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The Causes of Temperature (Geophysics)
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Chad


In: Ramsbottom
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Wireloop wrote:
Could you elaborate a bit Chad?


Conventional sundials can be up to a quarter of an hour out, depending upon the time of year, but analemmic ones are very accurate. The modern one below uses an analemmic gnomon (the bit that casts the shadow), others have a conventional gnomon but replace the hour markers with individual analemmic figures.



This is how it works.


Not sure how the ancients made the corrections, but the first recorded reference to an analemmic sundial is (if we can believe anything from the Roman era) via the accounts of Vitruvius (first century BC)... and our good friend Ptolomy was supposed to be dicking around with them a couple of hundred years later.
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Chad


In: Ramsbottom
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Wireloop wrote:
And since we've taken this path into the jungle of symbology, what do you think of the opening line from John?

In the beginning was the Logos, and the Logos was with God, and the Logos was God. He (it) was with God in the beginning. Through him (it) all things were made; without him (it) nothing was made that has been made. In him (it) was life, and that life was the light of all mankind. The light shines in the darkness, and the darkness has not overcome it.

You're inviting me to tread into waters I would normally try to avoid... (I'm a simple engineer who leaves this sort of thing to deeper thinker)... but I would equate the Logos with divine logic (for etymological continuity) or reasoning, rather than the word of God.

Logo (as in the modern usage) as a symbol is tempting, but it is a shortened form of logogram... and it is the 'gram' bit that is etymologically connected to 'symbol' not the 'logo' bit.

But I'm here to be educated.
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Wireloop


In: Detroit
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Chad wrote:
You're inviting me to tread into waters I would normally try to avoid... (I'm a simple engineer who leaves this sort of thing to deeper thinker)... but I would equate the Logos with divine logic (for etymological continuity) or reasoning, rather than the word of God.


You're too modest.....I think you hit it on the nose. Logos, to ancient man, was an amalgamation of word, logic, speech, reasoning, speculation, measurement, ratio. In some regards it is very similar to Quintessence which was the 'source' and 'creator' of the other elements which composed the Universe. In the platonic Judaism of Philo, Logos is the creative reasoning of God, which much like the 'fire' of the Stoics, acts as the mediating principle which creates and detroys 'existence'. This too is how 'John' (above) uses the term.

Euclid and Plato also envision the universe as being constructed by one principle. The Logos of Extreme and Mean.
You see the whole goal of Euclid's Elements is to teach the 'student' Geometry. NO, IT'S NOT.
The goal is to release the prisoner from his cave, the hostage from his capture, by showing him the 'reason' for/of the Universe. Revealing Deus Ex Machina.
Euclid is showing the hostage how (in 13 'chapters') to construct the Universe via the 5 platonic solids. The Logos of the Extreme and Mean is the crux.

Euclid:
http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/propVI30.html

Plato Timaeus:
[31b] Wherefore, in order that this Creature might resemble the all perfect Living Creature in respect of its uniqueness, for this reason its Maker made neither two Universes nor an infinite number, but there is and will continue to be this one generated Heaven, unique of its kind. Now that which has come into existence must needs be of bodily form, visible and tangible; yet without fire nothing could ever become visible, nor tangible without some solidity, nor solid without earth. Hence, in beginning to construct the body of the All, God was making it of fire and earth. But it is not possible that two things alone should be conjoined without a third; [31c] for there must needs be some intermediary bond to connect the two. And the fairest of bonds is that which most perfectly unites into one both itself and the things which it binds together; and to effect this in the fairest manner is the natural property of proportion. For whenever the middle term of any three numbers, cubic or square [32a] is such that as the first term is to it, so is it to the last term, and again, conversely, as the last term is to the middle, so is the middle to the first,—then the middle term becomes in turn the first and the last, while the first and last become in turn middle terms, and the necessary consequence will be that all the terms are interchangeable, and being interchangeable they all form a unity.
Now if the body of the All [32b] had had to come into existence as a plane surface, having no depth, one middle term would have sufficed to bind together both itself and its fellow-terms; but now it is otherwise: for it behoved it to be solid of shape, and what brings solids into unison is never one middle term alone but always two.1 Thus it was that in the midst between fire and earth God set water and air, and having bestowed upon them so far as possible a like ratio one towards another—air being to water as fire to air, and water being to earth as air to water, —he joined together and constructed a Heaven visible and tangible.


