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# The Golden Ratio

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### #16 Dragonwind

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Posted 30 July 2013 - 09:11 AM

What's interesting is how much historical design uses the golden ratio and formal geometric shape, yet modern day design is now far more organic. Partly because of computer programs, 'innovative style', partly due to land planning parcels of land not being geometric and partly because of client requirements (creating a unique building, safety factors, tennacy utilization etc). A few times as an architect/urban planner I have used all sorts of mathematics, ratios and geometric shapes in modern design typology (ie not copying classical architecture styles)...but my staff and clients don't care about it haha!!

### #17 Mario Dantas

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Posted 31 July 2013 - 01:41 PM

Harte, on 29 July 2013 - 08:25 PM, said:

I see that now 1.5 = 1.618...

Close enough?

Hardly.

1.5, after all, is rational.  Phi is irrational.

I guess that doesn't matter to some people though.

Harte

You are correct they aren't the same figures, although i hope you agree that they are very close, approximately a difference of a tenth...

Maybe one could consider rounding that number?

Quote

Rounding is often done on purpose to obtain a value that is easier to write and handle than the original. It may be done also to indicate the accuracy of a computed number; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is better stated as "about 123,500."

On the other hand, rounding introduces some round-off error in the result. Rounding is almost unavoidable in many computations — especially when dividing two numbers in integeror fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating point representation with a fixed number of significant digits. In a sequence of calculations, these rounding errors generally accumulate, and in certain ill-conditioned cases they may make the result meaningless.

Accurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as "the table-maker's dilemma".
Rounding has many similarities to the quantization that occurs when physical quantities must be encoded by numbers or digital signals.
http://en.wikipedia.org/wiki/Rounding

The dimensions of the plain (157 Km x 104 Km) proposed by Ulf Richter, (and i advise you to read his work on Plato´s Atlantic metrics): Plato´s Atlantis was in a River Delta http://www.black-sea...com/richter.pdf, are the same as the rectangle i have shown you. Maybe it is a coincidence, maybe not.

100 km is already larger than the length of the island where i live (the largest island in Cape Verde), and to consider a man made plain even larger, is unbelievable to me. Meaning that the sheer size of the Plato´s monster plain and the golden mean rectangle are different by a tenth of the unit, and that is very aproximate?

Regards,
Mario Dantas

Edited by Mario Dantas, 31 July 2013 - 02:01 PM.

1. Catalog of Images

2. Was Atlantis in Greenland?
http://a7lan7is.blogspot.com

### #18 Mario Dantas

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Posted 31 July 2013 - 03:49 PM

DieChecker, on 29 July 2013 - 08:45 PM, said:

I still can't believe you've spent 6 years working on a google maps compilation error artifact. There is no evidence Greenland has moved noticably in the last 100,000 years.

If you call this a map compilation error artifact:

1. Catalog of Images

2. Was Atlantis in Greenland?
http://a7lan7is.blogspot.com

### #19 jaylemurph

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Posted 31 July 2013 - 05:58 PM

Mario Dantas, on 31 July 2013 - 01:41 PM, said:

100 km is already larger than the length of the island where i live (the largest island in Cape Verde), and to consider a man made plain even larger, is unbelievable to me. Meaning that the sheer size of the Plato´s monster plain and the golden mean rectangle are different by a tenth of the unit, and that is very aproximate?

Regards,
Mario Dantas

I feel much the same way about people who insist that Atlantis was srsly, totes a real place and not at a ficitonal, political metaphor.

--Jaylemurph

"... amongst the most obstinate of our opinions may be classed those which derive from discussions in which we affect to search for the truth, while in reality we are only fortifying prejudice."     -- James Fenimore Cooper, The Pathfinder

Deeply venial

### #20 Mario Dantas

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Posted 01 August 2013 - 12:42 PM

jaylemurph, on 31 July 2013 - 05:58 PM, said:

I feel much the same way about people who insist that Atlantis was srsly, totes a real place and not at a ficitonal, political metaphor.

