whit3rd wrote:
> On Tuesday, June 29, 2021 at 4:41:59 PM UTC-7, Phil Hobbs wrote:
>> whit3rd wrote:
>>> On Tuesday, June 29, 2021 at 3:27:15 PM UTC-7, jla...@highlandsniptechnology.com wrote:
>>>> On Tue, 29 Jun 2021 16:00:56 -0400, Phil Hobbs
>>>> <pcdhSpamM...@electrooptical.net> wrote:
>
>>>>> The balls will bounce around and bounce around forever, but none of them
>>>>> can ever jump off the table and hit the ceiling.
>>>
>>>> Couldn't that happen? Like five balls converge on one and transfer all
>>>> their momentum. That doesn't seem to violate any conservation rules.
>>>
>>> For momentum, each component is separately conserved. Five balls moving
>>> in the X-Y plane don't have Z-component momentum
>
>> 'T'aint a momentum issue. The table can supply any Z-component
>> required, and of course the initial momentum of the cue ball is enough
>> to make it bounce--as any beginning pool player knows. ;)
>
> If you use a cue ball with a different diameter than the other balls (not uncommon in
> quarter-to-play tables) then the table can supply momentum. Otherwise, it takes a fierce
> spin transfer at the cue or some kind of miracle to make that bounce.
>

Or even a vanishingly small one, plus an indefinitely long time bouncing
around.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

On 6/30/2021 7:54 AM, Clive Arthur wrote:
> That's a pretty good idea - add a simple weather station atop each mast and you
> could warn people to get the washing in a little in advance.

That only works if you do an active *forecast* for each of those
specific data collection points. I can count ~15 *networked*
"personal weather stations" within a mile of my home.
Temperatures currently reported vary from 85F to 89F.

One can argue that these aren't NBS-traceable instruments (and
who knows how carefully they are sited), but I'd wager that
there actually is that much variation in this small of an area
(changes in elevation, vegetation, natural features, etc.)

E.g., the nearest hospital is ~2.5 miles as the crow flies.
They will frequently have rain or even a dusting of snow (!)
while we won't see either.

["Spring" comes to the south end of my street two weeks earlier
than it does to my end -- just three blocks further north!
(as evidenced by when the various flora bloom)]

Which one(s) should be used to forecast *my* weather?

On Thursday, July 1, 2021 at 1:09:35 AM UTC+10, Phil Hobbs wrote:
> whit3rd wrote:
> > On Tuesday, June 29, 2021 at 4:41:59 PM UTC-7, Phil Hobbs wrote:
> >> whit3rd wrote:
> >>> On Tuesday, June 29, 2021 at 3:27:15 PM UTC-7, jla...@highlandsniptechnology.com wrote:
> >>>> On Tue, 29 Jun 2021 16:00:56 -0400, Phil Hobbs
> >>>> <pcdhSpamM...@electrooptical.net> wrote:
> >
> >>>>> The balls will bounce around and bounce around forever, but none of them
> >>>>> can ever jump off the table and hit the ceiling.
> >>>
> >>>> Couldn't that happen? Like five balls converge on one and transfer all
> >>>> their momentum. That doesn't seem to violate any conservation rules.
> >>>
> >>> For momentum, each component is separately conserved. Five balls moving
> >>> in the X-Y plane don't have Z-component momentum
> >
> >> 'T'aint a momentum issue. The table can supply any Z-component
> >> required, and of course the initial momentum of the cue ball is enough
> >> to make it bounce--as any beginning pool player knows. ;)
> >
> > If you use a cue ball with a different diameter than the other balls (not uncommon in
> > quarter-to-play tables) then the table can supply momentum. Otherwise, it takes a fierce
> > spin transfer at the cue or some kind of miracle to make that bounce.
> >
> Or even a vanishingly small one, plus an indefinitely long time bouncing
> around.

Happily, billiard tables are lossy. The balls stop rolling eventually. If you put spin on the ball, the rotational momentum decays faster than the translational momentum.

I did play billiards with theology students from time to time, and they didn't do anything miraculous - they were Methodists, so they may have been restraining themselves.

