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Manifold Clarification

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Frank Wimberly-2

Manifold Clarification

I said that no physical object is a manifold. This may be a better answer to Nick's question. The envelope of a cloud, if it could be defined, might be a manifold depending on cusps etc. Those might be handled by combining manifolds of different dimensions. This would not be a realizable project in my opinion.

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

Steve Smith

Re: Manifold Clarification

> I said that no physical object is a manifold. This may be a better
> answer to Nick's question. The envelope of a cloud, if it could be
> defined, might be a manifold depending on cusps etc. Those might be
> handled by combining manifolds of different dimensions. This would
> not be a realizable project in my opinion.
>
> Frank

More likely darn near a fractal surface... down to the size of a
condensed droplet of water? Ken Perlin's cloud-modeling comes to mind
(multi-scale if not literally fractal).

But model(ed/able) as an idealized manifold based on the triple-point of
water (or is that only clouds forming hail or sleet?)

Nick? mentioned "shroud" which I don't think has a mathematical
definition but i took it to mean something like a convex-hull
(shrink-wrapped surface). From work with Stephen on using imagery of
clouds (or plumes) to calibrate cameras and to estimate their shape as a
function of time, we have looked at things like silhouette analysis.

Clouds and plumes are not entirely opaque and I believe that is because
they are "porous'...   I'm not sure if there are examples in nature of
fully saturated water vapor... maybe only in a vacuum?   Clouds are
(I'm pretty sure) condensed droplets of water vapor dispersed among air
molecules (I suppose I could read up more on cloud science). Plumes
(smoke from a wildfire) are a little more complex but have a significant
component of water vapor/droplets as well as hydrocarbon particulates?
Guerin is surely much more up on this.   During the 2011 Cerro Grande
Fire, we had *baked* pine needles settling around our property... they
were not burned, but may have been fully charred (all volatiles
pyrolized), probably in such an oxygen poor environment that they
couldn't burn.   This was probably a "sorting" process... smaller bits
may have traveled further while larger ones (twigs and branches) fell
short(er)...

- Steve

- .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
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thompnickson2

Re: Manifold Clarification

Steve,

Before you came on FRIAM, during the slandering phase of my presentation, I argued that a cloud consisted of a complex surface each point on which met the following condition: the dewpoint temperature of the air of the air is equal to the ambient temperature of the air. Furthermore, "inside" this boundary, the dewpoint temp is above the ambient temperature, and outside it is below. Both dewpoint temperature This explains why cumulus clouds have flat bottoms: cumulus clouds are visualization of rising columns of air. As the air rises, its pressure and temperature fall, and when they fall below the dewpoint, we see the cloud.. Now this, like any description, is a model, and leaves out a lot of complexity. One of the complexities omitted is the fuzziness of the boundary, particularly at the top of the cloud. Another complexity left out by the model is supper cooled water vapor, which I gather occurs because water, to condense, has to find some particle to condense on. So there are parts of the cloud that are saturated but no condensation has occurred. In a fire cloud, I gather, not only does the fire add water vapor, it adds soot, so, I am guessing, condensation occurs more rapidly and also, guess heaped upon a guess, the release of the latent heat in the water vapor also occurs more vigorously than in a column of non fire related cumulus. A third complexity arises from the heat realized by the freezing of the condensed water. This two, requires nuclei, and so is delayed way above the freezing level of the atmosphere. When the rising column hits the stratosphere, there is a temperature inversion and further lifting ceases and the cloud, now ice crystals, spreads out laterally in the characteristic anvil.

This all I believe because it was shown unto me by God. If God was wrong about any of this, I do hope all you former pilots will correct me.

Some day I am going to take a meteorology course. Perhaps I will enroll in a meteorology program when I am 85.

Nick

Nicholas Thompson
Emeritus Professor of Ethology and Psychology
Clark University
[hidden email]
https://wordpress.clarku.edu/nthompson/

-----Original Message-----
From: Friam <[hidden email]> On Behalf Of Steve Smith
Sent: Friday, June 5, 2020 8:30 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] Manifold Clarification

> I said that no physical object is a manifold. This may be a better
> answer to Nick's question. The envelope of a cloud, if it could be
> defined, might be a manifold depending on cusps etc. Those might be
> handled by combining manifolds of different dimensions. This would
> not be a realizable project in my opinion.
>
> Frank

More likely darn near a fractal surface... down to the size of a condensed droplet of water? Ken Perlin's cloud-modeling comes to mind (multi-scale if not literally fractal).

But model(ed/able) as an idealized manifold based on the triple-point of water (or is that only clouds forming hail or sleet?)

Nick? mentioned "shroud" which I don't think has a mathematical definition but i took it to mean something like a convex-hull (shrink-wrapped surface). From work with Stephen on using imagery of clouds (or plumes) to calibrate cameras and to estimate their shape as a function of time, we have looked at things like silhouette analysis.