--Jaylemurph

Hello,

Personally, on the contrary, i try to have no problem in accepting people either insisting or giving up, all at once, the Atlantis theme. People are entitled to have their own opinions, you know? Perhaps Atlantis is not real or perhaps it is... can you prove that Atlantis was not real? Can you or anybody prove that Atlantis was a metaphor, as you put it? Why an intelligent person would ridicule another for peanuts? But you are a free person, do as you please.

It is a shameful thing for a person as enlightened as yourself to act as prejudice. I couldn't care less ABOUT how you feel about people, Jaylemurph!

" And now look again, and see what will naturally follow if the prisoners are released and disabused of their error. At first, when any of them is liberated and compelled suddenly to stand up and turn his neck round and walk and look towards the light, he will suffer sharp pains; the glare will distress him, and he will be unable to see the realities of which in his former state he had seen the shadows; and then conceive some one saying to him, that what he saw before was an illusion, but that now, when he is approaching nearer to being and his eye is turned towards more real existence, he has a clearer vision, -what will be his reply? And you may further imagine that his instructor is pointing to the objects as they pass and requiring him to name them, -will he not be perplexed? Will he not fancy that the shadows which he formerly saw are truer than the objects which are now shown to him?"
http://www.historygu...t/allegory.html

Regards,
Mario Dantas

1. Catalog of Images

2. Was Atlantis in Greenland?
http://a7lan7is.blogspot.com

### #21 Quaentum

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Posted 01 August 2013 - 02:19 PM

Mario Dantas, on 29 July 2013 - 04:37 PM, said:

Hi vitruvian12,

I don´t know what happened while i was editing my first post, everything just went upside down...

Here is the quote of Plato´s Critias:

http://classics.mit....to/critias.html

He says that the ditch was 10.000 stadia in length, not the plain:

Regarding the satellite image on Google Earth, it is supposed to be a rectangular shape. Although i have given up to show any similarity with a rectangle, it is there still:

Sorry for the typos...

Regards,
Mario Dantas

Plato also gives measurements of the island the mountain is on, the alternating rings of water and land surrounding the island. the length of the canal connecting the outermost ring of water to the sea and the distance the island is from the plain.

The plain and island are 50 stadia apart (5.6 miles)

inner water ring - 1 stadia
Outer Water ring - 3 stadia
Canal connecting outer water ring to sea - 50 stadia

From the middle of the island to the sea - 63.5 stadia (7.2 miles)

Now both the island with the mountain and the plain were in the center of the island of Atlantis.  Since the island with the mountain was 7.2 miles from the sea and that same island was only 5.6 miles from the plain then the edge of the plain can be no more than 13 miles from the sea.  If your supposed find is greater than that then it is not the plain of Atlantis.

AA LOGIC
They didn't use thousands of workers - oops forgot about the work camps
There's no evidence for ramps - You found one?...Bummer
Well we know they didn't use ancient tools to cut and shape the stones - Chisel marks?  Craps
I still say aliens built them!

### #22 Mario Dantas

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Posted 01 August 2013 - 06:19 PM

Quaetum,

There is a little problem with your assertions. Plato’s dimensioning system of Atlantis was simply too large to be true (in the opinion of Ulf Richter and mine too and many others). Of course this is all but a possibility, since we do not even know if Atlantis was real, in the first place. But, in the eventuality of it being true, there are many inconsistencies regarding the actual dimensions given by Plato.

I consider myself to have a “direct” approach on Atlantis, meaning that every detail in Plato “Critias” is taken as is, e.g. the existence of a huge island, surrounded by mountains, in front of Gibraltar, in the Atlantic having a huge central plain, a mountain near the plain, three rings around the city, a racecourse, etc. Nevertheless, the features i propose are only identical to Plato’s description, if everything is downsized, as proposed by Dr. Ulf Richter in “Plato’s Atlantis was in a River Delta”.

He says the following:

“If the plain of Atlantis had a size of 555 x 370 km, it would not be possible to recognize from its centre that it is encircled by mountain chains, due to their great distance.”