--
Bill Sloman, Sydney

On Tuesday, June 29, 2021 at 5:55:22 PM UTC-4, Phil Hobbs wrote:
> Fred Bloggs wrote:
> > On Tuesday, June 29, 2021 at 4:01:05 PM UTC-4, Phil Hobbs wrote:
> >> Fred Bloggs wrote:
> >>> Chaotic does not mean ultra-random as some people seem to think.
> >>> Chaotic systems are fundamentally deterministic dynamical
> >>> systems that have the property of exhibiting wildly different
> >>> outcomes as a function of the initial conditions. Small errors in
> >>> estimation/ measurement of initial conditions can result in
> >>> unusably large differences in predicted results. If the
> >>> prediction time scale is much smaller than the Lyapunov time, and
> >>> initial conditions are measured with precision, predicted
> >>> outcomes can have very good fidelity , and this is how they're
> >>> tamed analytically.
> >>>
> >>> "Chaos theory concerns deterministic systems whose behavior can,
> >>> in principle, be predicted. Chaotic systems are predictable for a
> >>> while and then 'appear' to become random. The amount of time that
> >>> the behavior of a chaotic system can be effectively predicted
> >>> depends on three things: how much uncertainty can be tolerated in
> >>> the forecast, how accurately its current state can be measured,
> >>> and a time scale depending on the dynamics of the system, called
> >>> the Lyapunov time. Some examples of Lyapunov times are: chaotic
> >>> electrical circuits, about 1 millisecond; weather systems, a few
> >>> days (unproven); the inner solar system, 4 to 5 million
> >>> years.[19] In chaotic systems, the uncertainty in a forecast
> >>> increases exponentially with elapsed time. Hence, mathematically,
> >>> doubling the forecast time more than squares the proportional
> >>> uncertainty in the forecast. This means, in practice, a
> >>> meaningful prediction cannot be made over an interval of more
> >>> than two or three times the Lyapunov time. When meaningful
> >>> predictions cannot be made, the system appears random."
> >>>
> >>> https://en.wikipedia.org/wiki/Chaos_theory
> >>>
> >> The kicker is that chaotic systems are very powerful noise
> >> amplifiers, and there is a fundamental limit to the precision of
> >> the initial conditions.
> >>
> >> If you have a frictionless pool table with perfectly elastic
> >> collisions, and break the rack normally, the position uncertainties
> >> of the balls grow exponentially with time. That is, a small error
> >> in aiming makes both balls go off at a slightly incorrect angle.
> >> That angular error grows linearly as the balls roll, causing the
> >> next collisions to be further off in aim. That causes more angular
> >> error, which turns into more aiming error on the next collisions,
> >> and so on.
> >>
> >> I don't have it handy, but I recall reading a calculation that
> >> showed that after 30 seconds of this, the amplified Heisenberg
> >> uncertainty became larger than the diameter of a ball, meaning that
> >> you could no longer--even in principle--predict which balls would
> >> collide next.
> >>
> >> Information is appearing in the universe at a very high rate all
> >> the time.
> >>
> >> Like many chaotic systems, the motions of these ideal pool balls
> >> have constraints, such as that the total energy of the system is
> >> constant. The balls will bounce around and bounce around forever,
> >> but none of them can ever jump off the table and hit the ceiling.
> >> As in epidemics, exponential growth just applies to the early
> >> stages. ;)
> >
> > I'm mainly concerned with short term (3 days) weather prediction. The
> > European model streams real time weather data into the simulation
> > continuously, which I assume means the initial conditions are
> > constantly being reset. There use tens if not hundreds of thousands
> > of real time sensor inputs, terrestrial and satellite. If a butterfly
> > flaps its wings in the Himalayas, they know about it. The price they
> > pay is 24 hour turnaround, but they are consistently dead on
> > accurate. It's a gold standard of weather prediction right now.
> Okay, but your thread title is completely misleading--if a system is
> deterministic, it doesn't stop after three days.

https://www.ecmwf.int/en/research/modelling-and-prediction

> Cheers
>
> Phil Hobbs
>
> --
> Dr Philip C D Hobbs
> Principal Consultant
> ElectroOptical Innovations LLC / Hobbs ElectroOptics
> Optics, Electro-optics, Photonics, Analog Electronics
> Briarcliff Manor NY 10510
>
> http://electrooptical.net
> http://hobbs-eo.com

