This overlaps other answers but maybe the different phrasing will suit you.

Suppose that it worked as you expected then odd things would happen. Suppose you have $4$kg of radioactive stuff with a half life of $1$ hour. You watch it for $1$ hour and, as expected, $2$kg remains. You expect the rest to go in one more hour. Now, I walk in but don't talk to you. I see $2$kg of stuff so I expect to see $1$kg after the same hour. So, after that hour is there $0$kg or $1$kg? The stuff with need to know who is looking at it and for how long.

Now, we will use the coin analogy. Start with $4$ coins and toss them every hour. Push aside the tails as decayed and throw the remainder after another hour. The most likely case is $4, 2, 1$ but other results are quite likely. Now throw $4000$, you probably won't get exactly $2000$ remaining after the first hour but the relative error will be smaller. By the time that you get to realistic quantities, e.g. $1$ mole which is $6 \times 10^{23}$ atoms, the difference from $3\times 10^{23}$ after one hour will be too small to measure. This time, the stuff does not need to know who is looking or for how long. Also, each atom does not need to know about the others.

This overlaps other answers but maybe the different phrasing will suit you.

Suppose that it worked as you expected then odd things would happen. Suppose you have $4$kg of radioactive stuff with a half life of $1$ hour. You watch it for $1$ hour and, as expected, $2$kg remains. You expect the rest to go in one more hour. Now, I walk in but don't talk to you. I see $2$kg of stuff so I expect to see $1$kg after the same hour. So, after that hour is there $0$kg or $1$kg? The stuff will need to know who is looking at it and for how long.

Now, we will use the coin analogy. Start with $4$ coins and toss them every hour. Push aside the tails as decayed and throw the remainder after another hour. The most likely case is $4, 2, 1$ but other results are quite likely. Now throw $4000$, you probably won't get exactly $2000$ remaining after the first hour but the relative error will be smaller. By the time that you get to realistic quantities, e.g. $1$ mole which is $6 \times 10^{23}$ atoms, the difference from $3\times 10^{23}$ after one hour will be too small to measure. This time, the stuff does not need to know who is looking or for how long. Also, each atom does not need to know about the others.

This overlaps other answers but maybe the different phrasing will suit you.

Suppose that it worked as you expected then odd things would happen. Suppose you have $4$kg of radioactive stuff with a half life of $1$ hour. You watch it for $1$ hour and, as expected, $2$kg remains. You expect the rest to go in one more hour. Now, I walk in but don't talk to you. I see $2$kg of stuff so I expect to see $1$kg after the same hour. So, after that hour is there $2$kg or $1$kg? The stuff with need to know who is looking at it and for how long.

Now, we will use the coin analogy. Start with $4$ coins and toss them every hour. Push aside the tails as decayed and throw the remainder after another hour. The most likely case is $4, 2, 1$ but other results are quite likely. Now throw $4000$, you probably won't get exactly $2000$ remaining after the first hour but the relative error will be smaller. By the time that you get to realistic quantities, e.g. $1$ mole which is $6 \times 10^{23}$ atoms, the difference from $3\times 10^{23}$ after one hour will be too small to measure. This time, the stuff does not need to know who is looking or for how long. Also, each atom does not need to know about the others.

This overlaps other answers but maybe the different phrasing will suit you.

Suppose that it worked as you expected then odd things would happen. Suppose you have $4$kg of radioactive stuff with a half life of $1$ hour. You watch it for $1$ hour and, as expected, $2$kg remains. You expect the rest to go in one more hour. Now, I walk in but don't talk to you. I see $2$kg of stuff so I expect to see $1$kg after the same hour. So, after that hour is there $0$kg or $1$kg? The stuff with need to know who is looking at it and for how long.

Now, we will use the coin analogy. Start with $4$ coins and toss them every hour. Push aside the tails as decayed and throw the remainder after another hour. The most likely case is $4, 2, 1$ but other results are quite likely. Now throw $4000$, you probably won't get exactly $2000$ remaining after the first hour but the relative error will be smaller. By the time that you get to realistic quantities, e.g. $1$ mole which is $6 \times 10^{23}$ atoms, the difference from $3\times 10^{23}$ after one hour will be too small to measure. This time, the stuff does not need to know who is looking or for how long. Also, each atom does not need to know about the others.