Why don't maesters know the circumference of the planet?

[RumHam]

Something besides the original topic here, but i noticed a quant little detail when comparing the great library to the citadel.

Did anyone noticed before, that Historical Alexandria and Oldtown actually have 2 very specific landmakrs in coman? Both have the world largest center of learning, and both have a hughe ass lighthouse not sitting to far from that.

Lets hope for Oldtown that both are not going to get the fate that the great library and Pharos got.

I couldn't help but think if Alexandria when I read this:

For scholars and students of history, the fall of Sallosh by the Silver Shore was especially tragic, for when that City of Scholars burned, its great library was not spared, and most of the history of the Tall Men and the peoples who had gone before them were lost for all time.

[TheDrunkenDornishman]

Martin likes big numbers, and Gregor was never actually accurately described as 8 foot tall, only closer to 8 than 7, still impossible for him to function how he does, but it is Martin-verse.

Well there was this man who was basically exactly Gregor's described size. So it apparently isn't impossible.

http://en.m.wikipedia.org/wiki/Angus_MacAskill

[Jasta11]

It probably hasn't actually been 8,000 years of absolutely nothing. If I recall correctly, the maesters put their estimates of when things happened as far more recently than what is widely considered true.

It's been several thousand years at the very least, Sam can bring up more than 700 commanders of the Watch IIRC, that's a lot.

[Lesk]

There are other issues here regarding the 'science' of Planetos. What about the timespan of a 'year'. I believe it has been quoted as being variable but anywhere between 7 to 10 Earth years judging by the cycle of seasons. This begs some questions. For instance, how can the inhabitants of Planetos know what an Earth year constitutes? In fact, it seems that there is no standard of measurement for a Planetos year as it is so variable in length. These issues imply one or more of the following:

Planetos revolves around the Sun more slowly and erratically than our Earth. What would cause it to be erratic? Possibly the gravitational effect of some other undiscovered heavenly body? What physical effects would this have?

Or...

Planetos' position in the Solar system means that it is further away from the Sun with the associated longer path, thus taking longer to revolve. This would not seem to be possible as the temperate nature of the planet seems similar to Earth, not to mention several other Mathematical imbalances regarding gravitational strength, etc. This would mean that the ASoIaF Sun would need to have completely different properties to ours. i.e. Larger/denser/newer/older etc.

Any astrophysicists out there?

[RumHam]

There are other issues here regarding the 'science' of Planetos. What about the timespan of a 'year'. I believe it has been quoted as being variable but anywhere between 7 to 10 Earth years judging by the cycle of seasons. This begs some questions. For instance, how can the inhabitants of Planetos know what an Earth year constitutes? In fact, it seems that there is no standard of measurement for a Planetos year as it is so variable in length. These issues imply one or more of the following:

Planetos revolves around the Sun more slowly and erratically than our Earth. What would cause it to be erratic? Possibly the gravitational effect of some other undiscovered heavenly body? What physical effects would this have?

Or...

Planetos' position in the Solar system means that it is further away from the Sun with the associated longer path, thus taking longer to revolve. This would not seem to be possible as the temperate nature of the planet seems similar to Earth, not to mention several other Mathematical imbalances regarding gravitational strength, etc. This would mean that the ASoIaF Sun would need to have completely different properties to ours. i.e. Larger/denser/newer/older etc.

Any astrophysicists out there?

[What is the cycle of a year? Why do they count years when seasons are strange?]

Twelve moon tuns to a year, as on earth. Even on our earth, years have nothing to do with the seasons, or with the cycles of the moon. A year is a measure of a solar cycle, of how long it takes the earth to make one complete revolution around the sun. The same is true for the world of Westeros. Seasons do not come into it.

http://www.westeros.org/Citadel/SSM/Entry/Asshai.com_Forum_Chat

[Ser Leftwich]

Magic, not physics. Also, 12 (or 13) moons to a year.

ETA: :ninja: 'ed

[Ser Arthur Hightower]

Well there was this man who was basically exactly Gregor's described size. So it apparently isn't impossible.

http://en.m.wikipedia.org/wiki/Angus_MacAskill

Wow, I am surprised to see that, good find.