On 6/29/2021 6:24 PM, jlarkin@highlandsniptechnology.com wrote:
> On Tue, 29 Jun 2021 12:10:45 -0700 (PDT), Fred Bloggs
> <bloggs.fredbloggs.fred@gmail.com> wrote:
>
>> Chaotic does not mean ultra-random as some people seem to think. Chaotic systems are fundamentally deterministic dynamical systems that have the property of exhibiting wildly different outcomes as a function of the initial conditions. Small errors in estimation/ measurement of initial conditions can result in unusably large differences in predicted results. If the prediction time scale is much smaller than the Lyapunov time, and initial conditions are measured with precision, predicted outcomes can have very good fidelity , and this is how they're tamed analytically.
>>
>> "Chaos theory concerns deterministic systems whose behavior can, in principle, be predicted. Chaotic systems are predictable for a while and then 'appear' to become random. The amount of time that the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the Lyapunov time. Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days (unproven); the inner solar system, 4 to 5 million years.[19] In chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast. This means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When
>> meaningful predictions cannot be made, the system appears random."
>>
>> https://en.wikipedia.org/wiki/Chaos_theory
>
> In real-life systems, social/economic/climactic, we have only crude
> knowledge of the element behavior, the couplings, or the initial
> state. People and clouds don't behave like planets.
Mercury's orbit is highly chaotic over time frames of only a few tens of
millions of years into the future, which isn't much on the scale of
geological time. Measurement error of bigger than about an mm today will
throw it off completely if you try to run that model 100 million years
forward.
> People too used to power think they can understand, hence should
> control, societies and economics. They usually screw things up.
>

On Wed, 30 Jun 2021 18:48:20 -0400, bitrex <user@example.net> wrote:

>On 6/29/2021 6:24 PM, jlarkin@highlandsniptechnology.com wrote:
>> On Tue, 29 Jun 2021 12:10:45 -0700 (PDT), Fred Bloggs
>> <bloggs.fredbloggs.fred@gmail.com> wrote:
>>
>>> Chaotic does not mean ultra-random as some people seem to think. Chaotic systems are fundamentally deterministic dynamical systems that have the property of exhibiting wildly different outcomes as a function of the initial conditions. Small errors in estimation/ measurement of initial conditions can result in unusably large differences in predicted results. If the prediction time scale is much smaller than the Lyapunov time, and initial conditions are measured with precision, predicted outcomes can have very good fidelity , and this is how they're tamed analytically.
>>>
>>> "Chaos theory concerns deterministic systems whose behavior can, in principle, be predicted. Chaotic systems are predictable for a while and then 'appear' to become random. The amount of time that the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the Lyapunov time. Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days (unproven); the inner solar system, 4 to 5 million years.[19] In chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast. This means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When
>>> meaningful predictions cannot be made, the system appears random."
>>>
>>> https://en.wikipedia.org/wiki/Chaos_theory
>>
>> In real-life systems, social/economic/climactic, we have only crude
>> knowledge of the element behavior, the couplings, or the initial
>> state. People and clouds don't behave like planets.
>
>Mercury's orbit is highly chaotic over time frames of only a few tens of
>millions of years into the future, which isn't much on the scale of
>geological time. Measurement error of bigger than about an mm today will
>throw it off completely if you try to run that model 100 million years
>forward.
>

The weather here is chaotic on the scale of one day. The stock market
is too.

On Wednesday, June 30, 2021 at 5:59:28 PM UTC-7, John Larkin wrote:

> The weather here is chaotic on the scale of one day. The stock market
> is too.

The weather here was just as hot as the five-days-earlier forecasts told us.
My stocks don't get traded on the scale of one day. Do yours?

What's your timescale measure algorithm? Does it take twenty-sided dice?

