Junior high/middle school seems like a much more appropriate time/place to expose kids to a plethora of subjects they wouldn’t necessarily choose on their own. These aren’t grades that universities look at for admissions, so there’s a lot less on the line for kids.
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Not having heard that before, but knowing that Engineering, as an academic discipline normally involves a lot of partial differential equations, I went a looking on the interweb.
https://www.reddit.com/r/AskEngineers/comments/45ormi/what_kind_of_maths_is_involved_in_engineering/
Engineers design to code, and the codes don’t really involve advanced math. Instead, the codes and norms overspecify, and these overspecifications tend to swamp the extra accuracy that would be gained by using Differential Equations.
I can see two additional problems. First, many if not most differential equations do not have exact solutions. Thus, a numerical solution must be calculated. The accuracy of the numerical solution depends on a host of factors-- stability of the algorithm, for one. Second, each component in an engineering project can be expected to exhibit some variance from the ideal. Properly accounting for these variations increases the complexity of the math involved.
The harder the math, the more likely a mistake will come up. And that could be disastrous. Best to use one’s math knowledge as a way of appreciating the problem, and not necessarily solving the problem.
But hey-- I’m not a engineer.
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I had to look up loop on Wikipedia and I am still not sure which one you are referring to, but any argument that starts with “Pfft” (which I now know how to spell) gets my vote.
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i’m really just making fun of myself 
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Playing devil’s advocate here, but wouldn’t understanding the proportions and mechanics of how human bodies are constructed be extremely helpful in creating robots that don’t fall over when they try to kick something?
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I had to look up loop on Wikipedia and I am still not sure which one you are referring to,
Probably this one.
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Under a Trump administration, It won’t be called “al jabr” anymore.
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Sure, and that’s why they should study biology, to see how muscles and bones and parts of the human body function if they want to make humanoid robots. Life drawing isn’t really about the mechanics of the human body, it’s more about studying shape, mass, and form, and learning how to capture gestures and poses quickly with your lines.
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something, something…Uncanny Valley…something, something. 
That was the point where I really started understanding it well. Using numbers just caused problems with my dyscalculia.
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Put it this way. It certainly helps me in my job to understand Maxwell’s equations well enough that I know which way changing a given parameter will push the system, but I have never actually had to solve Maxwell’s equations since I left school. That’s all under the hood in the software tools we use, and, typically, if we needed it done differently, we would tell our vendors, and they would actually implement the feature we need. If I had to hack together a PDE solver to do it myself, then yes, it would probably indicate that we were in trouble.
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I went to the math ones, not the programming one. Pick yer favorite, loop from algebra, loop from graph theory or a loop from topology. We’ll all be doing loop-de-loops! (or loop-the-loops?)
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Judging by your video, how about
Looks like heavy, heavy stuff.
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I tried looking up loop on wikipedia it said see recursion which said see loop.
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In your example —assuming we screen the whole population and ignore false negatives, just for the sake of not having to break out a pen and paper— then each genuinely sick person is going to be hiding in a pool of 10,000 healthy false positives. So taken alone I’m not going to be swayed too much by the positive test, even though on the face of it it’s a really good one. They’re rather more likely to die in some random accident in the next year than have the disease we’re testing for.
That’s why taking a decent history and looking for physical signs should precede ordering relevant tests, which really only serve to confirm a suspicion that’s already there. And also why decently designed healthcare systems restrict access to specialists by screening through General / Family Practitioners. That way the pool of patients the specialists see already has a higher incidence of the rare diseases they’re good at treating as the GP screening has changed the prior probabilities.
It’s the odd combination of needing a good grasp of a variety of different sciences and practical hands-on skills; a bit a maths; the judgement to know when to act decisively and when to watch and wait; and all with a human touch, that make Medicine an Art. And really hard to get right to everyone’s satisfaction.
Your logic is sound. We don’t actually have to actively screen the whole population if the disease eventually manifests itself in such a way that it becomes a matter of record and we therefore know the true incidence rate. But absolutely correct that by combining risk factors or other multiple indicators to drastically change the prior probabilities (basically intelligently filter the population so that within the population sub-set the disease is no-longer rare) is the way that less-than perfect tests are made useful, even if the disease incidence rate in the population-at-large is extremely low.
Engineering has become increasingly computational. Practical analytic solutions exist for a vanishingly small subset of real world problems. Prior to widespread availability of numerical methods, real world problems were usually drastically simplified so that they could be solved. The solutions were approximate due to the simplifications, and a safety factor applied so stuff didn’t fall down or fail. The real trick was knowing ahead of time which simplifications mattered, and which did not.
In the world of numerical solutions we still simplify to produce our models, of course, but the cost of adding complexity to the model and consequent computations is not as steeply exponential as it was in an analytical world, were one quickly reached a threshold of actual “solvability”. In the numerical world, you just take longer or buy/lease a bigger computer. The new “downside” is that our models are now often unnecessarily complex.
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It’s only the logic I was always taught and try to pass on. It’s also the logic that the structure of the UK’s NHS was built around. If it isn’t being taught to recent medical graduates then it’s a crying shame.
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Be careful, I tried that kind of joke on @OtherMichael and he’s been kicking my ass ever since repeatedly.
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But it is amazing the number of people who will conclude that a positive result in a test that has a 5% false positive rate means that they are 95% likely to have the disease is quite alarming. Especially amongst those who should know better.