*Sits there for 5 minutes trying to come up with some clever argument. Can't think of anything and looks sad.*

[Ser Arthur Hightower]

This could be explained by my theory that the speed of light is extremely variable near Planetos. That would explain why the moon phase is almost always wrong much better than "GRRM doesn't care about have moon phases match his calendar" - even if he just didn't care what would be the correct phase for it's time and position, he should still be right some of the time, and he isn't. I believe this is deliberate, not only does it explain a number of other odd details in the series, it would also affect the ability to measure the planet by extrapolating the curvature, because the apparent distance to the horizon would vary based on the speed of light where the observer was. The Maesters almost certainly know how to measure distance and the basic math to extrapolate circumference from it - maybe they have tried in the past and gave up because they could not all agree on a single figure because they all got different measurements.

How would the speed of light vary and how would that affect any of this?

Light travels the circumference of the earth 7 times a second, it could decrease by a significant factor and no one would notice, however since light's speed is one of its fundamental properties it is debatable if it would even count as light or function in the same way.

The point is there is no reason to assume the maesters or whoever else doesn't have a decent estimate of the earth's radius/circumference (though if they know one they know the other, unless you would like to argue that the don't know π, since there is as much evidence for that as them not estimating the worlds circumference).

[Mal Malenkirk]

Well there was this man who was basically exactly Gregor's described size. So it apparently isn't impossible.

http://en.m.wikipedia.org/wiki/Angus_MacAskill

It's not impossible to be almost 8 feet tall. It's impossible to be almost 8 feet tall and a comptetent fighter. This guy looks like he could fight well to you?

In a fight, it's better to be bigger until it starts affetcting your speed and coordination too much. The biggest combat sport champion ever is probably Nikolai Valuev at 7'1''. He was physically a freak of nature who proved to be a competent but unspectacular champion (8 win 2 defeat in championship bout, good but nothing to write the hall of fame about) and he retired due to joints and bone problem (who'd have guessed?).

[Varysfan]

I mean their naval navigation is soooo drastically behind what they should be capable of in terms of comparison to our own history. Sailing out of land is considered ill advised....

Earth doesn't have krakens, mystery plagues, an ocean people have never sailed across and returned to tell the tale despite many know. attempts over centuries!

[TheSovereignGrave]

It's not impossible to be almost 8 feet tall. It's impossible to be almost 8 feet tall and a competent fighter. This guy looks like he could fight well to you?

In a fight, it's better to be bigger until it starts affecting your speed and coordination too much. The biggest combat sport champion ever is probably Nikolai Valuev at 7'1''. He was physically a freak of nature who proved to be a competent but unspectacular champion (8 win 2 defeat in championship bout, good but nothing to write the hall of fame about) and he retired due to joints and bone problem (who'd have guessed?).

We also have giants and a race of men whose average seems to be about equal to Gregor's height. This is just one of those things that's rationalized by 'it's cool' unless Gregor turns out to be part giant or something and his height is magic.

[Kyll.Ing.]

This could be explained by my theory that the speed of light is extremely variable near Planetos. That would explain why the moon phase is almost always wrong much better than "GRRM doesn't care about have moon phases match his calendar" - even if he just didn't care what would be the correct phase for it's time and position, he should still be right some of the time, and he isn't. I believe this is deliberate, not only does it explain a number of other odd details in the series, it would also affect the ability to measure the planet by extrapolating the curvature, because the apparent distance to the horizon would vary based on the speed of light where the observer was. The Maesters almost certainly know how to measure distance and the basic math to extrapolate circumference from it - maybe they have tried in the past and gave up because they could not all agree on a single figure because they all got different measurements.

Thing is - there are a bunch of things in nature connected to the speed of light. Time dilation due to relativity, for instance, but more famously: E = mc². If Martin is skilled enough in physics to come up with the explanation "the speed of light varies a lot in this world", and taking that into account when writing, he should also be skilled enough to know the mass-energy relationship and how it ties in to chemical reactions: Long story short: If you double the speed of light, you quadruple the energy released from any atomic interaction. Lighting a match in a "2x lightspeed" scenario would be akin to having a firecracker go off in your hand. Similarly, you could halve the speed of light, and a bonfire wouldn't give off enough energy to even sustain itself. A lot of things would go "boom" or "whimper" if you tried to mess with the speed of light. And let's not even mention perception of colour...