On 6/30/2021 8:59 PM, John Larkin wrote:
> On Wed, 30 Jun 2021 18:48:20 -0400, bitrex <user@example.net> wrote:
>
>> On 6/29/2021 6:24 PM, jlarkin@highlandsniptechnology.com wrote:
>>> On Tue, 29 Jun 2021 12:10:45 -0700 (PDT), Fred Bloggs
>>> <bloggs.fredbloggs.fred@gmail.com> wrote:
>>>
>>>> Chaotic does not mean ultra-random as some people seem to think. Chaotic systems are fundamentally deterministic dynamical systems that have the property of exhibiting wildly different outcomes as a function of the initial conditions. Small errors in estimation/ measurement of initial conditions can result in unusably large differences in predicted results. If the prediction time scale is much smaller than the Lyapunov time, and initial conditions are measured with precision, predicted outcomes can have very good fidelity , and this is how they're tamed analytically.
>>>>
>>>> "Chaos theory concerns deterministic systems whose behavior can, in principle, be predicted. Chaotic systems are predictable for a while and then 'appear' to become random. The amount of time that the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the Lyapunov time. Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days (unproven); the inner solar system, 4 to 5 million years.[19] In chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast. This means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When
>>>> meaningful predictions cannot be made, the system appears random."
>>>>
>>>> https://en.wikipedia.org/wiki/Chaos_theory
>>>
>>> In real-life systems, social/economic/climactic, we have only crude
>>> knowledge of the element behavior, the couplings, or the initial
>>> state. People and clouds don't behave like planets.
>>
>> Mercury's orbit is highly chaotic over time frames of only a few tens of
>> millions of years into the future, which isn't much on the scale of
>> geological time. Measurement error of bigger than about an mm today will
>> throw it off completely if you try to run that model 100 million years
>> forward.
>>
>
> The weather here is chaotic on the scale of one day. The stock market
> is too.
>
Weather report fort southeast Massachusetts on Sunday evening said there
was going to be severe thunderstorms tonight 90% probability and there
were, a real rip-roarer that went on for about an hour with lightning
flashes like a Berlin discotheque. Brief thunderstorms and downpours are
pretty common here during the summer but tonights was extra-spicy.
Power stayed up though, not even a flicker. the local utility seem to
have been keeping the trees trimmed and tidy lately

On 6/30/2021 9:07 PM, whit3rd wrote:
> On Wednesday, June 30, 2021 at 5:59:28 PM UTC-7, John Larkin wrote:
>
>> The weather here is chaotic on the scale of one day. The stock market
>> is too.
>
> The weather here was just as hot as the five-days-earlier forecasts told us.
> My stocks don't get traded on the scale of one day. Do yours?
>
> What's your timescale measure algorithm? Does it take twenty-sided dice?
>

Some accurately predicted big-ass cells moving thru:

<https://imgur.com/a/ohm2Aq2>

Someone probably going to post a nice picture of lightning strikes on
the Pru and John Hancock towers on Reddit

On 6/30/2021 6:07 PM, whit3rd wrote:
> On Wednesday, June 30, 2021 at 5:59:28 PM UTC-7, John Larkin wrote:
>
>> The weather here is chaotic on the scale of one day. The stock market
>> is too.
>
> The weather here was just as hot as the five-days-earlier forecasts told us.

Our weather forecasts are surprisingly accurate -- a week to 10 days out.
Typically, the temperature is all that is predicted as precipitation
is almost always "zero".

But, daytime highs and nighttime lows (at the official recording station)
are usually spot on.

Today, 50% chance of rain and, amusingly, it actually did so. But, I imagine
only in parts of town (225 sq miles -- about the size of chitown, 5 times
larger than San Francisco or Boston -- and with mountains on several sides).

Tomorrow, 80% -- which could just as easily translate to *nothing* for my
neighborhood -- or, a full on storm. <shrug> But, I'll wager that I will find
rain *somewhere* in town...

> My stocks don't get traded on the scale of one day. Do yours?
>
> What's your timescale measure algorithm? Does it take twenty-sided dice?

On 6/29/2021 2:10 PM, Fred Bloggs wrote:
> Chaotic does not mean ultra-random as some people seem to think. Chaotic systems are fundamentally deterministic dynamical systems that have the property of exhibiting wildly different outcomes as a function of the initial conditions. Small errors in estimation/ measurement of initial conditions can result in unusably large differences in predicted results. If the prediction time scale is much smaller than the Lyapunov time, and initial conditions are measured with precision, predicted outcomes can have very good fidelity , and this is how they're tamed analytically.
>
> "Chaos theory concerns deterministic systems whose behavior can, in principle, be predicted. Chaotic systems are predictable for a while and then 'appear' to become random. The amount of time that the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the Lyapunov time. Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days (unproven); the inner solar system, 4 to 5 million years.[19] In chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast. This means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When meaningful predictions cannot be made, the system appears random."
>
> https://en.wikipedia.org/wiki/Chaos_theory
>
The double-rod pendulum example in the link is fascinating.