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tech / sci.physics.relativity / Re: the optimizing spider

SubjectAuthor
* the optimizing spiderRichD
+* Re: the optimizing spiderStan Fultoni
|+* Re: the optimizing spiderMikko
||+* Re: the optimizing spiderMaciej Wozniak
|||`- Re: the optimizing spiderRoss A. Finlayson
||+* Re: the optimizing spiderStan Fultoni
|||+* Re: the optimizing spiderRichD
||||`- Re: the optimizing spiderStan Fultoni
|||`* Re: the optimizing spiderMikko
||| +* Re: the optimizing spiderStan Fultoni
||| |`* Re: the optimizing spiderMikko
||| | +* Re: the optimizing spiderStan Fultoni
||| | |`* Re: the optimizing spiderMikko
||| | | `* Re: the optimizing spiderStan Fultoni
||| | |  `* Re: the optimizing spiderMikko
||| | |   `- Re: the optimizing spiderStan Fultoni
||| | `* Re: the optimizing spiderRichD
||| |  `* Re: the optimizing spiderMikko
||| |   `* Re: the optimizing spiderRichD
||| |    `- Re: the optimizing spiderStan Fultoni
||| `- Re: the optimizing spiderMaciej Wozniak
||`* Re: the optimizing spiderRichD
|| `* Re: the optimizing spiderTom Roberts
||  `* Re: the optimizing spiderRichD
||   `- Re: the optimizing spiderStan Fultoni
|`- Re: the optimizing spiderRichD
`- Re: the optimizing spiderrotchm

Pages:12
the optimizing spider

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Subject: the optimizing spider
From: r_delane...@yahoo.com (RichD)
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 by: RichD - Thu, 12 May 2022 18:59 UTC

Given a Tom Collins glass, 4" high, 6" circumference.
A spider sits on the outside, 1" from the bottom.
A fly lands on the inside, 1" from the top, on the opposite
side. The spider, who aced the calculus of variations,
takes the shortest route and pounces.
What route, what distance?

No calculator allowed.

This is on topic, as it involves shortest path on a curved manifold.

--
Rich

Re: the optimizing spider

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Date: Thu, 12 May 2022 15:33:47 -0700 (PDT)
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Subject: Re: the optimizing spider
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Thu, 12 May 2022 22:33 UTC

On Thursday, May 12, 2022 at 11:59:45 AM UTC-7, RichD wrote:
> Given a Tom Collins glass, 4" high, 6" circumference. A spider sits on
> the outside, 1" from the bottom. A fly lands on the inside, 1" from the
> top, on the opposite side. The spider, who aced the calculus of variations,
> takes the shortest route and pounces. What route, what distance?
> This is on topic, as it involves shortest path on a curved manifold.

Obviously 5", but this isn't an example of a curved manifold, because
the intrinsic curvature of a cylindrical surface is zero, i.e., the surface
of a cylinder is intrinsically flat.

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: rot...@gmail.com (rotchm)
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 by: rotchm - Fri, 13 May 2022 01:16 UTC

On Thursday, May 12, 2022 at 2:59:45 PM UTC-4, RichD wrote:
> Given a Tom Collins glass, 4" high, 6" circumference.
> A spider sits on the outside, 1" from the bottom.
> A fly lands on the inside, 1" from the top, on the opposite
> side. The spider, who aced the calculus of variations,
> takes the shortest route and pounces.
> What route, what distance?
>
> No calculator allowed.

This is a trivial riddle, and no one in their right mind would even think of calculus or calculus of variations to solve such a simple problem. A little high school geometry/math suffices.

Re: the optimizing spider

<t5ktt5$krg$1@dont-email.me>

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From: mikko.le...@iki.fi (Mikko)
Newsgroups: sci.physics.relativity
Subject: Re: the optimizing spider
Date: Fri, 13 May 2022 09:29:57 +0300
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 by: Mikko - Fri, 13 May 2022 06:29 UTC

On 2022-05-12 22:33:47 +0000, Stan Fultoni said:

> On Thursday, May 12, 2022 at 11:59:45 AM UTC-7, RichD wrote:
>> Given a Tom Collins glass, 4" high, 6" circumference. A spider sits on
>> the outside, 1" from the bottom. A fly lands on the inside, 1" from the
>> top, on the opposite side. The spider, who aced the calculus of variations,
>> takes the shortest route and pounces. What route, what distance?
>> This is on topic, as it involves shortest path on a curved manifold.
>
> Obviously 5", but this isn't an example of a curved manifold, because
> the intrinsic curvature of a cylindrical surface is zero, i.e., the surface
> of a cylinder is intrinsically flat.