Clouds and plumes are not entirely opaque and I believe that is because they are "porous'... I'm not sure if there are examples in nature of fully saturated water vapor... maybe only in a vacuum? Clouds are (I'm pretty sure) condensed droplets of water vapor dispersed among air molecules (I suppose I could read up more on cloud science). Plumes (smoke from a wildfire) are a little more complex but have a significant component of water vapor/droplets as well as hydrocarbon particulates? Guerin is surely much more up on this. During the 2011 Cerro Grande Fire, we had *baked* pine needles settling around our property... they were not burned, but may have been fully charred (all volatiles pyrolized), probably in such an oxygen poor environment that they couldn't burn. This was probably a "sorting" process... smaller bits may have traveled further while larger ones (twigs and branches) fell short(er)...

- Steve

- .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
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- .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
FRIAM Applied Complexity Group listserv
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thompnickson2

Re: Manifold Clarification

In reply to this post by Frank Wimberly-2

So, Frank. Think of the coast of England/Scotland. It is infinitely indented. Anytime we draw a map of it, we enclose every point on that coast line and an area that is not within that coastline. So, wrap England in plastic film and pull the film as tight as we can. We have a shroud. Is there a mathematical name for that? OK, now, let the plastic be infinitely flexible, and let us suck all the air out of the space between the shroud and the coastline. What do we have now? Is there a mathematical name for that?

Let me give them both names. Let me call one a shroud and the other a super shrink wrap. I can imagine some mathematician, just for the hell of it, spending a life time working out what the area is between the shroud and the super shrink wrap. And then, having worked all that out, claiming, as do you, that none of these entities, shroud, ssw, or area between, exist in nature. They are mathematical objects, only.

Which is why Hywel used to say what he used to say about mathematics. Am I write about any of this?

Nick

Nicholas Thompson

Emeritus Professor of Ethology and Psychology

Clark University

[hidden email]

https://wordpress.clarku.edu/nthompson/

From: Friam <[hidden email]> On Behalf Of Frank Wimberly
Sent: Friday, June 5, 2020 8:07 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: [FRIAM] Manifold Clarification

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

Frank Wimberly-2

Re: Manifold Clarification

Recall that I said that if the envelope of a cloud could be defined and specified it would probably be a manifold. "Envelope" is a mathematical concept.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Fri, Jun 5, 2020, 9:47 PM <[hidden email]> wrote:

So, Frank. Think of the coast of England/Scotland. It is infinitely indented. Anytime we draw a map of it, we enclose every point on that coast line and an area that is not within that coastline. So, wrap England in plastic film and pull the film as tight as we can. We have a shroud. Is there a mathematical name for that? OK, now, let the plastic be infinitely flexible, and let us suck all the air out of the space between the shroud and the coastline. What do we have now? Is there a mathematical name for that?

Let me give them both names. Let me call one a shroud and the other a super shrink wrap. I can imagine some mathematician, just for the hell of it, spending a life time working out what the area is between the shroud and the super shrink wrap. And then, having worked all that out, claiming, as do you, that none of these entities, shroud, ssw, or area between, exist in nature. They are mathematical objects, only.

Which is why Hywel used to say what he used to say about mathematics. Am I write about any of this?

Nick

Nicholas Thompson
Emeritus Professor of Ethology and Psychology
Clark University
[hidden email]
https://wordpress.clarku.edu/nthompson/

From: Friam <[hidden email]> On Behalf Of Frank Wimberly
Sent: Friday, June 5, 2020 8:07 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: [FRIAM] Manifold Clarification

I said that no physical object is a manifold. This may be a better answer to Nick's question. The envelope of a cloud, if it could be defined, might be a manifold depending on cusps etc. Those might be handled by combining manifolds of different dimensions. This would not be a realizable project in my opinion.

Frank
---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM
- .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
FRIAM Applied Complexity Group listserv
Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam
un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/

Steve Smith

Re: Manifold Clarification

In reply to this post by thompnickson2

Sounds pretty good to me... sorry I missed it! And Frank's invocation
of "envelope" vs "shroud" seems correct and apt.

Now you are both enlisted to respond when Guerin asks you to go out and
take a picture of your sky/clouds in some direction.

