Brad Nelson
Administrator
עַבְדְּךָ֔ אֶת־ הַתְּשׁוּעָ֥ה הַגְּדֹלָ֖ה הַזֹּ֑את
Posts: 11,047
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Post by Brad Nelson on Apr 25, 2022 9:49:37 GMT -8
When "You go, girl" goes bad. I watched this first video with the girl giving the explanation. I didn't get it. And it seemed like she had simply skipped over the problem. Am I stupid? Clearly there are mathematical concepts that go completely over my head. But I felt sure that it was the explanation that was lacking. Sure enough, I ran into another video that totally debunked it. Granted, I had to watch segments of this several times to wrap my mind around it. But the explanation for this seeming paradox is explained succinctly by noting there is no paradox. It's simply an illusion.
I got this vision of this first chick getting "You go, girls" without a thought. But I indeed did stop and think, although I have little natural talent for advanced mathematics. And something seemed missing. I wonder if this is what the emphasis on "STEM" for girls is getting us in many cases. Bamboozlement.
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Post by kungfuzu on Apr 25, 2022 19:13:39 GMT -8
I am no mathematical genius, but I saw the problem with this girl's demonstration about 2 minutes into the video. First, she doesn't seem to know that such wheels are still used to measure area in ground work in construction, so the are easily measurable. The ancient Egyptians used them in building the pyramids.
As to why this problem seemed to confuse so many great mathematicians, (if it actually did) I can only speculate that like many very intelligent people, they often over complicated things. The "can't see the forest for the trees" syndrome. The circumference of a circle is determined by its diameter i.e. the Pi of the circle. No diameter, no Pi. No Pi, no circle. From the girl's presentation, one could easily see that the diameter of the large wheel was greater/longer than the small inner wheel, so if one made a wheel with the smaller diameter and rolled it next to the larger-diameter wheel, one would immediately see that it had more rotations over the same distance.
Simply picking some spot on a wheel does not constitute an actual wheel. A wheel is a whole object. The term wheels within wheels only applies to different-sized wheels spinning like cogs in a watch. Some are smaller and some are larger.
If one took this girl's ideas or faux presentation to their logical conclusion, it seems to me that all wheels, regardless of size should rotate at the same rate.
Maybe I am missing something, but this video was a waste of time. I couldn't get through more than 4 minutes or so.
A much more interesting question, to my mind, would have been the different speeds at which various points on a wheel move, depending on the diameters chosen. The equator of the earth travels a much greater distance than the pole, even though they both make one rotation per day.
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Brad Nelson
Administrator
עַבְדְּךָ֔ אֶת־ הַתְּשׁוּעָ֥ה הַגְּדֹלָ֖ה הַזֹּ֑את
Posts: 11,047
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Post by Brad Nelson on Apr 26, 2022 7:02:31 GMT -8
Frankly, that was the easy demonstration missing in both videos. The conundrum comes from the visual that intuitively looks as if the inner circle is rolling the same distance. It's an interesting (as I'm convinced by that second video) visual illusion (or, really, a conning of our intuition).
What I was waiting for was for someone to cut out that inner circle and roll it next to the larger-diameter one (as you said). It would show us in a second that this is a visual illusion (or a misdirection of our intuition). Both would obviously roll different distances after one rotation.
The second video made the point (however obscurely) that the distance any point on the wheel moves (absolute movement) in one rotation is not the same as simply measuring the circumference. As both videos showed (but the first one glossed over), the closer the points are to the center, the less distance they travel. The second video noted that the only point on the wheel that traveled the same absolute distance as the circumference of the wheel was the exact center. An interesting point.
Like I said, I do not have the kind of advanced mathematical brain that can grasp a lot of concepts. But I do love a good puzzle. But what I learned from this was the "You go girl" aspect. Reading the comments to the video was telling. No on questioned this chick. And I do think this girl had gotten so used to being praised merely for opening her mouth that she got lazy...or just never learned some of the concepts to begin with. Reminds me of that chick in the biotech firm who bamboozled investors with what amounted to mere rhetoric bolstered by a "You go girl" attitude.
So she is basically making a rhetorical argument (by mouthing pre-canned platitudes). She is not making a logical argument. And yet fawning praise from the commenters. And I'm quite aware that there are some very smart women out there who could think mathematical circles around me. But there are "affirmative action" poser as well out there. Or those who learn to bamboozle with mere rhetoric.
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