Can you guess how our analemma might relate to all of this?
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Chad


In: Ramsbottom
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Can you guess how our analemma might relate to all of this?

It binds the irregular daily movement of Sol (in terms of three dimensional space and time) into a unified form.

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Wireloop


In: Detroit
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Chad wrote:

It binds the irregular daily movement of Sol (in terms of three dimensional space and time) into a unified form.



Yes, I agree. Nice graph.
But does this 'unified form' relate to the Plato's (and Euclid's, Philo's, John's,, etc...) Unified Theory of the Universe in any way? In other words, does it relate to the "division of a 'line' into Extreme and Mean Ratio" (the Logos)?

There are an infinite amount of discontinuous proportions (porportions which have four terms, like a,b,c,d or 2,4,3,6):
a : b : : c : d
2 : 4 : : 3 : 6
two is to four as three is to six

There are an infnite amount of continuous proportion (proportions which have three terms like a,b,c or 2,4,8):
a : b : : b : c
2 : 4 : : 4 : 8
two is four as four is to eight

But there is only ONE proportion which rules them all. A proportion with only TWO TERMS like a : b : : b : ?.

Remember what Plato said in his Unified Theory:
And the fairest of bonds is that which most perfectly unites into one both itself and the things which it binds together; and to effect this in the fairest manner is the natural property of proportion. For whenever the middle term of any three numbers, cubic or square is such that as the first term is to it, so is it to the last term and again, conversely, as the last term is to the middle, so is the middle to the first,—then the middle term becomes in turn the first and the last, while the first and last become in turn middle terms, and the necessary consequence will be that all the terms are interchangeable, and being interchangeable they all form a unity.


Let's plug in some numbers and see if we can ascertain what Plato is talking about in his Unified Theory.

For whenever the middle term (1.618) of any three numbers, cubic or square is such that as the first term (1) is to it (1.618), so is it (1.618) to the last term (1 + 1.618)


1 / 1.618 = 1.618 / 1+1.618
a : b : : b : (a+b)
You see only TWO TERMS, a and b
or
1 and 1.618.

I cringe when people say "The Golden Ratio IS 1.618.....".
It is not!
The Golden Ratio IS the reasoning principle of the Prime Mover. It IS the movement of Unity away from itself and into itself. It IS 'The Creation Process', and one way to grasp it is by the mathematical expression of the proportion 1 : 1.618.
1.618 is not Divine. It must paired with Unity (1) in order to be 'Divine'.

Can we find this proportion, this 'Divine Logos', in our analemma?
It 'should' be there right?
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Chad


In: Ramsbottom
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Can we find this proportion, this 'Divine Logos', in our analemma?
It 'should' be there right?

Took me a little while (I was wrongly looking in the geometry)... then I found it.

The smaller upper lobe is created in about 140 days... the larger lobe accounts for the remainder of the year.

225 / 140 = 1.607

Not sure what to make of all this!

(This is just an estimate... The actual crossover point is hard to determine on the diagrams, so it might be even closer to the Golden Ratio if you could sub-divide days.)
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Wireloop


In: Detroit
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Chad wrote:
225 / 140 = 1.607

(This is just an estimate... The actual crossover point is hard to determine on the diagrams, so it might be even closer to the Golden Ratio if you could sub-divide days.)


Fantastic.. This is what I found years ago and reported it amongst various people in this group on another site. You can check questgroup.org for the details and I'm fairy confident that nobody else has found this yet. We are plowing virgin ground here.