There are two distinct optimal paths and one non-optimal straight path so
the space is not Euclidean.

Mikko

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Fri, 13 May 2022 07:19 UTC

On Friday, 13 May 2022 at 08:30:01 UTC+2, Mikko wrote:

> There are two distinct optimal paths and one non-optimal straight path so
> the space is not Euclidean.

See, poor halfbrain: the Euclidean axiom is "between two
points there is exactly one straight path". It is not
"between two points there is exactly one optimal path".
As long as even your bunch of idiots is seeing exactly
one straight path - the space is Euclidean for sure.

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Fri, 13 May 2022 13:34 UTC

On Thursday, May 12, 2022 at 11:30:01 PM UTC-7, Mikko wrote:
> On 2022-05-12 22:33:47 +0000, Stan Fultoni said:
>
> > On Thursday, May 12, 2022 at 11:59:45 AM UTC-7, RichD wrote:
> >> Given a Tom Collins glass, 4" high, 6" circumference. A spider sits on
> >> the outside, 1" from the bottom. A fly lands on the inside, 1" from the
> >> top, on the opposite side. The spider, who aced the calculus of variations,
> >> takes the shortest route and pounces. What route, what distance?
> >> This is on topic, as it involves shortest path on a curved manifold.
> >
> > Obviously 5", but this isn't an example of a curved manifold, because
> > the intrinsic curvature of a cylindrical surface is zero, i.e., the surface
> > of a cylinder is intrinsically flat.
>
> There are two distinct optimal paths and one non-optimal straight path so
> the space is not Euclidean.

The space has a non-Euclidean *global* topology, but it is locally intrinsically
flat everywhere except the rim (which is removable in this idealization of
a thin surface).

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: r_delane...@yahoo.com (RichD)
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 by: RichD - Fri, 13 May 2022 20:35 UTC

On May 12, Stan Fultoni wrote:
>> Given a Tom Collins glass, 4" high, 6" circumference. A spider sits on
>> the outside, 1" from the bottom. A fly lands on the inside, 1" from the
>> top, on the opposite side. The spider takes the shortest route and pounces.
>> What route, what distance?
>> This is on topic, as it involves shortest path on a curved manifold.
>
> Obviously 5", but this isn't an example of a curved manifold, because
> the intrinsic curvature of a cylindrical surface is zero, i.e., the surface
> of a cylinder is intrinsically flat.

The universe might be a cylinder shape, due to gravitational curvature.
You call that a flat space?

--
Rich

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: r_delane...@yahoo.com (RichD)
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 by: RichD - Fri, 13 May 2022 20:40 UTC

On May 12, Mikko wrote:
>>> Given a Tom Collins glass, 4" high, 6" circumference. A spider sits on
>>> the outside, 1" from the bottom. A fly lands on the inside, 1" from the
>>> top, on the opposite side. The spider takes the shortest route and pounces.
>>> What route, what distance?
>>> This is on topic, as it involves shortest path on a curved manifold.
>
> > Obviously 5", but this isn't an example of a curved manifold, because
> > the intrinsic curvature of a cylindrical surface is zero, i.e., the surface
> > of a cylinder is intrinsically flat.
>
> There are two distinct optimal paths and one non-optimal straight path so
> the space is not Euclidean.

??

If the spider aims a flashlight into the glass, the light beam will find
the shortest path to the fly. Which makes a photon smarter than
95% of the hominids I've met.

--
Rich

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: r_delane...@yahoo.com (RichD)
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 by: RichD - Fri, 13 May 2022 21:12 UTC

On May 13, Stan Fultoni wrote:
>>>> Given a Tom Collins glass, 4" high, 6" circumference. A spider sits on
>>>> the outside, 1" from the bottom. A fly lands on the inside, 1" from the
>>>> top, on the opposite side. The spider takes the shortest route and pounces.
>>>> What route, what distance?
>>>> This is on topic, as it involves shortest path on a curved manifold.
>
>>> Obviously 5", but this isn't an example of a curved manifold, because
>>> the intrinsic curvature of a cylindrical surface is zero, i.e., the surface
>>> of a cylinder is intrinsically flat.
>
>> There are two distinct optimal paths and one non-optimal straight path so
>> the space is not Euclidean.
>
> The space has a non-Euclidean *global* topology, but it is locally intrinsically
> flat everywhere except the rim (which is removable in this idealization of
> a thin surface).