I will transcribe from Ulf Richter’s own work, the chapter which deals with the dimensioning problem in Atlantis:

Quote

We have, indeed, an example that a famous Greek author gave wrong information by transforming Egyptian length units into  Greek "stades". This was Herodotus, the  "father of history" , who gave all distances in Egypt (in stades) much longer as they are in reality, while he reported all the distances in Greece correctly. The usual explanation for this error is that he has mixed up the Egyptian units of measurement, obviously taken from an Egyptian itinerary, before he transformed them into stades. A similar error could have taken place while the Egyptian priest narrated the Atlantis story to Solon. It is self-evident that the priest gave all the distances in Egyptian units of measurement, as they were written in the ancient texts, and Solon wrote them down as he heard them for later transformation into Greek stades. When he returned to Greece he had no opportunity for this calculation or forgot it. His heirs (Dropides, Critias the Elder and Critias the Younger) found in Solon´s notes only the figures without the units of measurement
and obviously thought it must be stades (especially since in their time, due to the busy trade with the Greeks, even the Egyptian people were using Greek stades in addition to their own units), and Critias passed this (erroneous) information on to Plato.

I feel that this is a very probable error in the long chain of tradition between the Saitic priest and Plato. Which unit of measurement was commonly used by the ancient Egyptians? It was the "Royal Cubit" or "Meh" (0,524 m) and for longer distances the "Khet" = 100 "Royal Cubits" (1 khet = 52,4 meters = 172 feet) /7/ When we take this "khet" for what Plato called "stade", we get much more probable dimensions for Atlantis than those mentioned before. (See table 2, column 3):

a) The size of the level plain is 105 x 157 km (16475 sq.km, a little smaller than the Peloponesos-peninsula in Greece).

b ) The diameter of the central city of Atlantis is 6,7 km (The city of Rome in the late times of the Roman empire (Aurelian wall) had a diameter of 6 km and about one million inhabitants).

c) The racecourse for horses is 52 m wide and 3 kilometers long, like one of the larger modern racecourses.

d) The canal round the plain is 524 km long, 52 m wide and 8,7 m deep. (The forerunner of the Suez canal, built by pharaoh Necho and king Dareios of Persia about 500 BC, was 180 km long, 45 m wide and had a depth of 5.5 m; see table 1)

e) The bridges over the circular canals are 8,7 m wide, comparable with the breadth of medieval bridges. f) The temple of Poseidon has a size of
26 x 52 m, a very reasonable size compared with the famous Poseidon temple in Paestum/Italy (24 x 60 m).

But couldn´t it be the case that with the introduction of the “Khet”-dimensions some measures were too small to be credible? Was it possible that on the canal from the sea to the harbour with a width of 26,2 m two triremes could meet? A Greek trireme from classical times was 37 m long, had an overall beam of 5,5 m and a height of about 4 m /8/. The oars had a length of 4,2 m, but due to their oblique position relative to the surface of the sea, and one third of their length being inside the ship, the horizontal space needed for using one oar is only 2,7 m .

Was the central island at 262 m diameter big enough to contain all the reported buildings: temple of Poseidon and Cleito, Royal Palace (Crit.116C), separate baths for the kings, for private citizens and for horses, the guard-house for the most trustworthy spearmen (Crit.117C) and the sacred grove of Poseidon (Crit.117B) ?

The Acropolis in Athens (120 x 280 m) has an area of about 30000 sq.m compared with 54000 sq.m for the central island of Atlantis. We can conclude that it makes sense to take Egyptian “Khets” instead of Greek “Stades” for getting a better interpretation of the dimensions of Atlantis in Plato's “Critias”.
http://www.black-sea-atlantis.com/richter.pdf

My findings are completely within the logic of smaller scale Atlantis, as i stated in the beginning. Alas, i could not possibly measure all details since many are small and difficult to capture with Google earth.

Regards,
Mario Dantas

Edited by Mario Dantas, 01 August 2013 - 06:36 PM.

1. Catalog of Images

2. Was Atlantis in Greenland?
http://a7lan7is.blogspot.com

### #23 The_Spartan

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Posted 01 August 2013 - 06:46 PM

I seriously don't understand ..what the heck does a hypothetical crawling of an island have to do with the golden ratio??
smell a hijack!