> Steve,
>
> Before you came on FRIAM, during the slandering phase of my presentation, I argued that a cloud consisted of a complex surface each point on which met the following condition: the dewpoint temperature of the air of the air is equal to the ambient temperature of the air. Furthermore, "inside" this boundary, the dewpoint temp is above the ambient temperature, and outside it is below. Both dewpoint temperature This explains why cumulus clouds have flat bottoms: cumulus clouds are visualization of rising columns of air. As the air rises, its pressure and temperature fall, and when they fall below the dewpoint, we see the cloud.. Now this, like any description, is a model, and leaves out a lot of complexity. One of the complexities omitted is the fuzziness of the boundary, particularly at the top of the cloud. Another complexity left out by the model is supper cooled water vapor, which I gather occurs because water, to condense, has to find some particle to condense on. So !
> there are parts of the cloud that are saturated but no condensation has occurred. In a fire cloud, I gather, not only does the fire add water vapor, it adds soot, so, I am guessing, condensation occurs more rapidly and also, guess heaped upon a guess, the release of the latent heat in the water vapor also occurs more vigorously than in a column of non fire related cumulus. A third complexity arises from the heat realized by the freezing of the condensed water. This two, requires nuclei, and so is delayed way above the freezing level of the atmosphere. When the rising column hits the stratosphere, there is a temperature inversion and further lifting ceases and the cloud, now ice crystals, spreads out laterally in the characteristic anvil.
>
> This all I believe because it was shown unto me by God. If God was wrong about any of this, I do hope all you former pilots will correct me.
>
> Some day I am going to take a meteorology course. Perhaps I will enroll in a meteorology program when I am 85.
>
> Nick
>
> Nicholas Thompson
> Emeritus Professor of Ethology and Psychology
> Clark University
> [hidden email]
> https://wordpress.clarku.edu/nthompson/
>
>
>
> -----Original Message-----
> From: Friam <[hidden email]> On Behalf Of Steve Smith
> Sent: Friday, June 5, 2020 8:30 PM
> To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
> Subject: Re: [FRIAM] Manifold Clarification
>
>
>> I said that no physical object is a manifold. This may be a better
>> answer to Nick's question. The envelope of a cloud, if it could be
>> defined, might be a manifold depending on cusps etc. Those might be
>> handled by combining manifolds of different dimensions. This would
>> not be a realizable project in my opinion.
>>
>> Frank
> More likely darn near a fractal surface... down to the size of a condensed droplet of water? Ken Perlin's cloud-modeling comes to mind (multi-scale if not literally fractal).
>
> But model(ed/able) as an idealized manifold based on the triple-point of water (or is that only clouds forming hail or sleet?)
>
> Nick? mentioned "shroud" which I don't think has a mathematical definition but i took it to mean something like a convex-hull (shrink-wrapped surface). From work with Stephen on using imagery of clouds (or plumes) to calibrate cameras and to estimate their shape as a function of time, we have looked at things like silhouette analysis.
>
> Clouds and plumes are not entirely opaque and I believe that is because they are "porous'... I'm not sure if there are examples in nature of fully saturated water vapor... maybe only in a vacuum? Clouds are (I'm pretty sure) condensed droplets of water vapor dispersed among air molecules (I suppose I could read up more on cloud science). Plumes (smoke from a wildfire) are a little more complex but have a significant component of water vapor/droplets as well as hydrocarbon particulates? Guerin is surely much more up on this. During the 2011 Cerro Grande Fire, we had *baked* pine needles settling around our property... they were not burned, but may have been fully charred (all volatiles pyrolized), probably in such an oxygen poor environment that they couldn't burn. This was probably a "sorting" process... smaller bits may have traveled further while larger ones (twigs and branches) fell short(er)...
>
> - Steve
>
>
>
> - .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> archives: http://friam.471366.n2.nabble.com/
> FRIAM-COMIC http://friam-comic.blogspot.com/
>
>
> - .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> archives: http://friam.471366.n2.nabble.com/
> FRIAM-COMIC http://friam-comic.blogspot.com/

thompnickson2

Re: Manifold Clarification

I am pretty sure grandson Miles would do that for Steve; I don't own a camera.

n

Nicholas Thompson
Emeritus Professor of Ethology and Psychology
Clark University
[hidden email]
https://wordpress.clarku.edu/nthompson/

-----Original Message-----
From: Friam <[hidden email]> On Behalf Of Steve Smith
Sent: Friday, June 5, 2020 9:57 PM
To: [hidden email]
Subject: Re: [FRIAM] Manifold Clarification

Sounds pretty good to me... sorry I missed it! And Frank's invocation of "envelope" vs "shroud" seems correct and apt.

Now you are both enlisted to respond when Guerin asks you to go out and take a picture of your sky/clouds in some direction.

