As we were driving back home from his percussion lesson, Omar (the 12-year old Nadjling) said, "Baba, future does not exist."
"How so?" I replied.
He said, "Well, future is not here, it is unknown, and when it occurs it is present. So, there is only past and present."
This took me by complete surprise and I retorted, "This is an interesting thought and I would have to think about it."
Then, the math connection came when he continued, "The future is undefined and when it is experienced it is not a future; it is the present then." The Physicist in me could not help but think of contrast between the deterministic interpretation of the world by classical Physics versus the quantum mechanical probabilistic approach to physical phenomena. In addition, I thought of the wave function collapse from a "nebulous/combined state" to a definite state once one performs an experiment with elementary particles.
For a kid to hit on an idea such as this is fascinating. So, I encouraged him to jot down such things when he thinks of them in the future.
Afterwards I gave Omar the example of how knowing the current position, velocity, and acceleration of a probe we are sending to Pluto for instance, we can predict its future position, velocity, and acceleration and this is how we are able to get such probes that far and with incredible precision. I was trying to convey the idea of the deterministic nature of classical Physics.
But, before I went far with the idea, he interjected by mentioning the take-home test that he mentioned earlier in our trip and he was going to take when we get back home and said, "I am going to cheat." Alarmed by unethical behavior I was going to start giving him a big lecture but he interrupted by explaining, "I have to do a decay experiment and instead of taking out sixes of dice, I will just take out evens." I said, "Why would you do that?" He replied, "This way the decay rate will be a half." To this I commented, "This is not cheating; this is clever! But, why take out the evens and not the odds?" To which he answered, "Evens have only one prime number." Ok!
Fast forward and Omar is at home. He thought he had 100 dice (the required starting number given in the test directions) around the house but he found only 49. So, he shared with me the following thought, "Would it be ok to just use 49 and whatever I get I divide by 49 and multiply by 100 to make the experiment match a 100-dice roll?" This being a test, I told him that would have to be his decision. Deep inside, the father in me could not help but feel proud of the kid's divergent thinking and resourcefulness. In the end he decided to keep the experiment simple, straightforward, and he used 100 coins.
Omar is lucky that his father knows about math and is willing to give-and-take with him in such musings and I just hope that the many Omars out there would be equally fortunate and benefit from such exchanges with adults (teachers, parents, older siblings, etc.) around them. So, if we (the math/science teachers) are the only adults that kids may get this mental gymnastics opportunity from we must seize it with earnest passion and great patience for it would help them grow as thinkers and flourish as math/science lovers.
Happy Valentines Day & please share musings of your students or your own kids in the comments section.
Thank you and take great care! :-)
"How so?" I replied.
He said, "Well, future is not here, it is unknown, and when it occurs it is present. So, there is only past and present."
This took me by complete surprise and I retorted, "This is an interesting thought and I would have to think about it."
Then, the math connection came when he continued, "The future is undefined and when it is experienced it is not a future; it is the present then." The Physicist in me could not help but think of contrast between the deterministic interpretation of the world by classical Physics versus the quantum mechanical probabilistic approach to physical phenomena. In addition, I thought of the wave function collapse from a "nebulous/combined state" to a definite state once one performs an experiment with elementary particles.
For a kid to hit on an idea such as this is fascinating. So, I encouraged him to jot down such things when he thinks of them in the future.
Afterwards I gave Omar the example of how knowing the current position, velocity, and acceleration of a probe we are sending to Pluto for instance, we can predict its future position, velocity, and acceleration and this is how we are able to get such probes that far and with incredible precision. I was trying to convey the idea of the deterministic nature of classical Physics.
But, before I went far with the idea, he interjected by mentioning the take-home test that he mentioned earlier in our trip and he was going to take when we get back home and said, "I am going to cheat." Alarmed by unethical behavior I was going to start giving him a big lecture but he interrupted by explaining, "I have to do a decay experiment and instead of taking out sixes of dice, I will just take out evens." I said, "Why would you do that?" He replied, "This way the decay rate will be a half." To this I commented, "This is not cheating; this is clever! But, why take out the evens and not the odds?" To which he answered, "Evens have only one prime number." Ok!
Fast forward and Omar is at home. He thought he had 100 dice (the required starting number given in the test directions) around the house but he found only 49. So, he shared with me the following thought, "Would it be ok to just use 49 and whatever I get I divide by 49 and multiply by 100 to make the experiment match a 100-dice roll?" This being a test, I told him that would have to be his decision. Deep inside, the father in me could not help but feel proud of the kid's divergent thinking and resourcefulness. In the end he decided to keep the experiment simple, straightforward, and he used 100 coins.
Omar is lucky that his father knows about math and is willing to give-and-take with him in such musings and I just hope that the many Omars out there would be equally fortunate and benefit from such exchanges with adults (teachers, parents, older siblings, etc.) around them. So, if we (the math/science teachers) are the only adults that kids may get this mental gymnastics opportunity from we must seize it with earnest passion and great patience for it would help them grow as thinkers and flourish as math/science lovers.
Happy Valentines Day & please share musings of your students or your own kids in the comments section.
Thank you and take great care! :-)