[DSB]

why does orthodox science not dishonestly claim to have answers to unanswerable questions?

honesty, perhaps.

spinning rock ball among spinning rock/gas ball theory is only that' a theory.

oblate spheroid earth model theory, and heliocentric solar system models are not facts.

[DSB]

Thing is - there are a bunch of things in nature connected to the speed of light. Time dilation due to relativity, for instance, but more famously: E = mc². If Martin is skilled enough in physics to come up with the explanation "the speed of light varies a lot in this world", and taking that into account when writing, he should also be skilled enough to know the mass-energy relationship and how it ties in to chemical reactions: Long story short: If you double the speed of light, you quadruple the energy released from any atomic interaction. Lighting a match in a "2x lightspeed" scenario would be akin to having a firecracker go off in your hand. Similarly, you could halve the speed of light, and a bonfire wouldn't give off enough energy to even sustain itself. A lot of things would go "boom" or "whimper" if you tried to mess with the speed of light. And let's not even mention perception of colour...

wow.

can i buy a flagon of snake oil?

fire not sustaining itself in a variable light speed environment is akin to denying the vibration of a slammed shut dustbin lid in a variable sound speed environment.

even the high priests of scientism now preach variable light speed, within the dogma of black holes, part of the super-gravity parable.

[Kyll.Ing.]

^Such effects of varying light speed would only be significant for significant fluctuations in light speed - as would be required for the moon to appear to change phase randomly (as in, the light speed varies so drastically that reflected light from the moon may take seconds, minutes or weeks to reach the "Earth"). We're not talking about variations of a few hundredths of a percent, we're talking varying orders of magnitude. For such dramatic fluctuations, E=mc² would give pretty wonky results of chemical reactions, and people's colour perception would be completely screwed - when the light speed changes, so would the wavelengths of light for given frequencies. And the human eye can only see a pretty narrow band of wavelengths along the electromagnetic spectrum. You would get a Doppler effect while standing still, the world would appear to turn blue or red completely at random (or even more, depending on how much light speed is altered - under certain conditions you would be able to see heat, or even radio waves). A world in which the value of c varies by several orders of magnitude seemingly at random, wouldn't work very well.

[Taenqyrhae]

How would the speed of light vary and how would that affect any of this?

Light travels the circumference of the earth 7 times a second, it could decrease by a significant factor and no one would notice, however since light's speed is one of its fundamental properties it is debatable if it would even count as light or function in the same way.

The point is there is no reason to assume the maesters or whoever else doesn't have a decent estimate of the earth's radius/circumference (though if they know one they know the other, unless you would like to argue that the don't know π, since there is as much evidence for that as them not estimating the worlds circumference).

When light passes through a media that reduces it's speed the light is refracted - that is why a straight stick immersed in water appears to bend at the surface. If the speed of light was different at different times and/or places on Planetos, due to magic, that would make measuring distances by triangulation impossible.

My theory is that there is some magical force on Planetos that has caused the speed of light (and therefore, time) to be variable across the surface of the planet in different places and times. There are a few good clues that suggest that GRRM may be doing this.

1. The lunar phase problem I mentioned above. If Moonos revolves around Planetos and Planetos revolves around Sunos, and there is no second sun, it is physically impossible for the lunar phases to be what they are described as in the many places in the series where the moon rising is described. If the moon rises at sunset, it's going to be full, because it is on the opposite side of the planet as the sun. GRRM describes a crescent moon rising at sunset, and if you think about it you'll realize why that is impossible - UNLESS the light you are seeing reflected from the moon represents where it was a couple of weeks ago.

2. The appearance of Moonos changing as one gets closer to Valyria. If we suppose that there is a magical effect that is affecting the speed of light that is centered on Valyria, it would distort the appearance of Moonos as the light from it changed speed on it's way to your retina, just like things look different under rippling water.

3. There are many clues that the flow of time is variable on Planetos, including major discrepancies in different historical accounts from different places, the apparently slow technological progress, the occasional night that lasts years, the fact that there are species of hominids that had to have been isolated from homo sapiens for millions of years to speciate but live right next to anatomically modern humans, and the fact that the Maesters have not been able to measure the size of Planetos with their more-than-adequate math and Myrish looking glass technologies.