At what scale does the locally flat geometry become curved?
The given problem is long distance, so the local flatness argument fails.

--
Rich

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Fri, 13 May 2022 23:23 UTC

On Friday, May 13, 2022 at 2:12:54 PM UTC-7, RichD wrote:
> On May 13, Stan Fultoni wrote:
> >>>> Given a Tom Collins glass, 4" high, 6" circumference. A spider sits on
> >>>> the outside, 1" from the bottom. A fly lands on the inside, 1" from the
> >>>> top, on the opposite side. The spider takes the shortest route and pounces.
> >>>> What route, what distance?
> >>>> This is on topic, as it involves shortest path on a curved manifold.
> >
> >>> Obviously 5", but this isn't an example of a curved manifold, because
> >>> the intrinsic curvature of a cylindrical surface is zero, i.e., the surface
> >>> of a cylinder is intrinsically flat.

The universe might be a cylinder shape, due to gravitational curvature.
You call that a flat space?

Yes, a cylindrical space is metrically flat. You are confusing an embedding
topology involving extrinsic curvature versus intrinsic metrical curvature, such
as in a gravitational field.

> >> There are two distinct optimal paths and one non-optimal straight path so
> >> the space is not Euclidean.
> >
> > The space has a non-Euclidean *global* topology, but it is locally intrinsically
> > flat everywhere except the rim (which is removable in this idealization of
> > a thin surface).
>
> At what scale does the locally flat geometry become curved?

Again, a cylindrical space has no metrical (intrinsic) curvature. The fact that
different slices are identified with each other, is topological, not metrical.
For example, in the glass riddle, there are infinitely many metrically straight
lines from spider to fly, because of the cyclical topology, but the space is
everywhere flat.

> The given problem is long distance, so the local flatness argument fails.

First, there is no "argument", simply statements of fact. Second, local flatness
does not fail, and indeed you don't even need the cylindrical topology, since you
aren't circumnavigating the glass when following the shorted of the straight
lines from spider to fly. Just take the cylinder and unfold the interior to exterior
like a sock, and slice along one line and lay it flat. You have a flat 3x4 rectangle,
and you are going along the diagonal. Curvature is not involved. There is
zero metrical curvature on this surface.

Re: the optimizing spider

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 by: Tom Roberts - Sat, 14 May 2022 01:03 UTC

On 5/13/22 3:40 PM, RichD wrote:
> If the spider aims a flashlight into the glass, the light beam will find
> the shortest path to the fly.

No it won't. The SPIDER must aim the flashlight at the fly -- the light
itself is incapable of that.

The light beam will follow the null geodesic corresponding to its
initial conditions, which are determined by the position and orientation
of the flashlight; the light beam doesn't "find" anything.

Tom Roberts

Re: the optimizing spider

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 by: Mikko - Sat, 14 May 2022 07:57 UTC

On 2022-05-13 13:34:54 +0000, Stan Fultoni said:

> On Thursday, May 12, 2022 at 11:30:01 PM UTC-7, Mikko wrote:
>> On 2022-05-12 22:33:47 +0000, Stan Fultoni said:
>>
>>> On Thursday, May 12, 2022 at 11:59:45 AM UTC-7, RichD wrote:
>>>> Given a Tom Collins glass, 4" high, 6" circumference. A spider sits on
>>>> the outside, 1" from the bottom. A fly lands on the inside, 1" from the
>>>> top, on the opposite side. The spider, who aced the calculus of variations,
>>>> takes the shortest route and pounces. What route, what distance?
>>>> This is on topic, as it involves shortest path on a curved manifold.
>>>
>>> Obviously 5", but this isn't an example of a curved manifold, because
>>> the intrinsic curvature of a cylindrical surface is zero, i.e., the surface
>>> of a cylinder is intrinsically flat.
>>
>> There are two distinct optimal paths and one non-optimal straight path so
>> the space is not Euclidean.
>
> The space has a non-Euclidean *global* topology, but it is locally
> intrinsically
> flat everywhere except the rim (which is removable in this idealization of
> a thin surface).