So actually if you use an astronomy program (like Starry Night) you can emulate the analemma and then pinpoint the crossover point between lobes. I found the the ratio to be closer to 226 / 139 than 225 / 140. But it is somewhere between 225 / 140 and 226 / 139, ie. between 1.607 and 1.625. This is also dependant upon where in the leap cycle we are.

We know now that the analemma is constant in space (size), and constant in time (Golden Ratio). Regardless of location.

Not sure what to make of all this!


I understand Earth's point (positon, situation and orientation) in the Solar System to be much like the crossover point on the analemma.

Earth's place is unique in that it is the only place in the universe which is, as far as we know, 'alive'. And it is quite probable that without our unique type of 'weather', life itself would not be possible. It is said that there are three parameters that affect the size and shape of the analemma: tilt, eccentricity, and the angle between the apse line and the line of solstices. It is also these three parameters which supposedly 'give us weather'. I propose that Logos gives us weather (in fact I propose that it gives us everything), and that the orientation of the three parameters did not happen by accident or independently, but in accordance with our Solar System's division of space/time into extreme and mean ratio, ie. divine convergence. We just havn't 'found' it yet, however Logos (being consistent) has given us the ability to perceive itself : )

In the beginning was the Logos, and the Logos was with God, and the Logos was God. It was with God in the beginning. Through it all things were made; without it nothing was made that has been made. In it was life, and that life was the light of men. The light shines in the darkness, but the darkness has not understood it.


So let's do some reverse engineering.
What day(s) of the year is the crossover point on the analemma?
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Mick Harper
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In: London
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Don't forget that SLOT Theory has to be factored in.
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Ishmael


In: Toronto
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Mick Harper wrote:
Don't forget that SLOT Theory has to be factored in.


Not as much as you think.
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Chad


In: Ramsbottom
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What day(s) of the year is the crossover point on the analemma?

August 30th and April 12th/13th
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Wireloop


In: Detroit
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Chad wrote:
What day(s) of the year is the crossover point on the analemma?

August 30th and April 12th/13th


Right.
April 12th to August 30th is 140 days, and August 30th to April 12th is 225 days.
225 / 140 = 1.60714

April 13th to August 30th is 139 days, and August 30th to April 13th is 226 days.
226 / 139 = 1.62589

So the average is:
1.62589 + 1.60714 = 3.2330
3.2330 / 2 = 1.6165

And since the solar year has 365.242 days and not 365.00 days explains why the average of 1.6165 is actually a smidgin 'low'. When the leap year is factored in and adjusted to each lobe accordingly I suspect that the average would be precisely 1.618.

So now I return to the idea of my initial post a few days back.
Is there a certain day of the year that represents the average annual temperature of the planet?

So, on this hunch, I decided to investigate the weather to see if the analemma had any influence. I found that the average annual temperature for Detroit is 50.3 degrees, and the average daily temperature in Detroit on April 18th is 50.3 degrees. This is mighty close to April 13th I thought, so I decided to look at other locations. I found that several (20 or so) other locations (coastal, inland, north hemisphere, south hemisphere, high altitude, tropical, arctic, etc...) hovered around this April 13th point. Some being early April, late April, mid May, mid March, etc... I suspect that a couple of hundred readings will give us a good convergence, and I'm leaning towards April13th...but I'm not willing to sacrifice the needed time at this point to confim my guess.

The other analemma point is August 30th, but I haven't had time to investigate that yet. Actually I have not looked at any of this stuff in a few years, but it's coming back to me slowly.

Anyway, for anybody interested, these two sites will give us enough data to begin crunching more locations. Perhaps we can start another topic exclusively for data. Slow and steady wins the race.

http://www.weatherbase.com/weather/weather.php3?s=73527&refer=&cityname=Detroit-Michigan-United-States-of-America

http://www.weather.com/weather/wxclimatology/daily/USMI0229?climoMonth=4
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Wireloop


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I crunched some more numbers.
In the 'chart' below each row contains a location, followed by annual mean temp, followed by the date which best represents the annual mean temp, followed by a number which represents that date in a 365 day year.

