Where a rule stops working
Every idea has limits. Evidence finds them.
A good rule for a spring
A rule says: each 100 g stretches a spring by 4.9 cm. It has worked well for 1, 2 and 3 masses.
Will the rule work for 7 masses too?
What this lesson covers
The idea
Even successful theories have limits and may fail under new conditions or more precise measurements; scientific ideas are rejected only on evidence, never opinion or belief, and stay open to improvement as new evidence appears.
A good rule for a spring
A rule says: *each 100 g stretches a spring by 4.9 cm.* It has worked well for 1, 2 and 3 masses.
Will the rule work for 7 masses too?
- Yes, it always worked
- Not sure. We should test it
- No, rules never work
Test the rule
Hang more masses. Green dots match the rule. Red dots do not.
No idea is beyond question
Even successful theories have limits and may fail in new conditions or with more precise measurements. Ideas are rejected only on evidence, never opinion or belief, and stay open to improvement.
The rule was not thrown away. We now know it works up to a limit, and we can improve it. This openness to being corrected by nature is a strength of science.
- Masses | Rule says | Observed
- 3 | 14.7 cm | 14.7 cm
- 5 | 24.5 cm | 24.5 cm
- 7 | 34.3 cm | 46.1 cm
Notes
Even successful theories have limits. They are rejected only on evidence, never opinion or belief, and stay open to improvement. No theory is final.
Check yourself
On what basis are scientific ideas rejected or changed?
A very successful rule fails when tested with 7 masses. Is science weak?
When may a successful theory fail?
The rule says 5 masses stretch the spring by 24.5 cm. The observed stretch for 7 masses is 46.1 cm, but the rule says 34.3 cm. By how many cm does the spring stretch more than the rule predicts?
Answer: 11.8 cm
46.1 − 34.3 = 11.8 cm. This mismatch shows the rule’s limit.
- On opinion or belief. Opinions and beliefs do not change science. Evidence does.
- On evidence that does not fit them — correct. Yes. Nature is the judge.
- On who says it loudest. Loud voices are not evidence.
- Yes, science is unreliable. A failure found by testing helps improve the idea.
- No. Finding limits is a strength: the rule can now be improved — correct. Yes. Science corrects itself.
- No, because the observation must be wrong. The observation is evidence and cannot be dismissed without checking.
- Never, once it is successful. No theory is ever final.
- Under new conditions, or when measurements become more precise — correct. Yes. That is how limits show up.
- Only when a scientist is unhappy with it. Feelings do not matter.