Topologically a glass is equivalent to a ball but for the problem it isn't.
Locally most of its surface is Euclidean but the problem isn't local.
One of Euclid's axioms is two distinct points can be connected with one
and only one straight lines but that is false in the problem space as
there are infinitely many straight lines that connect the initial position
of the spider to the position of the fly. Therefore the problem si very
non-Euclidean.

Mikko

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Subject: Re: the optimizing spider
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Sat, 14 May 2022 08:27 UTC

On Saturday, May 14, 2022 at 12:57:38 AM UTC-7, Mikko wrote:
> There are two distinct optimal paths and one non-optimal straight path

No, there are infinitely many straight paths, involving circumnavigation of the cylinder, but those are obviously not relevant. The fact that we can go half way around in either direction is also trivial.

> Topologically a glass is equivalent to a ball...

Nope, the "glass" is idealized as a cylindrical surface, which is not topologically equivalent to a ball.

> Locally most of its surface is Euclidean but the problem isn't local.

The region of the surface that is relevant is perfectly Euclidean, given that we unfold the exterior, and we have a flat rectangular Euclidean region, 4" x 3", and the solution is given by the Pythagorean theorem 4^2 + 3^2 = 5^2. This is perfectly Euclidean. The fact that the surface is a topological cylinder is irrelevant, because the shortest path obviously does not involve circumnavigation (like the infinitely many other straight paths).

> One of Euclid's axioms is two distinct points can be connected with one
> and only one straight lines but that is false in the problem space as
> there are infinitely many straight lines that connect the initial position
> of the spider to the position of the fly.

The infinitely many straight paths around the cylinder were explained previously, consistent with the fact that the surface is everywhere metrically flat, and has the topology of a cylinder... which is irrelevant to the puzzle, aside from the two symmetrical directions.

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: r_delane...@yahoo.com (RichD)
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 by: RichD - Sat, 14 May 2022 18:01 UTC

On May 13, tjrob137 wrote:
>> If the spider aims a flashlight into the glass, the light beam will find
>> the shortest path to the fly.
>
> No it won't. The SPIDER must aim the flashlight at the fly -- the light
> itself is incapable of that.
> The light beam will follow the null geodesic corresponding to its
> initial conditions, which are determined by the position and orientation
> of the flashlight; the light beam doesn't "find" anything.

Yes. And when aimed correctly, Fermat tells us the null
geodesic minimizes the time of flight from spider to fly.
Very convenient and intelligent, considering that the spider
values time over length optimization.

We can also approach it using dynamic programming, a method
which optimizes a path from destination to source; justified,
here, by the fact that the laws of physics are time reversible.
Then, considering only the photons which found the spider, we
find they took the path of least time, a problem they solved
instantly. Whereas, a human has to solve simultaneous equations,
hobbled by the fact that calculus chokes at the rim's discontinuity.

Ergo, photons are smarter than neurons.
QED

--
Rich

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Sat, 14 May 2022 18:51 UTC

On Saturday, May 14, 2022 at 11:01:19 AM UTC-7, RichD wrote:
> ...calculus chokes at the rim's discontinuity.

Calculus doesn't choke, and anyway there is no need for calculus in this riddle, since it's just a straight line on a flat surface (unfolded) between two specified points at the opposite corners of a rectangle with edges lengths 4" and 3".

> Ergo, photons are smarter than neurons.

The question involved a spider, and it takes the average person about 0.5 seconds to see the answer, but the spider wouldn't follow that path. Regarding photons, you can't just "release a photon" and expect it to find its way to the fly, and even if you release many photons, or use "optimum aiming" which a human brain figures out, and you consider a particular reception event, it isn't correct to naively say that the photon followed the stationary path, because the amplitude of reaching that event is the sum of the amplitudes for all possible paths, and from considering the constructive and destructive interference effects of the complex amplitudes we can derive the approximate "straight line" dominance for long range massless interactions in empty space. True, simulating continuous quantum phenomena computationally can be difficult, which is why some people expect quantum computers to surpass classical computers for some tasks... such as calculation the behavior of quantum systems!