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### #24 Quaentum

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Posted 01 August 2013 - 07:08 PM

Mario Dantas, on 01 August 2013 - 06:19 PM, said:

Quaetum,

There is a little problem with your assertions. Plato’s dimensioning system of Atlantis was simply too large to be true (in the opinion of Ulf Richter and mine too and many others). Of course this is all but a possibility, since we do not even know if Atlantis was real, in the first place. But, in the eventuality of it being true, there are many inconsistencies regarding the actual dimensions given by Plato.

I consider myself to have a “direct” approach on Atlantis, meaning that every detail in Plato “Critias” is taken as is, e.g. the existence of a huge island, surrounded by mountains, in front of Gibraltar, in the Atlantic having a huge central plain, a mountain near the plain, three rings around the city, a racecourse, etc. Nevertheless, the features i propose are only identical to Plato’s description, if everything is downsized, as proposed by Dr. Ulf Richter in “Plato’s Atlantis was in a River Delta”.

He says the following:

“If the plain of Atlantis had a size of 555 x 370 km, it would not be possible to recognize from its centre that it is encircled by mountain chains, due to their great distance.”

I will transcribe from Ulf Richter’s own work, the chapter which deals with the dimensioning problem in Atlantis:

http://www.black-sea-atlantis.com/richter.pdf

My findings are completely within the logic of smaller scale Atlantis, as i stated in the beginning. Alas, i could not possibly measure all details since many are small and difficult to capture with Google earth.

Regards,
Mario Dantas

It still comes down to whether the Google artifact you feel is the plain is less than 13 miles from the sea.  If not then that artifact can not be the plain.

Also since Green land is larger than Plato's Atlantis, saying that Plato's measurements were too large would reduce the size of the island further and even more show that Greenland never could have been Atlantis.

Mario Dantas, on 31 July 2013 - 03:49 PM, said:

If you call this a map compilation error artifact:

It's called your view of Atlantis which doesn't fit with known evidence.

AA LOGIC
They didn't use thousands of workers - oops forgot about the work camps
There's no evidence for ramps - You found one?...Bummer
Well we know they didn't use ancient tools to cut and shape the stones - Chisel marks?  Craps
I still say aliens built them!

### #25 jaylemurph

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Posted 01 August 2013 - 09:01 PM

Mario Dantas, on 01 August 2013 - 12:42 PM, said:

Hello,

Personally, on the contrary, i try to have no problem in accepting people either insisting or giving up, all at once, the Atlantis theme. People are entitled to have their own opinions, you know? Perhaps Atlantis is not real or perhaps it is... can you prove that Atlantis was not real? Can you or anybody prove that Atlantis was a metaphor, as you put it? Why an intelligent person would ridicule another for peanuts? But you are a free person, do as you please.

It is a shameful thing for a person as enlightened as yourself to act as prejudice. I couldn't care less ABOUT how you feel about people, Jaylemurph!

" And now look again, and see what will naturally follow if the prisoners are released and disabused of their error. At first, when any of them is liberated and compelled suddenly to stand up and turn his neck round and walk and look towards the light, he will suffer sharp pains; the glare will distress him, and he will be unable to see the realities of which in his former state he had seen the shadows; and then conceive some one saying to him, that what he saw before was an illusion, but that now, when he is approaching nearer to being and his eye is turned towards more real existence, he has a clearer vision, -what will be his reply? And you may further imagine that his instructor is pointing to the objects as they pass and requiring him to name them, -will he not be perplexed? Will he not fancy that the shadows which he formerly saw are truer than the objects which are now shown to him?"
http://www.historygu...t/allegory.html

Regards,
Mario Dantas

I have maintained an active prejudice against laziness (defined as a lack of rigorous thinking) and misinformation masquerading as real history for some time. I will continue to do so for some time, I hope.

(Not that I'm accusing you of deliberately passing misinformation, though.)

But yes, I can prove Atlantis was metaphor. Very simply. It's done via a simple process called "actualyl reading the the Republic" -- also known as the first place to actually menion Altantis. However, few people advocating a real Atlantis have done so as it would require reading an otherwise dry philosophical text. Atlantis is clearly set up as an antithesis to Plato's ideal Republic. You can choose to ignore that historical and literary context, and continue looking for a real place called Atlantis, and then make detours for Oz, Middle Earth, Barsoom and Narnia, since all those places have exactly as much call to be regarded as a real place.