4. Determining when seasons will change is a complicated and esoteric process that requires special Maesters. Why and how? We know that magic is responsible for the strange "seasons" and the Maesters are clearly more scientific in their thinking. I think that, over the thousands of years, they have learned the complexities about how the warped space around Planetos affects their astronomical observations and they are able to, with a lot of work, account for those differences - but it's not something the common man could do like stone age humans did by just watching where the sun rises. Stonehenge would be worthless as a calendar if lightspeed was variable and the moon and sun were not always at the location their light appears to be coming from.

[Taenqyrhae]

^Such effects of varying light speed would only be significant for significant fluctuations in light speed - as would be required for the moon to appear to change phase randomly (as in, the light speed varies so drastically that reflected light from the moon may take seconds, minutes or weeks to reach the "Earth"). We're not talking about variations of a few hundredths of a percent, we're talking varying orders of magnitude. For such dramatic fluctuations, E=mc² would give pretty wonky results of chemical reactions, and people's colour perception would be completely screwed - when the light speed changes, so would the wavelengths of light for given frequencies. And the human eye can only see a pretty narrow band of wavelengths along the electromagnetic spectrum. You would get a Doppler effect while standing still, the world would appear to turn blue or red completely at random (or even more, depending on how much light speed is altered - under certain conditions you would be able to see heat, or even radio waves). A world in which the value of c varies by several orders of magnitude seemingly at random, wouldn't work very well.

A scientifically realistic world with a speed of light that was much different than ours would have a lot of those problems, I agree. I read a science fiction story once where there was a murder mystery on a spaceship that was difficult to solve because, when the spaceship was using it's FTL drive, the speed of light on board the ship was low enough that you could see a person visibly change color whether they were moving towards you or away from you. It was a really neat idea, but for the reasons you mentioned above it would cause some serious problems right down to the molecular level. The author was aware of that, but wanted to tell a neat story involving relativity so he ignored it. Just like in "The Girl, the Gold Watch, and Everything", a scientist invents a device that can speed up the bearer so that to them time appears to have nearly stop. He makes a small concession towards realism when he describes that everything turns redder to the user when the device is activated, but in reality that would only happen if time was slowed by a relatively small percentage, not slowed to the point where you can see bullets slowly moving by. There would be absolutely no visible light at all for the user, and if they could somehow push themselves through the air at the speeds they were traveling, walking would create devastating shockwaves that wiped out everything for miles around. Does it make it a bad story? No, it's a lot of fun, you just have to accept that it is fantasy, and some things are not realistic for the sake of the story. ASoIaF already combines some scientific realism with a system of heredity that is not realistic, along with magic and causality-defeating communication through time.

If GRRM wanted to make a magical field that affects time, he would know that such a thing would affect the speed of light - and would realize that if he maintained realism in how this magical effect worked in every way down to the subatomic level, it would make the story impossible. That would only mean anything if this was a hard science fiction series, and ASoIaF is fantasy. GRRM has written actual science fiction that has played fast and loose with the laws of physics for the sake of making the story work, so I'm sure he would not have a problem with making the speed of light only affect some things and not others. If he has FTL and time travel in science fiction stories, he wouldn't have a problem with magic that warps time without all the realistic physical effects of that happening.

Fantasy does not mean that the laws of physics MUST be either completely ignored or followed completely. For instance, if you had a fantasy story where a character has a magical bow that fires arrows so fast they break the sound barrier, it would be a cool detail to describe the arrows making a cracking sound from the sonic boom as they passed, and leaving vapor trails of condensation behind them. One wouldn't say "You can't have realistic scientific details like that while ignoring that a bow like that would destroy the arrows it fired and be impossible to draw by a human-sized creature unless they had skeletons and muscles made of something other than flesh and blood". It's fantasy! Just like Star Wars with it's swooshing spaceships and laser swords.

[Ser Arthur Hightower]

When light passes through a media that reduces it's speed the light is refracted - that is why a straight stick immersed in water appears to bend at the surface. If the speed of light was different at different times and/or places on Planetos, due to magic, that would make measuring distances by triangulation impossible.

My theory is that there is some magical force on Planetos that has caused the speed of light (and therefore, time) to be variable across the surface of the planet in different places and times. There are a few good clues that suggest that GRRM may be doing this.

