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Show HN: I was curious about spherical helix, ended up making this visualization

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Re: Show HN: I was curious about spherical helix, ended up making this visualization

#101

Post by latexr »

addaon wrote: post #93

> …which we know isn't actually chaotic. It's just a path defined by mathematical functions. I don't know what function is being presented, so I can't speak to whether it demonstrates chaotic behavior -- but the whole /point/ of chaos is that it's an emergent property of deterministic mathematical functions. Perhaps the author meant "random" or "non-deterministic" rather than "chaotic"?

> the whole /point/ of chaos is that it's an emergent property of deterministic mathematical functions.

I believe you. But the colloquial definition (I’m looking at a dictionary right now) is “complete disorder and confusion”; “a state of things in which chance is supreme”; “the inherent unpredictability in the behavior of a complex natural system”. That path fits that apparent definition. The post is written in a way that a relative layman would understand, so it makes sense to speak/write in a way non-mathematicians would expect.

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#102

Post by srean »

taco_emoji wrote: post #99
srean wrote: post #3

These used to be super important in early oceanic navigation. It is easier to maintain a constant bearing throughout the voyage. So that's the plan sailors would try to stick close to. These led to let loxodromic curves or rhumb lines. https://en.m.wikipedia.org/wiki/Rhumb_line Mercator maps made it easier to compute what that bearing ought to be. https://en.m.wikipedia.org/wiki/Mercator_projection This configuration…

Don't forget this post, which spawned a discussion of Rhumb lines etc. in the comments: https://news.ycombinator.com/item?id=44962767

I had missed this one ! Thanks.

It is indeed raining spherical geometry today.

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#103

Post by egwor »

jacobolus wrote: post #55
srean wrote: post #3

These used to be super important in early oceanic navigation. It is easier to maintain a constant bearing throughout the voyage. So that's the plan sailors would try to stick close to. These led to let loxodromic curves or rhumb lines. https://en.m.wikipedia.org/wiki/Rhumb_line Mercator maps made it easier to compute what that bearing ought to be. https://en.m.wikipedia.org/wiki/Mercator_projection This configuration…

You inspired me to submit one of my 2022 projects https://observablehq.com/@jrus/spheredisksample https://news.ycombinator.com/item?id=44963521 to fit the trend of the day. People may also enjoy https://observablehq.com/@jrus/sphere-resample

In my early teens I used to try to create something like a equirectangular projection because when drawing it, it looked cool. Obviously I had no idea that it was called this. I was trying to draw reflections of a square window onto a sphere, and then I moved on to trying to cover the sphere in a checkered pattern. This is awesome to see, thank you!

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#104

Post by altruios »

skalidindi3 wrote: post #98
addaon wrote: post #93

> …which we know isn't actually chaotic. It's just a path defined by mathematical functions. I don't know what function is being presented, so I can't speak to whether it demonstrates chaotic behavior -- but the whole /point/ of chaos is that it's an emergent property of deterministic mathematical functions. Perhaps the author meant "random" or "non-deterministic" rather than "chaotic"?

^^^ This is an extremely underrated nitpick. I am guessing that the HN audience would be / should be interested in that distinction. Mathematically speaking, chaos is an extreme sensitivity to initial conditions, and is very much still in line with deterministic systems. The resulting output, while seemingly random (since there is no easily identifiable pattern), is mathematically and conceptually different from actu…

'actual' or 'true' randomness is a rabbit hole.

https://en.wikipedia.org/wiki/Randomness

It really depends on the exact definition of what you are quantifying 'random' to be.

There is no proof (in the mathematical sense) of real randomness.

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#106

Post by lotyrin »

altruios wrote: post #104
skalidindi3 wrote: post #98

Earlier quoted context omitted.

^^^ This is an extremely underrated nitpick. I am guessing that the HN audience would be / should be interested in that distinction. Mathematically speaking, chaos is an extreme sensitivity to initial conditions, and is very much still in line with deterministic systems. The resulting output, while seemingly random (since there is no easily identifiable pattern), is mathematically and conceptually different from actu…

'actual' or 'true' randomness is a rabbit hole. https://en.wikipedia.org/wiki/Randomness It really depends on the exact definition of what you are quantifying 'random' to be. There is no proof (in the mathematical sense) of real randomness.

I use "Random" to mean chaotic (extreme sensitivity to initial conditions) but with unknown (or unknowable) initial conditions.

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#107

Post by TheOtherHobbes »

altruios wrote: post #104
skalidindi3 wrote: post #98

Earlier quoted context omitted.

^^^ This is an extremely underrated nitpick. I am guessing that the HN audience would be / should be interested in that distinction. Mathematically speaking, chaos is an extreme sensitivity to initial conditions, and is very much still in line with deterministic systems. The resulting output, while seemingly random (since there is no easily identifiable pattern), is mathematically and conceptually different from actu…

'actual' or 'true' randomness is a rabbit hole. https://en.wikipedia.org/wiki/Randomness It really depends on the exact definition of what you are quantifying 'random' to be. There is no proof (in the mathematical sense) of real randomness.

There are a number of sophisticated tests for randomness. You can't prove absolute randomness in any Platonic sense, but you can certainly assess a source for different properties that are useful in applications that require randomness.

In this example the path is neither chaotic (in the formal sense) nor random, because a Fourier transform would identify the harmonic components.

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#108

Post by Theodores »

alias_neo wrote: post #82

Really nice visualisation. Does anyone know of any tooling I could use to do some plotting like this in 3D space even a fraction as nice looking as OPs? I'm not a web dev but I am a dev, but would prefer something high enough level that I can focus on the "what" (to plot) rather than the "how".

In the olden 8-bit days, we would have to do this in BASIC or assembler with a 3D library that we would have to write ourselves. Then we would run out of memory.

Later on - about a quarter of a century ago - we had VRML which enables anyone to just focus on the what rather than the how. But VRML always needed a plugin to download, which was no fun at all in the dial-up days. We almost had a 3D web, but no, it ended up 2D.

I digress. However, if you want 3D plots without having to reinvent the wheel, three.js is fit for purpose, with the right CodePen example to get you started.

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#110

Post by addaon »

latexr wrote: post #101
addaon wrote: post #93

> …which we know isn't actually chaotic. It's just a path defined by mathematical functions. I don't know what function is being presented, so I can't speak to whether it demonstrates chaotic behavior -- but the whole /point/ of chaos is that it's an emergent property of deterministic mathematical functions. Perhaps the author meant "random" or "non-deterministic" rather than "chaotic"?

> the whole /point/ of chaos is that it's an emergent property of deterministic mathematical functions. I believe you. But the colloquial definition (I’m looking at a dictionary right now) is “complete disorder and confusion”; “a state of things in which chance is supreme”; “the inherent unpredictability in the behavior of a complex natural system”. That path fits that apparent definition. The post is written in a wa…

> That path fits that apparent definition.

Then saying it "isn't actually chaotic" is mis-aligned with the layman's understanding, and the disagreement is not explained (either by explaining a more technical definition, or otherwise).

I continue to think that substituting "non-deterministic" or "random" would be more both understandable to the layman, and more correct to the advanced reader.

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