> Steve,
>
> Before you came on FRIAM, during the slandering phase of my presentation, I argued that a cloud consisted of a complex surface each point on which met the following condition: the dewpoint temperature of the air of the air is equal to the ambient temperature of the air. Furthermore, "inside" this boundary, the dewpoint temp is above the ambient temperature, and outside it is below. Both dewpoint temperature This explains why cumulus clouds have flat bottoms: cumulus clouds are visualization of rising columns of air. As the air rises, its pressure and temperature fall, and when they fall below the dewpoint, we see the cloud.. Now this, like any description, is a model, and leaves out a lot of complexity. One of the complexities omitted is the fuzziness of the boundary, particularly at the top of the cloud. Another complexity left out by the model is supper cooled water vapor, which I gather occurs because water, to condense, has to find some particle to condense on. So !
> there are parts of the cloud that are saturated but no condensation has occurred. In a fire cloud, I gather, not only does the fire add water vapor, it adds soot, so, I am guessing, condensation occurs more rapidly and also, guess heaped upon a guess, the release of the latent heat in the water vapor also occurs more vigorously than in a column of non fire related cumulus. A third complexity arises from the heat realized by the freezing of the condensed water. This two, requires nuclei, and so is delayed way above the freezing level of the atmosphere. When the rising column hits the stratosphere, there is a temperature inversion and further lifting ceases and the cloud, now ice crystals, spreads out laterally in the characteristic anvil.
>
> This all I believe because it was shown unto me by God. If God was wrong about any of this, I do hope all you former pilots will correct me.
>
> Some day I am going to take a meteorology course. Perhaps I will enroll in a meteorology program when I am 85.
>
> Nick
>
> Nicholas Thompson
> Emeritus Professor of Ethology and Psychology Clark University
> [hidden email] https://wordpress.clarku.edu/nthompson/
>
>
>
> -----Original Message-----
> From: Friam <[hidden email]> On Behalf Of Steve Smith
> Sent: Friday, June 5, 2020 8:30 PM
> To: The Friday Morning Applied Complexity Coffee Group
> <[hidden email]>
> Subject: Re: [FRIAM] Manifold Clarification
>
>
>> I said that no physical object is a manifold. This may be a better
>> answer to Nick's question. The envelope of a cloud, if it could be
>> defined, might be a manifold depending on cusps etc. Those might be
>> handled by combining manifolds of different dimensions. This would
>> not be a realizable project in my opinion.
>>
>> Frank
> More likely darn near a fractal surface... down to the size of a condensed droplet of water? Ken Perlin's cloud-modeling comes to mind (multi-scale if not literally fractal).
>
> But model(ed/able) as an idealized manifold based on the triple-point
> of water (or is that only clouds forming hail or sleet?)
>
> Nick? mentioned "shroud" which I don't think has a mathematical definition but i took it to mean something like a convex-hull (shrink-wrapped surface). From work with Stephen on using imagery of clouds (or plumes) to calibrate cameras and to estimate their shape as a function of time, we have looked at things like silhouette analysis.
>
> Clouds and plumes are not entirely opaque and I believe that is because they are "porous'... I'm not sure if there are examples in nature of fully saturated water vapor... maybe only in a vacuum? Clouds are (I'm pretty sure) condensed droplets of water vapor dispersed among air molecules (I suppose I could read up more on cloud science). Plumes (smoke from a wildfire) are a little more complex but have a significant component of water vapor/droplets as well as hydrocarbon particulates? Guerin is surely much more up on this. During the 2011 Cerro Grande Fire, we had *baked* pine needles settling around our property... they were not burned, but may have been fully charred (all volatiles pyrolized), probably in such an oxygen poor environment that they couldn't burn. This was probably a "sorting" process... smaller bits may have traveled further while larger ones (twigs and branches) fell short(er)...
>
> - Steve
>
>
>
> - .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
> FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn
> GMT-6 bit.ly/virtualfriam un/subscribe
> http://redfish.com/mailman/listinfo/friam_redfish.com
> archives: http://friam.471366.n2.nabble.com/
> FRIAM-COMIC http://friam-comic.blogspot.com/
>
>
> - .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
> FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn
> GMT-6 bit.ly/virtualfriam un/subscribe
> http://redfish.com/mailman/listinfo/friam_redfish.com
> archives: http://friam.471366.n2.nabble.com/
> FRIAM-COMIC http://friam-comic.blogspot.com/

- .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
FRIAM Applied Complexity Group listserv
Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/

- .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -..
FRIAM Applied Complexity Group listserv
Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam
un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/

Steve Smith

Re: Manifold Clarification

> I am pretty sure grandson Miles would do that for Steve; I don't own a camera.

I think he'd be happy with a nice sketch.

No smartphone? I captured mine for him tonight with the webcam on my
laptop from my deck.