1. The lunar phase problem I mentioned above. If Moonos revolves around Planetos and Planetos revolves around Sunos, and there is no second sun, it is physically impossible for the lunar phases to be what they are described as in the many places in the series where the moon rising is described. If the moon rises at sunset, it's going to be full, because it is on the opposite side of the planet as the sun. GRRM describes a crescent moon rising at sunset, and if you think about it you'll realize why that is impossible - UNLESS the light you are seeing reflected from the moon represents where it was a couple of weeks ago.

2. The appearance of Moonos changing as one gets closer to Valyria. If we suppose that there is a magical effect that is affecting the speed of light that is centered on Valyria, it would distort the appearance of Moonos as the light from it changed speed on it's way to your retina, just like things look different under rippling water.

3. There are many clues that the flow of time is variable on Planetos, including major discrepancies in different historical accounts from different places, the apparently slow technological progress, the occasional night that lasts years, the fact that there are species of hominids that had to have been isolated from homo sapiens for millions of years to speciate but live right next to anatomically modern humans, and the fact that the Maesters have not been able to measure the size of Planetos with their more-than-adequate math and Myrish looking glass technologies.

4. Determining when seasons will change is a complicated and esoteric process that requires special Maesters. Why and how? We know that magic is responsible for the strange "seasons" and the Maesters are clearly more scientific in their thinking. I think that, over the thousands of years, they have learned the complexities about how the warped space around Planetos affects their astronomical observations and they are able to, with a lot of work, account for those differences - but it's not something the common man could do like stone age humans did by just watching where the sun rises. Stonehenge would be worthless as a calendar if lightspeed was variable and the moon and sun were not always at the location their light appears to be coming from.

Thanks for the physics lesson, I did actually show up for those, and am perfectly aware that when passing through matter of varying densities the speed of light changes. However your original comment (and the one I am now responding to) both seem to suggest that the speed of light changes randomly in westeros, I further pointed out that the speed of light is such that unless it is changed by a huge factor it would be basically impossible to notice.

If it took the light from the moon 2 weeks to get to earth then light would be traveling at about 317 m/s, which means that two guys on top of the wall waving at each other would notice the effect, and they would actually hear thunder/lightening before they saw it.

Martin isn't a physicist, a chemist, a biologist, or a mathematician, worse the internet wasn't what it is today in 1996, so he wouldn't have the resources that we have today to figure out all the things about the science behind westeros. He has confirmed the cause behind planetos' seasons is magical, there is no real world scientific basis for how it works.

The Braavosi have a system of timekeeping based on the hour, so measurements of the sun and its movements cannot be that difficult to collect.

The other big problem with your assertion is the amount of light hitting something every second: if the speed of light is randomly faster then more photons will be hitting your eyes every second, and the world will be much brighter, slow it down as far as you have suggested and there is too little light to see anything.

[Taenqyrhae]

Thanks for the physics lesson, I did actually show up for those, and am perfectly aware that when passing through matter of varying densities the speed of light changes. However your original comment (and the one I am now responding to) both seem to suggest that the speed of light changes randomly in westeros, I further pointed out that the speed of light is such that unless it is changed by a huge factor it would be basically impossible to notice.

If it took the light from the moon 2 weeks to get to earth then light would be traveling at about 317 m/s, which means that two guys on top of the wall waving at each other would notice the effect, and they would actually hear thunder/lightening before they saw it.

Martin isn't a physicist, a chemist, a biologist, or a mathematician, worse the internet wasn't what it is today in 1996, so he wouldn't have the resources that we have today to figure out all the things about the science behind westeros. He has confirmed the cause behind planetos' seasons is magical, there is no real world scientific basis for how it works.

The Braavosi have a system of timekeeping based on the hour, so measurements of the sun and its movements cannot be that difficult to collect.

The other big problem with your assertion is the amount of light hitting something every second: if the speed of light is randomly faster then more photons will be hitting your eyes every second, and the world will be much brighter, slow it down as far as you have suggested and there is too little light to see anything.

I would agree if ASoIaF was hard science fiction, but it's fantasy. He doesn't have to obey all the laws of physics, just the ones that are necessary for the story. It doesn't have to be all or nothing. You can have a fantasy story have some things that are completely unrealistic and impossible scientifically, and other things that are realistic, that's not inconsistency in that genre. "How did that dwarf know that the rock he dropped on the elves below would continue to fall downwards and accelerate? This is a fantasy story, the laws of gravity don't apply!"