes that in this way, that civilization arrogantly showed its power.
Reference Answer:
Example Question 8: A.
Example Question 9: 26.2; 25.2.
Class!