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 by: Mikko - Sun, 15 May 2022 07:42 UTC

On 2022-05-14 08:27:23 +0000, Stan Fultoni said:

> On Saturday, May 14, 2022 at 12:57:38 AM UTC-7, Mikko wrote:
>> There are two distinct optimal paths and one non-optimal straight path
>
> No, there are infinitely many straight paths, involving
> circumnavigation of the cylinder, but those are obviously not relevant.
> The fact that we can go half way around in either direction is also
> trivial.

That there is more than one straight path is sufficient to show that the
space is non-Euclidean. It is true that there are infinitely many paths
but obviously the shortest path is one of the three I mentioned.

>> Topologically a glass is equivalent to a ball...
>
> Nope, the "glass" is idealized as a cylindrical surface, which is not
> topologically equivalent to a ball.

The glass is more than just a cylindrical surface. The bottom is an
essential part of the problem space. Also important is that the inner
and outer surface are distinct.

>> Locally most of its surface is Euclidean but the problem isn't local.

> The region of the surface that is relevant is perfectly Euclidean,
> given that we unfold the exterior, and we have a flat rectangular
> Euclidean region, 4" x 3", and the solution is given by the Pythagorean
> theorem 4^2 + 3^2 = 5^2. This is perfectly Euclidean. The fact that
> the surface is a topological cylinder is irrelevant, because the
> shortest path obviously does not involve circumnavigation (like the
> infinitely many other straight paths).

The metric structure of the glass is important as the problem involves
metric concepts. But one must prove that no path through the bottom
is shorter than 5" so the bottom cannot be ignored.

>> One of Euclid's axioms is two distinct points can be connected with
>> one> and only one straight lines but that is false in the problem space
>> as> there are infinitely many straight lines that connect the initial
>> position> of the spider to the position of the fly.

> The infinitely many straight paths around the cylinder were explained
> previously, consistent with the fact that the surface is everywhere
> metrically flat, and has the topology of a cylinder... which is
> irrelevant to the puzzle, aside from the two symmetrical directions.

That I didn't mention the infinitely many other paths and their ovious
irrelevancy is obviously unimportant because of their obvious irrelevancy.

Mikko

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Sun, 15 May 2022 12:42 UTC

On Saturday, 14 May 2022 at 09:57:38 UTC+2, Mikko wrote:
> On 2022-05-13 13:34:54 +0000, Stan Fultoni said:
>
> > On Thursday, May 12, 2022 at 11:30:01 PM UTC-7, Mikko wrote:
> >> On 2022-05-12 22:33:47 +0000, Stan Fultoni said:
> >>
> >>> On Thursday, May 12, 2022 at 11:59:45 AM UTC-7, RichD wrote:
> >>>> Given a Tom Collins glass, 4" high, 6" circumference. A spider sits on
> >>>> the outside, 1" from the bottom. A fly lands on the inside, 1" from the
> >>>> top, on the opposite side. The spider, who aced the calculus of variations,
> >>>> takes the shortest route and pounces. What route, what distance?
> >>>> This is on topic, as it involves shortest path on a curved manifold.
> >>>
> >>> Obviously 5", but this isn't an example of a curved manifold, because
> >>> the intrinsic curvature of a cylindrical surface is zero, i.e., the surface
> >>> of a cylinder is intrinsically flat.
> >>
> >> There are two distinct optimal paths and one non-optimal straight path so
> >> the space is not Euclidean.
> >
> > The space has a non-Euclidean *global* topology, but it is locally
> > intrinsically
> > flat everywhere except the rim (which is removable in this idealization of
> > a thin surface).
> Topologically a glass is equivalent to a ball but for the problem it isn't.
> Locally most of its surface is Euclidean but the problem isn't local.
> One of Euclid's axioms is two distinct points can be connected with one
> and only one straight lines but that is false in the problem space as
> there are infinitely many straight lines that connect the initial position
> of the spider to the position of the fly. Therefore the problem si very
> non-Euclidean.

Bull shit. The problem is described as
Euclidean and solved as Euclidean. Since your
idiot guru has refuted basic math - your moronic
ideology is doing everything to discredit it. That's
all.
Who said the route of the spider will be straight?

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Sun, 15 May 2022 15:30 UTC

On Sunday, May 15, 2022 at 12:42:33 AM UTC-7, Mikko wrote:
> >> There are two distinct optimal paths and one non-optimal straight path
> >
> > No, there are infinitely many straight paths, involving
> > circumnavigation of the cylinder, but those are obviously not relevant.
> > The fact that we can go half way around in either direction is also
> > trivial.
>
> That there is more than one straight path is sufficient to show that the
> space is non-Euclidean.

