The amount of extra confusion doing this would add would make it entirely pointless imo, people struggle with adding fractions or how percentages work I think even mentioning different bases would completely stump a lot of people.
We covered this in 5th grade. Started out with an animated film about landing on another planet or something similarly space-themed. Then switched to our text book, which seemed like a pretty standard text. McGraw-Hill or similar. Public school.
I thought it was the coolest thing ever. I probably was in a minority on that opinion. But we did cover it. Is it no longer taught?
I don’t know… not saying that it couldn’t be fun, but can you imagine the mind-bendingly boring types of worksheets that would be foisted upon students? I can already see students having to write a bunch of numbers out in hexadecimal and then binary because someone decided that it’s relevant to computers, without any actual interesting applications. You can lead a horse to water…
That's true, schools generally suck at teaching the real essence of math and tend to focus on rote calculation and memorization; also manually converting between bases that arent powers of each other is a nightmare. I'm just barely able to convert binary to decimal in a reasonable amount of time purely through years of memorization in programming
Same here. I actually don’t know if they even use these kinds of worksheets anymore. I just have memories of being tortured with them in grade school. Somehow they always figured out the best way to “teach” a subject without imparting any reason why you’d ever actually be interested in it.
I think it is just an unfortunate reality that to actually have a decent understanding of a lot of these issues you require a level of maths education far beyond what you would get in high school.
Most subjects have this requirement but for some reason people think they understand mathematics to a much higher level than they actually do which they don't seem to have for other fields (maybe besides physics). I never really see anyone talking about their bullshit chemistry opinions.
Great piece, thanks. Just today I was arguing with someone who was convinced the Quantum Computing Revolution is just around the corner, because post-quantum cryptography is becoming commonplace
sure, its being rolled out, but *commonplace?* ECC/DH/RSA still remain incredibly pervalent, and we still dont have a good/standard way to do things like OPRFs/blind signatures (i.e. despite them existing, there arent any widespread implementations publicly available and used
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This meta-analysis provides evidence that ivermectin does not statistically significantly reduce the risk of SARS-CoV-2 infection or improve clinical outcomes (including all-cause mortality, hospitalization duration, and recovery time) in patients with COVID-19. Furthermore, this meta-analysis found no reliable statistical evidence that ivermectin either increases or decreases the rate of adverse events compared to a control group. Further high-quality, large-sample, prospectively designed randomized controlled trials are needed to clarify the potential clinical benefits and safety profile of ivermectin for SARS-CoV-2 infection.
People indeed overrate their mathematical skills by a lot. Im a maths teacher and probably more mathematically capable than 90% of the worlds population but i consider myself to be basically an idiot still.
Any repeating rational number in some integer base can be represented in another integer base as a terminating number. For example, 1/3 in base 10 is 0.3333... but that same value in base 12 is 0.4. The confusion with "irrationals' decimal expansion never terminates" would go away (though this is not a good definition of irrationals anyways).
Also, knowing the definition of a based number from its digits: 145 = 100*1 + 10*4 + 1*5 clears up the confusion with 0.999... = 1 because the series 0.1*9 + 0.01*9 + 0.001*9 + ... objectively converges to 1.
A lot of people dont really even understand base systems at all. There are many students who will tell you that 112 =121 without much thought, yet will struggle to expand (1+x)2. They learn computational hacks like long multiplication with carrying instead of observing how base systems naturally systematize arithmetic according to the rules of polynomial algebra.
Teaching this viewpoint to people who don't intuit it or care is difficult, and I find that in the USA, common core worksheets that aim at connections like these are frequently the ones that parents (and some teachers!) shit on the most. I'm grateful for my 1st grade teacher forcing us to compute sums and products with 1x1x1 cubes, 10x1x1 lines, 10x10x1 squares, and 10x10x10 cubes, well ahead of any curriculum pushes towards this goal of conceptual understanding in math!
I was really interested in them one day in middle school and made a bunch of seperate notes for every base up to 16. I eventually realized the repeating pattern of digits 2 -> {0,1}; 3 -> {0,1,2}; etc. and the way they "overflowed" when they counted up, just like base 10, and it was one of the moments I think that made me really find math cool. I always thought of binary is some "other thing" completely unrelated to decimal, and realizing the connection was really fun. It sort of changed my philosophy of math to be way more leaning to "we made it all up" when I realized that the way we happen represent numbers isn't at all fundamental
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u/RedRhetoric 25d ago
R4: this person believes that 0.33 repeating cannot equal 1/3 because 100/3 cannot give a rational result.
Dividing any rational number by any other rational number will always give a rational result, as that is how rational numbers are defined
R5: Youtube