I cannot, however, prove Atlantis is not real. I cannot prove anything is not real, or is not anything else. It's not how logic works at a basic level. And if you can't apply basic logic to a question, then I feel like you may not be suited to the sort of literary and historical critcism necessary to justify your claims about a real Atlantis. Especially inasmuch as suggesting Atlantis was a real place means overturning the work many, many scholars who can and do submit to rigorous thinking and strict logical thought.

--Jaylemurph

"... amongst the most obstinate of our opinions may be classed those which derive from discussions in which we affect to search for the truth, while in reality we are only fortifying prejudice."     -- James Fenimore Cooper, The Pathfinder

Deeply venial

### #26 Mario Dantas

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Posted 01 August 2013 - 09:05 PM

Quaentum, on 01 August 2013 - 07:08 PM, said:

It still comes down to whether the Google artifact you feel is the plain is less than 13 miles from the sea.  If not then that artifact can not be the plain.

Also since Green land is larger than Plato's Atlantis, saying that Plato's measurements were too large would reduce the size of the island further and even more show that Greenland never could have been Atlantis.

It's called your view of Atlantis which doesn't fit with known evidence.

Quaetum,

I really don't know what to say! I have always tried to discuss this subject in an honest and relaxed way, but i sense that people cannot take it like that.

But, returning to what you said:

I don't actually know how far is the plain from the sea, plain and simple, but it is not 13 miles, that is for sure. Most of the images from Google earth are "enhanced" with an image manipulator software (GIMP) and i could not see anything before that manipulation. There was always a big white (snow), impeaching me to use the scale adequately. Only in a few cases did i manage to make the pictures with the proper scaling. Furthermore, and i ask for forgiveness, but i do not recall such mention by Plato of a 13 mile distance between the plain and the sea...

Regarding the size of Atlantis, i ask where, again, does it explicitly say that Atlantis was smaller than Greenland's dimensions, as you said?

Known evidence does not always mean veracity or undisputed truth.

PS: Hey Spartan, do not get excited! I will not derail this thread anymore, satisfied? I can even ask moderators to remove all my comments, if that makes you happier...

Regards,
Mario Dantas

1. Catalog of Images

2. Was Atlantis in Greenland?
http://a7lan7is.blogspot.com

### #27 Mario Dantas

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Posted 01 August 2013 - 11:44 PM

jaylemurph, on 01 August 2013 - 09:01 PM, said:

I have maintained an active prejudice against laziness (defined as a lack of rigorous thinking) and misinformation masquerading as real history for some time. I will continue to do so for some time, I hope.

(Not that I'm accusing you of deliberately passing misinformation, though.)

But yes, I can prove Atlantis was metaphor. Very simply. It's done via a simple process called "actualyl reading the the Republic" -- also known as the first place to actually menion Altantis. However, few people advocating a real Atlantis have done so as it would require reading an otherwise dry philosophical text. Atlantis is clearly set up as an antithesis to Plato's ideal Republic. You can choose to ignore that historical and literary context, and continue looking for a real place called Atlantis, and then make detours for Oz, Middle Earth, Barsoom and Narnia, since all those places have exactly as much call to be regarded as a real place.

I cannot, however, prove Atlantis is not real. I cannot prove anything is not real, or is not anything else. It's not how logic works at a basic level. And if you can't apply basic logic to a question, then I feel like you may not be suited to the sort of literary and historical critcism necessary to justify your claims about a real Atlantis. Especially inasmuch as suggesting Atlantis was a real place means overturning the work many, many scholars who can and do submit to rigorous thinking and strict logical thought.

--Jaylemurph

Jaylemurph,

I Just felt like showing that the rectangular image (which might not even exist...) was in a perfect golden ratio proportion...

I have read the Republic (or not) and the reference to Makaron Nesoi (Macaronesia) is dear to me as i live in Cape Verde.

If one think that sometimes men's reason and logic can be faulty...

There should not be a problem in questioning things, since science is well founded and can easily deal with most known problems...

But, it took more than forty years for science's acknowledgment that Wegener's continents had indeed moved, i ask how many more, for Atlantis?