The point is that the relevant portion of the space is Euclidean, both metrically and topologically, since it is equally obvious that (1) the optimum path does not involve circumnavigations, and (2) the optimum path does not involve the bottom of the glass. Also, the glass is tacitly stipulated to be idealized with zero thickness (since no thickness is specified, and any non-zero thickness would change the answer.)

> The glass is more than just a cylindrical surface. The bottom is an
> essential part of the problem space. Also important is that the inner
> and outer surface are distinct.

Nope, see above. It's obvious that the desired path does not involve the bottom, and the problem treats the glass as a cylindrical surface with zero thickness (else the answer would be different).

> >> Locally most of its surface is Euclidean but the problem isn't local.
>
> > The region of the surface that is relevant is perfectly Euclidean,
> > given that we unfold the exterior, and we have a flat rectangular
> > Euclidean region, 4" x 3", and the solution is given by the Pythagorean
> > theorem 4^2 + 3^2 = 5^2. This is perfectly Euclidean. The fact that
> > the surface is a topological cylinder is irrelevant, because the
> > shortest path obviously does not involve circumnavigation (like the
> > infinitely many other straight paths).
>
> The metric structure of the glass is important as the problem involves
> metric concepts.

Again, the relevant region of the glass is both metrically and topologically flat.

> One must prove that no path through the bottom is shorter than 5" so
> the bottom cannot be ignored.

It's just as obvious that the shortest path does not cross the bottom as that it doesn't involve circumnavigations.

> That I didn't mention the infinitely many other paths and their obvious
> irrelevancy is obviously unimportant because of their obvious irrelevancy..

You're being inconsistent, because you agree that the circumnavigation paths are obviously irrelevant, justifying that you didn't mention them when you enumerated "three possible paths", and yet you insist that the equally obviously irrelevant paths across the bottom must be mentioned. The consistent view is that none of the obviously irrelevant paths are relevant, and the glass is idealized with zero thickness, and so the only relevant space is the flat rectangular region (unfolded) with edge lengths 4" and 3", and the solution is the straight diagonal given by the Pythagorean theorem 3^2 + 4^2 = 5^2. This simply does not involve any non-Euclidean geometry, either metrically or topologically, because the non-Euclidean paths are obviously irrelevant, because of (as you say) their obvious irrelevancy.

Re: the optimizing spider

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Subject: Re: the optimizing spider
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 by: Mikko - Sun, 15 May 2022 16:33 UTC

On 2022-05-15 15:30:34 +0000, Stan Fultoni said:

> On Sunday, May 15, 2022 at 12:42:33 AM UTC-7, Mikko wrote:
>>>> There are two distinct optimal paths and one non-optimal straight path>
>>>> >> > No, there are infinitely many straight paths, involving> >
>>>> circumnavigation of the cylinder, but those are obviously not
>>>> relevant.> > The fact that we can go half way around in either
>>>> direction is also> > trivial.
>>
>> That there is more than one straight path is sufficient to show that
>> the> space is non-Euclidean.
> The point is that the relevant portion of the space is Euclidean, both
> metrically and topologically, since it is equally obvious that (1) the
> optimum path does not involve circumnavigations, and (2) the optimum
> path does not involve the bottom of the glass. Also, the glass is
> tacitly stipulated to be idealized with zero thickness (since no
> thickness is specified, and any non-zero thickness would change the
> answer.)

The optimum path does not involve the bottom because the numbers in the
problem statement ara what they are. With some other numbers the path
crossing the bottom is shorter. Meaning of numbers is not obvious to
everybody. Therefore I would regard the non-optimality of the circum-
navigations more obvious than the non-optimality of the bottom crossing.

>> The glass is more than just a cylindrical surface. The bottom is an>
>> essential part of the problem space. Also important is that the inner>
>> and outer surface are distinct.

> You're being inconsistent, because you agree that the circumnavigation
> paths are obviously irrelevant, justifying that you didn't mention them
> when you enumerated "three possible paths", and yet you insist that the
> equally obviously irrelevant paths across the bottom must be mentioned.