>
> n
>
> Nicholas Thompson
> Emeritus Professor of Ethology and Psychology
> Clark University
> [hidden email]
> https://wordpress.clarku.edu/nthompson/
>
>
>
> -----Original Message-----
> From: Friam <[hidden email]> On Behalf Of Steve Smith
> Sent: Friday, June 5, 2020 9:57 PM
> To: [hidden email]
> Subject: Re: [FRIAM] Manifold Clarification
>
> Sounds pretty good to me... sorry I missed it! And Frank's invocation of "envelope" vs "shroud" seems correct and apt.
>
> Now you are both enlisted to respond when Guerin asks you to go out and take a picture of your sky/clouds in some direction.
>
>
>> Steve,
>>
>> Before you came on FRIAM, during the slandering phase of my presentation, I argued that a cloud consisted of a complex surface each point on which met the following condition: the dewpoint temperature of the air of the air is equal to the ambient temperature of the air. Furthermore, "inside" this boundary, the dewpoint temp is above the ambient temperature, and outside it is below. Both dewpoint temperature This explains why cumulus clouds have flat bottoms: cumulus clouds are visualization of rising columns of air. As the air rises, its pressure and temperature fall, and when they fall below the dewpoint, we see the cloud.. Now this, like any description, is a model, and leaves out a lot of complexity. One of the complexities omitted is the fuzziness of the boundary, particularly at the top of the cloud. Another complexity left out by the model is supper cooled water vapor, which I gather occurs because water, to condense, has to find some particle to condense on. S!
> o !
>> there are parts of the cloud that are saturated but no condensation has occurred. In a fire cloud, I gather, not only does the fire add water vapor, it adds soot, so, I am guessing, condensation occurs more rapidly and also, guess heaped upon a guess, the release of the latent heat in the water vapor also occurs more vigorously than in a column of non fire related cumulus. A third complexity arises from the heat realized by the freezing of the condensed water. This two, requires nuclei, and so is delayed way above the freezing level of the atmosphere. When the rising column hits the stratosphere, there is a temperature inversion and further lifting ceases and the cloud, now ice crystals, spreads out laterally in the characteristic anvil.
>>
>> This all I believe because it was shown unto me by God. If God was wrong about any of this, I do hope all you former pilots will correct me.
>>
>> Some day I am going to take a meteorology course. Perhaps I will enroll in a meteorology program when I am 85.
>>
>> Nick
>>
>> Nicholas Thompson
>> Emeritus Professor of Ethology and Psychology Clark University
>> [hidden email] https://wordpress.clarku.edu/nthompson/
>>
>>
>>
>> -----Original Message-----
>> From: Friam <[hidden email]> On Behalf Of Steve Smith
>> Sent: Friday, June 5, 2020 8:30 PM
>> To: The Friday Morning Applied Complexity Coffee Group
>> <[hidden email]>
>> Subject: Re: [FRIAM] Manifold Clarification
>>
>>
>>> I said that no physical object is a manifold. This may be a better
>>> answer to Nick's question. The envelope of a cloud, if it could be
>>> defined, might be a manifold depending on cusps etc. Those might be
>>> handled by combining manifolds of different dimensions. This would
>>> not be a realizable project in my opinion.
>>>
>>> Frank
>> More likely darn near a fractal surface... down to the size of a condensed droplet of water? Ken Perlin's cloud-modeling comes to mind (multi-scale if not literally fractal).
>>
>> But model(ed/able) as an idealized manifold based on the triple-point
>> of water (or is that only clouds forming hail or sleet?)
>>
>> Nick? mentioned "shroud" which I don't think has a mathematical definition but i took it to mean something like a convex-hull (shrink-wrapped surface). From work with Stephen on using imagery of clouds (or plumes) to calibrate cameras and to estimate their shape as a function of time, we have looked at things like silhouette analysis.
>>
>> Clouds and plumes are not entirely opaque and I believe that is because they are "porous'... I'm not sure if there are examples in nature of fully saturated water vapor... maybe only in a vacuum? Clouds are (I'm pretty sure) condensed droplets of water vapor dispersed among air molecules (I suppose I could read up more on cloud science). Plumes (smoke from a wildfire) are a little more complex but have a significant component of water vapor/droplets as well as hydrocarbon particulates? Guerin is surely much more up on this. During the 2011 Cerro Grande Fire, we had *baked* pine needles settling around our property... they were not burned, but may have been fully charred (all volatiles pyrolized), probably in such an oxygen poor environment that they couldn't burn. This was probably a "sorting" process... smaller bits may have traveled further while larger ones (twigs and branches) fell short(er)...
>>
>> - Steve
>>
>>
>>
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jon zingale

Re: Manifold Clarification

This post was updated on .

In reply to this post by Frank Wimberly-2

Barry,

I was hoping you would sketch out more of your objection
to my claim that the Alexander horned sphere provides an
example of a fractal space whose topology is given simply
as a sphere. In speech, I can feel pressured to make the
best of the few words I have room to express and sometimes
at the expense of accuracy. Analysis of the Alexander horned
sphere (and the space it encloses) is a bit more nuanced
than I let on, the details of which may be helpful for our
discussion of clouds. OTOH, Friam discussions are sometimes
nothing short of a bombastic free-for-all where injecting
aporia or the occasional first order footnote is about
*as good as one can hope for*. If it turns out to help our
discussion here, I will dust off my copy of *Hocking & Young*.

Yes, a discussion of limit points would be necessary for
investigating the topology of this pathological object.
Analysis of its interior and exterior yield very different
results, while the ball is simply connected its boundary
is not. Somehow, this off-the-top-of-my-head example
seemed to be relevant enough to Nick's itch that I hoped
it would slow things down.