It is my opinion Plato tells us about a sort of "continental drift" of Atlantis. It existed before, in front of Gibraltar, and afterwards, "moved" to an unknown place. As in Pangaea broke up, America was also in front of Africa and moved...

If something like a Pangaean formation existed, in our planet, until the end the last ice age, and had "collapsed" because of the shock of an asteroid, there would be no clear evidence proving that this in fact had happened. The simpler explanation is the best explanation, most of the times, but probably not in Plato's Atlantis case and others...

Geoids

It is believed that, "in the whole universe", continents can only move slowly, but this cannot be entirely true, since for as long as you have applied a strong enough impacting force to a buoyant object, it will move, be it a ship in the ocean, or a continent upon hot magma.

Somewhere in the universe there are planets like ours which can witness severe and fast continental movement. It cannot be impossible...

Apologies to the original poster, i did not mean to speak of my theory, per se, but rather to show this golden mean rectangle "structure", in the center of Greenland.

I will say no more of it here!

Regards,
Mario Dantas

1. Catalog of Images

2. Was Atlantis in Greenland?
http://a7lan7is.blogspot.com

### #28 kmt_sesh

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Posted 02 August 2013 - 02:31 AM

I must agree with Spartan. This thread is about the Golden Ratio, not Atlantis of any of its spin-off hypotheses. If this trend continues I will just close this thread.

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### #29 jaylemurph

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Posted 02 August 2013 - 03:05 AM

Mario Dantas, on 01 August 2013 - 11:44 PM, said:

Jaylemurph,

I Just felt like showing that the rectangular image (which might not even exist...) was in a perfect golden ratio proportion...

I have read the Republic (or not) and the reference to Makaron Nesoi (Macaronesia) is dear to me as i live in Cape Verde.

If one think that sometimes men's reason and logic can be faulty...

There should not be a problem in questioning things, since science is well founded and can easily deal with most known problems...

But, it took more than forty years for science's acknowledgment that Wegener's continents had indeed moved, i ask how many more, for Atlantis?

It is my opinion Plato tells us about a sort of "continental drift" of Atlantis. It existed before, in front of Gibraltar, and afterwards, "moved" to an unknown place. As in Pangaea broke up, America was also in front of Africa and moved...

If something like a Pangaean formation existed, in our planet, until the end the last ice age, and had "collapsed" because of the shock of an asteroid, there would be no clear evidence proving that this in fact had happened. The simpler explanation is the best explanation, most of the times, but probably not in Plato's Atlantis case and others...

Geoids

It is believed that, "in the whole universe", continents can only move slowly, but this cannot be entirely true, since for as long as you have applied a strong enough impacting force to a buoyant object, it will move, be it a ship in the ocean, or a continent upon hot magma.

Somewhere in the universe there are planets like ours which can witness severe and fast continental movement. It cannot be impossible...

Apologies to the original poster, i did not mean to speak of my theory, per se, but rather to show this golden mean rectangle "structure", in the center of Greenland.

I will say no more of it here!

Regards,
Mario Dantas

I agree with you this isn't the correct arena for a discussion about the historical reality of Atlantis (heaven knows there are already sufficient threads for that elsewhere),and offer my apologies to whomsoever requires them for dragging this thread off-topic. But maybe we can spar over Atlantis elsewhere.

--Jaylemurph

"... amongst the most obstinate of our opinions may be classed those which derive from discussions in which we affect to search for the truth, while in reality we are only fortifying prejudice."     -- James Fenimore Cooper, The Pathfinder

Deeply venial

### #30 kmt_sesh

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Posted 02 August 2013 - 03:11 AM

jaylemurph, on 02 August 2013 - 03:05 AM, said:

I agree with you this isn't the correct arena for a discussion about the historical reality of Atlantis (heaven knows there are already sufficient threads for that elsewhere),and offer my apologies to whomsoever requires them for dragging this thread off-topic. But maybe we can spar over Atlantis elsewhere.

--Jaylemurph

That's all right. More than anyone I allowed it to go on too far. Like you said, there are any number of Atlantis threads to resurrect, and Mario happens to have one himself.

Or, dare I say, someone could start a new one.

But you didn't hear me say that.

The evil overlord mummy moderator has spoken.

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