Maths, youtube, brilliance
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Maths, youtube, brilliance
I can't breathe.
- George Floyd, 25th May 2020
- George Floyd, 25th May 2020
It's weird, but I don't really see it as... weird. I'm not a mathematician, of course, but it seems like a case of defining a set of conditions and viewing them during supposed "changes." But, the underlying set of conditions hasn't also changed - They're all relative. Too keep from running all over the place while trying to measure one thing, the definition keeps being applied in its original form. I understand why and can understand why the results can be useful, but I don't see the results as absolute. IOW - They're true, within the scope of the exercise, but the exercise itself is purpose-built or destined to produce those results.
Just bloviating...
Just bloviating...
- red assassin
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This is one of my favourite counterintuitive results in maths. The first time I heard about it was reading this post, and I definitely had to think about it for a while. I like the volume explanation given in that post.
A still more glorious dawn awaits, not a sunrise, but a galaxy rise, a morning filled with 400 billion suns - the rising of the Milky Way
This doesn't seem strange to me at all.
I studied mostly applied mathematics at university, but we all did some basic analysis (pure maths) in the first year. What that taught me was that you don't assume anything - you prove it once and then you move on and can use that proof. If you stick to the abstract then you don't go far wrong. What the video and article do is bring the abstract into the sphere (no pun intended) of the individual experience and invite people to use their intuition. As the article says - that can lead astray. Although I've not seen this particular one before, I guess I've seen enough - and have the training - to focus on what's known (the equations) and not on my intuition.
I studied mostly applied mathematics at university, but we all did some basic analysis (pure maths) in the first year. What that taught me was that you don't assume anything - you prove it once and then you move on and can use that proof. If you stick to the abstract then you don't go far wrong. What the video and article do is bring the abstract into the sphere (no pun intended) of the individual experience and invite people to use their intuition. As the article says - that can lead astray. Although I've not seen this particular one before, I guess I've seen enough - and have the training - to focus on what's known (the equations) and not on my intuition.
Rapier - The Orifice of all Knowledge
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That was an enjoyable watch.
Yes and no. Weird mathematics has a strange habit of becoming relevant in the most unexpected situations. In fact quite often such "exercises" actually come from real-world problems, which have been shown to be equivalent to solving a geometrical calculation.Morkonan wrote:It's weird, but I don't really see it as... weird. I'm not a mathematician, of course, but it seems like a case of defining a set of conditions and viewing them during supposed "changes." But, the underlying set of conditions hasn't also changed - They're all relative. Too keep from running all over the place while trying to measure one thing, the definition keeps being applied in its original form. I understand why and can understand why the results can be useful, but I don't see the results as absolute. IOW - They're true, within the scope of the exercise, but the exercise itself is purpose-built or destined to produce those results.
- jack775544
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It is a very interesting problem with some interesting consequences that appear in computer science because of it. I remember learning about this for the first time and having my mind blown from it.
One of the side effects of the problems in that video is that distance starts to loose its meaning and if you have a set of data points then the distance from one point to any other point will be roughly the same. This gets important since if you normally want to compare 2 things you would measure the distance between them to see how different they are, but it becomes near impossible in high dimensional space. This notion is called the 'Curse of Dimensionality' if you want to look into it further.
I really like the problem since it is some cool abstract maths that actually has some very real effects in how certain computer algorithms work.
One of the side effects of the problems in that video is that distance starts to loose its meaning and if you have a set of data points then the distance from one point to any other point will be roughly the same. This gets important since if you normally want to compare 2 things you would measure the distance between them to see how different they are, but it becomes near impossible in high dimensional space. This notion is called the 'Curse of Dimensionality' if you want to look into it further.
I really like the problem since it is some cool abstract maths that actually has some very real effects in how certain computer algorithms work.
1940s - Various "computers" are "programmed" using direct wiring and switches. Engineers do this in order to avoid the tabs vs spaces debate.
A project I'm still working on, sporadically, for years... anthropometry. Specifically, applying it to 3D human objects so that morphs appear realistic, based on real-world measurements and ratios.CBJ wrote:The Curse of Dimensionality thing also came up a while back in a discussion about fighter jet pilot seats, whereby designing a seat for the "average" pilot turned out to be very dangerous because the number of different measurements (dimensions) being averaged was too high.
But, "averages" mean nothing other than to the one measurement that is averaged. It's the ratios of change that are important, not whether or not a human figure has completely average measurements.
Add age-related development and changes and, suddenly, everything becomes different and all the ratios get whacked...
Look at a crowd of people. Now, look at a herd of gazelles. Sure, we're human and are more in-tune with human characteristics. But, $@$%@, human phenotypical diveristy is off the darn charts! Why is this? (I have my own theories, but that's another topic.)
The point is that what we think is easily apparent... isn't. What appears logical... isn't reality. Fat goes here and here and here and ... sometimes here. Ratios between legs, trunk length, shoulders, arms... they're not friggin average and they don't change together in the same ratios. And, human faces? Forgetabboutit...
So, I toil on when I have the urge, trying to get a handle on it all. And, after every session, I find myself deeper down a rabbit-hole of variability that defies "average."
PS - Way back when, "ergonomics" was a rising discipline closely associated with what was then called "industrial psychology." That's where I first got hooked. Later, when I developed a fascination with 3D, it was a natural progression to combine the two.