Nick, Steve, Frank, et al.

Before we dive into Mandelbrot thumping, or some other
obnoxious witch hunt of popular mathematics, what exactly
is our goal? I don't mind beginning with Nick's definition of
a cloud, but only if that means we work to prove what is
and what is not an entailing theorem. Further, I will hope
that we *do not* confuse these theorems for truths about
our material world. I maintain that any definition we start
with will have *some* domain of applicability, but we are
far too along in our understanding of rhetoric (as a culture)
to waste time building strawmen. Granted this, if Nick wants
to use *shrouds* as a way of talking about Darboux sums
<https://en.wikipedia.org/wiki/Darboux_integral>
converging to Riemann Integrals, say, well fine. I am not
entirely sure there is any particular reason we need to
dive into an analytic hole, but hey. Nick, if there is a
question underlying all of this demand for technology,
please state it. EricC, however, helped me to feel justified
in claiming that asking *what is a cloud, really* is not a
productive question.

Jon

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Jochen Fromm-5

Re: Manifold Clarification

In reply to this post by thompnickson2

The coast of England is a classic example of a fractal, a self-similar object that has a broken dimension. A rectangle or a circle are two dimensional objects which have a one dimensional boundary, a line. The country of England has apparently the coast of England as a boundary which is neither a circle nor a rectangle. The more you zoom in, the more rugged it looks like. The coast has a fractal dimension higher than one, say 1.3 or 1.4. It is a measure how complicated the border is, how many points it contains.

The Stokes Theorem in mathematics says roughly that everything that flows through the boundary, for instance people, leads to an increase of the population density inside. The mathematical formulation is based on integrals of manifolds and is quite complicated, but in essence this is what it says as far as I understand it.

Your original question was about the boundary of a cloud. I think we can compare clouds to crowds at a rock concert. From the outside it looks like a unified entity, a flock of people or a cloud of droplets. From the inside you do not see the whole, just a mess of other people. If you fly with a plane through a cloud it is similar, you only see a kind of fog, and not the cloud as a whole. At the boundary there is a more or less sharp drop in the density of people in the crowd or droplets in the cloud. This sudden change in density can be considered as the boundary of the crowd or cloud.

-J.

-------- Original message --------

From: [hidden email]

Date: 6/6/20 05:48 (GMT+01:00)

To: 'The Friday Morning Applied Complexity Coffee Group' <[hidden email]>

Subject: Re: [FRIAM] Manifold Clarification

Which is why Hywel used to say what he used to say about mathematics. Am I write about any of this?

Nick

Nicholas Thompson

Emeritus Professor of Ethology and Psychology

Clark University

[hidden email]

https://wordpress.clarku.edu/nthompson/

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

Steve Smith

A Cloud (Thread?) Never Dies

In reply to this post by jon zingale

Jon -

Bombastic free-for-all is an apt description.

I think "what is a cloud" came up when I used my own "watching a cloud evolve" as an example of how one might begin to develop an intuition for higher-dimensional objects/phenomena through the limits of our visual system. This was for Dave's question about trying to develop an intuition for the 4-polytopes he thinks he observes/perceives/experiences in his dreams/visions.

I tossed in another extra degree of freedom in the discussion by introducing SimTable's aspirations to use the often-widely-visible skyscape of clouds and even more directly interestingly, smoke plumes for the primary purpose of calibrating multiple cameras whose view frustums might include the same clouds. This augments capturing or pre-stating the camera extrinsics (location/pose) and intrinsics (focal length/FOV, etc.) and the use of landscape features (skyline, etc.) for tweaking calibration. Smoke plumes, of course, have more direct utility to the problem at hand, of estimating and locating wildfire as it evolves.

The first observation about clouds is very intuitional and perhaps whimsical... maybe I really can't intuit anything about the distribution of atmospheric conditions by observing the evolution of a cloud... and the second is very practical and any mathematical abstractions obtained for that purpose are only as meaningful as they are useful. I appreciate your offering of the _Alexander Horned Sphere_ in that spirit.

Clouds are interesting "alternative" objects to say mountains or buildings because of there ephemerality and ambiguity of boundary, etc. This tangent may be of interest to those considering "what means object".

Over my shoulder in many of our zoom calls, sits a hand-painted and framed phrase by the hand (and mind?) of Thich Naht Hahn which states "A Cloud Never Dies". This use of the term "Cloud" references (for me) all of the observations above and many more. Thus the explosion of threads when things like this are discussed on FriAM.

Some of us are primarily an analytical bunch, wanting to dissect things down until we feel we understand (apprehend) the parts directly and then by extension, possibly understand the original whole in that way. Of course, the theme that brought this group together is bigger than that. Systems Thinking, Complexity, Synthesis, Emergence, Exaptation, Spandrels, Attractors, etc. are all complementary to the traditions of Analytical Thinking, yet compatible.