For example the first entry is for Delhi, India.
The annual mean temp in Delhi, India is 77 degrees.
The date of the year in which the mean temp is 77 degrees in Delhi, India is March 26th.
March 26th is the 85th day of the year.


Delhi, India 77 March, 26 85
Warsaw, Poland 47 April, 17 107
Stockholm, Sweden 43 April, 23 113
Sydney, Australia 64 April, 27 117
Vitim, Russia 22 April, 9 99
Lima, Peru 68 May, 12 132
Aqmola, Kazakhstan 33 April, 4 94
Tehran, Iran 64 April, 21 111
Cape Town, Africa 63 April, 20 110
Madrid, Spain 57 May, 3 123
Moscow, Russia 40 April, 9 99
Asuncion, Paraguay 74 April, 8 98
Fairbanks, Alaska 27 April, 8 98
Tokyo, Japan 60 April, 22 112
Base Orcadas, Antarctica 26 April, 23 113
Frederiskshab, Greenland 30 April, 22 112
Cairo, Egypt 71 April, 14 104
Hanoi, Vietnam 76 April, 14 104
Kabul, Afghanistan 55 April, 14 104
Riyadh, Saudi Arabia 79 April, 16 106
Hutag, Mongolia 32 April, 4 94
Denver, Colorado 51 April, 27 117
Fargo, North Dakota 41 April, 9 99
Toronto, Canada 46 April, 22 112
Saskatoon, Canada 34 April, 7 97
Tomsk, Russia 32 April, 11 101
Niamey, Niger 85 March, 1 60
Berlin, Germany 49 April, 20 110
London, England 50 April, 9 99
Belgrade, Serbia 53 April, 10 100
Mexico City, Mexico 63 March, 14 73
Alice Springs, Australia 70 April, 7 97
Wellington, New Zealand 55 April, 27 117
Tunis, Tunesia 66 May, 10 130
Chita, Russia 28 April, 7 97
Manila, Phillipines 82 March, 12 71
Jerusalem, Israel 61 April, 23 113
Magadan, Russia 27 April, 26 116
Edmonton, Canada 36 April, 5 95
Rio De Janeiro, Brazil 78 March, 24 83

So, when we total all 40 of the day numbers we end up with 4122.
4122 / 40 = 103.05
Therefore the average day number is 103.05.

103.05 = April 13th.

Its beginning to look like the mean date for the average land surface temp on earth is April 13th. This is in accordance with our prediction. However, we need more data!

Mick Harper wrote:
I am more than usually baffled by this. However, club rules insist an uncarping welcome be given to new ideas so, Wireloop, let's assume somebody manages to do all the calculations ... what would the best possible outcome (from your point of view) show?


You're looking at it.
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Mick Harper
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No, that cannot be right. It is true what you have discovered (if real) is completely astonishing but it cannot be 'the best possible outcome' since, as far as I can see, it would be merely an interesting correlation. It will only really zing when we find out the meaning of the correlation. Or find a practical application.

PS Can you explain in simple terms why it works in the southern hemisphere too?
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Hatty
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Wireloop wrote:
We know now that the analemma is constant in space (size), and constant in time (Golden Ratio). Regardless of location.
....
I understand Earth's point (positon, situation and orientation) in the Solar System to be much like the crossover point on the analemma.

Major 'sun-related' sites seem to be located on or near the 51st line of latitude, is this the equivalent of the cross-over point down here as opposed to up there?
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Chad


In: Ramsbottom
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Wireloop wrote:
The other analemma point is August 30th, but I haven't had time to investigate that yet.

Detroit (for example) is about 30 degrees hotter.

Mick wrote:
PS Can you explain in simple terms why it works in the southern hemisphere too?

This surprised me too.

My gut feeling was that April would work for t'North and August for t'South.
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