Even just an example that everyone is screaming about as logic-chopping and cheating is a good and important example worth thinking about That it's easy to add 2 pounds to 2 pounds and get 5 pounds, if you're using a scale that rounds 2.2 and 2.4 down to 2 and rounds 4.6 up to 5
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Replying to @arthur_affect @perdricof
The issue is common understanding for meaningful communication among a general public. On your example, how is that hypothetical scale better than the sort you encounter in real life? Seems definitively less precise, no?
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Replying to @Aya62335284 @perdricof
All scales that exist in the real world are this scale, it just depends on the scale (so to speak)
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The very fact that you think my hypothetical scale is some wacky fiction I invented that comes from some imaginary primitive civilization where they just don't know how to build scales is a sign of a deficiency in your education
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In fact it is the idea of a scale that NEVER gives a 2+2=5 result (or 0.0000000002 + 0.0000000002 = 0.0000000005) that is the impossible abstraction
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I am not just playing games with words here, I am stating a foundational principle about the concept of measurement and therefore the application of mathematics to the real world (and the whole concept of science) One that it is vital that ordinary people understand
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Replying to @arthur_affect @perdricof
Yes, rounding is a regular phenomenon (it exists less observably in real scales). Still a deflection from the issue of general understanding/ communication of meaning.
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Replying to @Aya62335284 @perdricof
Acting like it is actually important to train children to perform arithmetic functions and that any further education that disrupts their ability to do so is a dangerous distraction is, in fact, the tendentious distortion of meaning here
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Nobody is arguing against the naive idea of "2+2=4" We all know how that works If you're really confused about how the addition function works over the set of natural numbers, just pull out your phone and type it in
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The purpose of mathematical education is not to train kids to be calculators (Even the crappy standard curriculum I got in primary school included the idea that "no real-life numbers are exact", and how to deal with significant digits and rounding)
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I do still remember having to memorize multiplication tables in lower grades but yes modern math education is (or at least, should be) more about understanding the basics so you can punch the numbers in correctly.
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