So, on this list, I really have no other goal perhaps than to put "yet more perspectives on the table" on the off chance that someone will recognize one of them and provide some parallax that is useful (or interesting) to me. Well, that and to _scratch the itches_ that sometimes spontaneously jump up under the casts that others try to put around what they see to be a broken limb, thinking that reducing the degrees of freedom is the best way to "put it right".

We ARE the proverbial "Blind Men and the Elephant". Our meta-trickster made this observation weeks ago:

http://friam-comic.blogspot.com/2020/05/the-elephant-in-room.html

- Steve

On 6/5/20 11:13 PM, Jon Zingale wrote:

I was hoping you would sketch out more of your objection
to my claim that the Alexander horned sphere provides an
example of a fractal space whose topology is given simply
as a sphere. In speech, I can feel pressured to make the
best of the few words I have room to express and sometimes
at the expense of accuracy. Analysis of the Alexander horned
sphere (and the space it encloses) is a bit more nuanced
than I let on, the details of which may be helpful for our
discussion of clouds. OTOH, Friam discussions are sometimes
nothing short of a bombastic free-for-all where injecting
aporia or the occasional first order footnote is about
as good as one can hope for. If it turns out to help our
discussion here, I will dust off my copy of Hocking & Young.

Yes, a discussion of limit points would be necessary for
investigating the topology of this pathological object.
Analysis of its interior and exterior yield very different
results, while the ball is simply connected its boundary
is not. Somehow, this off-the-top-of-my-head example
seemed to be relevant enough to Nick's itch that I hoped
it would slow things down.

Nick, Steve, Frank, et al.

Before we dive into Mandelbrot thumping, or some other

obnoxious witch hunt of popular mathematics, what exactly

is our goal? I don't mind beginning with Nick's definition of

a cloud, but only if that means we work to prove what is

and what is not an entailing theorem. Further, I will hope

that we do not confuse these theorems for truths about

our material world. I maintain that any definition we start

with will have some domain of applicability, but we are

far too along in our understanding of rhetoric (as a culture)

to waste time building strawmen. Granted this, if Nick wants

to use shrouds as a way of talking about Darboux sums

converging to Riemann Integrals, say, well fine. I am not

entirely sure there is any particular reason we need to

dive into an analytic hole, but hey. Nick, if there is a

question underlying all of this demand for technology,

please state it. EricC, however, helped me to feel justified

in claiming that asking what is a cloud, really is not a

productive question.

Jon
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FRIAM Applied Complexity Group listserv
Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
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Frank Wimberly-2

Re: A Cloud (Thread?) Never Dies

Jon,

I see Alexander's horned sphere is defined in a problem in Spivak's book on differential geometry. I'm glad you mentioned it.

Frank

On Sat, Jun 6, 2020 at 9:24 AM Steve Smith <[hidden email]> wrote:

Jon -

Bombastic free-for-all is an apt description.

I think "what is a cloud" came up when I used my own "watching a cloud evolve" as an example of how one might begin to develop an intuition for higher-dimensional objects/phenomena through the limits of our visual system.   This was for Dave's question about trying to develop an intuition for the 4-polytopes he thinks he observes/perceives/experiences in his dreams/visions.

I tossed in another extra degree of freedom in the discussion by introducing SimTable's aspirations to use the often-widely-visible skyscape of clouds and even more directly interestingly, smoke plumes for the primary purpose of calibrating multiple cameras whose view frustums might include the same clouds.   This augments capturing or pre-stating the camera extrinsics (location/pose) and intrinsics (focal length/FOV, etc.) and the use of landscape features (skyline, etc.) for tweaking calibration.   Smoke plumes, of course, have more direct utility to the problem at hand, of estimating and locating wildfire as it evolves.

The first observation about clouds is very intuitional and perhaps whimsical... maybe I really can't intuit anything about the distribution of atmospheric conditions by observing the evolution of a cloud... and the second is very practical and any mathematical abstractions obtained for that purpose are only as meaningful as they are useful.    I appreciate your offering of the _Alexander Horned Sphere_ in that spirit.

Clouds are interesting "alternative" objects to say mountains or buildings because of there ephemerality and ambiguity of boundary, etc.   This tangent may be of interest to those considering "what means object".

Over my shoulder in many of our zoom calls, sits a hand-painted and framed phrase by the hand (and mind?) of Thich Naht Hahn which states "A Cloud Never Dies".   This use of the term "Cloud" references (for me) all of the observations above and many more.   Thus the explosion of threads when things like this are discussed on FriAM.

Some of us are primarily an analytical bunch, wanting to dissect things down until we feel we understand (apprehend) the parts directly and then by extension, possibly understand the original whole in that way.   Of course, the theme that brought this group together is bigger than that.   Systems Thinking, Complexity, Synthesis, Emergence, Exaptation, Spandrels, Attractors, etc. are all complementary to the traditions of Analytical Thinking, yet compatible.