As I don't agree that the path crossing the bottom is as obviously
irrelevant as any circumnavigating path I am not inconsistent.
But I find it funny that you introduced the circumnavigating paths
to the discussion and then talk a lot about them and keep calling
them irrelevant.

Mikko

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Sun, 15 May 2022 17:56 UTC

On Sunday, May 15, 2022 at 9:33:40 AM UTC-7, Mikko wrote:
> The optimum path does not involve the bottom because the numbers in the
> problem statement ara what they are. With some other numbers the path
> crossing the bottom is shorter. Meaning of numbers is not obvious to
> everybody. Therefore I would regard the non-optimality of the circum-
> navigations more obvious than the non-optimality of the bottom crossing.

The obviousness is certainly contingent on the stated parameters and other conditions. If we start talking about changing the conditions of the problem, then we can change the answer as well as the obviousness of some of the alternatives. Also, this depends to some extent on the tacit stipulations, e.g., is the glass sitting on a table, or is it levitating freely so that a spider could cross the exterior bottom? If it's on a table, then it could only cross the interior bottom, which would only be optimum (with the other stated conditions) if the circumference of the glass was over 53 inches, which is fairly ridiculous. Even if the glass is magically levitating and the spider can cross the exterior bottom, the circumference would need to be more than 30 inches, still rather ridiculous. Most people can see at a glance, without any calculations, that these paths are not the answer for the stated conditions, especially if the glass is sitting on a table.

> As I don't agree that the path crossing the bottom is as obviously
> irrelevant as any circumnavigating path I am not inconsistent.

Distinguishing different "levels of obviousness" of two obviously irrelevant things doesn't change the fact that they are both obviously irrelevant for the problem posed, and hence the problem really has nothing to do with "paths on a curved manifold" (meaning metrical curvature) as the OP mistakenly claimed.

> I find it funny that you introduced the circumnavigating paths
> to the discussion and then talk a lot about them and keep calling
> them irrelevant.

Well, I only mentioned them to point out that they are obviously irrelevant (a fact which seemed to elude you), so the fact that the surface is topologically a cylinder is irrelevant, and hence the obvious solution is really just a straight path on a metrically flat Euclidean space.

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: ross.fin...@gmail.com (Ross A. Finlayson)
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 by: Ross A. Finlayson - Sun, 15 May 2022 21:41 UTC

On Friday, May 13, 2022 at 12:19:31 AM UTC-7, maluw...@gmail.com wrote:
> On Friday, 13 May 2022 at 08:30:01 UTC+2, Mikko wrote:
>
> > There are two distinct optimal paths and one non-optimal straight path so
> > the space is not Euclidean.
> See, poor halfbrain: the Euclidean axiom is "between two
> points there is exactly one straight path". It is not
> "between two points there is exactly one optimal path".
> As long as even your bunch of idiots is seeing exactly
> one straight path - the space is Euclidean for sure.

Seems either "walk around to fly, jump over straight line",
or "jump over straight line, walk around to fly".

Or, you know, scuttle, I suppose spiders jump, and scuttle.

Outside is convex, inside is concave.

The catenary is a usual form, that though like the parabolic,
after the inverse square of the usual parabola, instead is as
the piece-wise connected segments of a path, down as they
were, according to a directional gradient.

Where great circles are the shortest distance on a sphere,
it will seem that the shorter distance will be less on the
convex outside and more on the concave inside.

Basically for the spider starting in the jar, lions eat or sleep,
in terms of that Buridan's donkey goes directly toward any
food it can see (and eats it).

Starting outside the jar, here the spider goes directly to
the side of the jar, or, directly outside the jar opposite
the spider. (Fly.)

The ratios what are cubic or cylindrical: works out units.

The 4/3 pi r ^ 3 is immediate for some reason, under that
it's rational where the diameter is 2, radius 1: ....

Giving the spider a great circle outside the jar, in the
potential, wells, summing the jar in the path integral
from the "line integral", what the spider floats in the jar.

I.e., "the" shortest path is as geonavigating: straight lines, ....

If the spider climbs up the jar, first, then it can see around.

I'd imagine it's much longer around than over.

But, here the point is going around, so that in relativistic terms,
the spider and fly and parallel transport, the jar.

For example on the floor....

Modeling "great circles as shortest distances" is for spherical flies, spiders, jars.

Here it's that under potential, they each have their unipotential.