So, on this list, I really have no other goal perhaps than to put "yet more perspectives on the table" on the off chance that someone will recognize one of them and provide some parallax that is useful (or interesting) to me.   Well, that and to _scratch the itches_ that sometimes spontaneously jump up under the casts that others try to put around what they see to be a broken limb, thinking that reducing the degrees of freedom is the best way to "put it right".

We ARE the proverbial "Blind Men and the Elephant".   Our meta-trickster made this observation weeks ago:

    http://friam-comic.blogspot.com/2020/05/the-elephant-in-room.html

- Steve

On 6/5/20 11:13 PM, Jon Zingale wrote:
I was hoping you would sketch out more of your objection
to my claim that the Alexander horned sphere provides an
example of a fractal space whose topology is given simply
as a sphere. In speech, I can feel pressured to make the
best of the few words I have room to express and sometimes
at the expense of accuracy. Analysis of the Alexander horned
sphere (and the space it encloses) is a bit more nuanced
than I let on, the details of which may be helpful for our
discussion of clouds. OTOH, Friam discussions are sometimes
nothing short of a bombastic free-for-all where injecting
aporia or the occasional first order footnote is about
as good as one can hope for. If it turns out to help our
discussion here, I will dust off my copy of Hocking & Young.

Yes, a discussion of limit points would be necessary for
investigating the topology of this pathological object.
Analysis of its interior and exterior yield very different
results, while the ball is simply connected its boundary
is not. Somehow, this off-the-top-of-my-head example
seemed to be relevant enough to Nick's itch that I hoped
it would slow things down.

Nick, Steve, Frank, et al.

Before we dive into Mandelbrot thumping, or some other

obnoxious witch hunt of popular mathematics, what exactly

is our goal? I don't mind beginning with Nick's definition of

a cloud, but only if that means we work to prove what is

and what is not an entailing theorem. Further, I will hope

that we do not confuse these theorems for truths about

our material world. I maintain that any definition we start

with will have some domain of applicability, but we are

far too along in our understanding of rhetoric (as a culture)

to waste time building strawmen. Granted this, if Nick wants

to use shrouds as a way of talking about Darboux sums

converging to Riemann Integrals, say, well fine. I am not

entirely sure there is any particular reason we need to

dive into an analytic hole, but hey. Nick, if there is a

question underlying all of this demand for technology,

please state it. EricC, however, helped me to feel justified

in claiming that asking what is a cloud, really is not a

productive question.

Jon
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Frank Wimberly
140 Calle Ojo Feliz
Santa Fe, NM 87505
505 670-9918

jon zingale

Re: A Cloud (Thread?) Never Dies

In reply to this post by Steve Smith

Frank,

Thanks for reminding me about Spivak's Differential Geometry series.
They had all 7(?) in the St. John's library, but last year volume one
disappeared. Thankfully, I found a pdf online. He mentions a text by

my point-set topology professor, Dr. Vick, on page 3! Do you think

St. John's will reimburse me $40 for my courtesy borrower card?

Jon

Frank Wimberly-2

Re: A Cloud (Thread?) Never Dies

I'm borrowed their volume 1 but then bought one. I'd better check that I didn't get confused. I doubt they'll give your $40 back. They'll say, "We have lots of other books you can read."

I checked. The one I have came from Amazon.

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 6, 2020, 10:03 PM Jon Zingale <[hidden email]> wrote:

Frank,

Thanks for reminding me about Spivak's Differential Geometry series.
They had all 7(?) in the St. John's library, but last year volume one
disappeared. Thankfully, I found a pdf online. He mentions a text by
my point-set topology professor, Dr. Vick, on page 3! Do you think
St. John's will reimburse me $40 for my courtesy borrower card?

Jon
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jon zingale

Re: A Cloud (Thread?) Never Dies

:) Yeah, I just mean because of Covid. Really, I am just joking anyway.
They don't need my $40 and I am glad to invest it. I kind of wish you
had their copy, then at least it would have a hope of being returned.
Maybe they could invest my $40 towards getting a new copy of vol 1.
I keep wanting to make yellow pig jokes or some other Spivakian
inside joke, maybe next time.

--
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Frank Wimberly-2

Re: A Cloud (Thread?) Never Dies

They can't find any yp references in his latest book "Physics for Mathematicians", a book I should read.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 6, 2020, 10:18 PM Jon Zingale <[hidden email]> wrote:

:) Yeah, I just mean because of Covid. Really, I am just joking anyway.
They don't need my $40 and I am glad to invest it. I kind of wish you
had their copy, then at least it would have a hope of being returned.
Maybe they could invest my $40 towards getting a new copy of vol 1.
I keep wanting to make yellow pig jokes or some other Spivakian
inside joke, maybe next time.

--
Sent from: http://friam.471366.n2.nabble.com/

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