That "lions sleep or eat" is the idea: there are only lions, what
sleep, or eat. One lion at a time, moves to another lion and
eats the other lion, removing the other lion. Then, this sampling
without replacement, is usually "so and so many, ...".

Here the point is "it's as a cylindrical boundary, between spider and fly".

The optimizing is what points in the vector gradient, what
results under the sum of terms the moments or state of things.

I.e. "optimal: must be same as gradient descent".

Then for example there's "optimal: optimal, but reverse".

Then, the opposite of gradient descent, spider and fly, is
for information between spider and fly.

Though that's a usual ensemble, here is for sheafs: what makes
why sheafs and vector bundles free transforms, ....

At any instant, before any motion, light will travel all the way in
terms of the instant's terms, its image: all the way out for example
sampling or converted to information.

That's giving it infinite speed with respect to classical motion,
the light, while it's effectively a "very large" speed, that in moving
terms, "the spider is also its image".

Then, when the spider for whatever is reason eats flies,
that in the theory there is only one spider and one fly
and it is to be eaten, by the spider, there's that as a
Buridan's donkey that goes directly to food and lion
that eats the other lion, fly, here is as above for this
large parallel (everywhere parallel) space in terms:
following the catenary in information, what results for
a sensible line integral: and why the catenary doesn't
solve the line integral.

Gravity's always information to the spider, fly, jar.

Eg "go directly to middle of jar, go to fly".

The curving inward and outward is for more concave less convex.

Here, what balances catenaries either way: pulling the chain. (What
results the least tension in the path, shortest path.)

(What results from equilibrium and "rest".)

So, catenaries, I think, where, all of relative motion is classical,
is that under information is collected what are changes in path,
what result for reaction what are rest paths in relativistic dynamics
and what are information-theoretic. (Relativistic dynamics,
classical dynamics.)

Re: the optimizing spider

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 by: Mikko - Mon, 16 May 2022 06:06 UTC

On 2022-05-15 17:56:20 +0000, Stan Fultoni said:

> Well, I only mentioned them to point out that they are obviously
> irrelevant (a fact which seemed to elude you)

That I didn't mention them does not mean that I considered them relevant.
Quite obviously.

Mikko

Re: the optimizing spider

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Subject: Re: the optimizing spider
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Mon, 16 May 2022 06:34 UTC

On Sunday, May 15, 2022 at 11:06:43 PM UTC-7, Mikko wrote:
>>>>> There are two distinct optimal paths and one non-optimal straight path
>>>>
>>>> No, there are infinitely many straight paths, involving circumnavigation
>>>> of the cylinder, but those are obviously not relevant. The fact that we can
>>>> go half way around in either direction is also trivial.
>>>
>>> That there is more than one straight path is sufficient to show that
>>> the space is non-Euclidean.
>>
> > Well, I only mentioned them to point out that they are obviously
> > irrelevant (a fact which seemed to elude you)
>
> That I didn't mention them does not mean that I considered them relevant.

You didn't mention them originally because you overlooked them, but when I mentioned them to correct your claim that there were just three straight paths, you repeated that the multiplicity of paths supported the idea that the riddle involves non-Euclidean space (see above), so I had to point out (again) that the topological paths involving circumnavigation or bottom-crossing, were clearly not relevant to the solution of the riddle. Hence the solution of the riddle does not involve non-Euclidean geometry... to the contrary, the solution is precisely to recognize that it doesn't involve non-Euclidean geometry, and you can instantly see the answer in your head.

Re: the optimizing spider

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Subject: Re: the optimizing spider
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 by: RichD - Mon, 16 May 2022 19:01 UTC

On May 15, Mikko wrote:
> That there is more than one straight path is sufficient to show that the
> space is non-Euclidean. It is true that there are infinitely many paths
> but obviously the shortest path is one of the three I mentioned.

What's the third?

--
Rich

Re: the optimizing spider

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 by: Mikko - Tue, 17 May 2022 07:59 UTC

On 2022-05-16 19:01:16 +0000, RichD said:

> On May 15, Mikko wrote:
>> That there is more than one straight path is sufficient to show that the
>> space is non-Euclidean. It is true that there are infinitely many paths
>> but obviously the shortest path is one of the three I mentioned.
>
> What's the third?

One non-optimal is up, down, crossing the bottom, up to the fly.

Mikko

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