Hydro-electric Power

What amuses me about the whole sub-subject is how readily people seem to embrace Langhorne's gross delusion.

Numerals are a calculation method. They have nothing much to do even with the development of number theory, never mind the _rest_ of advanced mathematics, the foundations of which were primarily laid by people who didn't even have the advantage of the relatively systematic Roman numerals. Rational vs. irrational numbers, the peculiar properties of 0 and 1 [the numbers, not the symbols for the numbers] and the operations that manifest those properties, quadratic, cubic and Diophantine [even special cases of biquadratic] equations, trigonometry, plane and elements of spherical geometry, even an early notion of limits, all these things predate Arabic numerals by as much as - or more than - a thousand years. And it took another thousand years or more _after_ that for many equally fundamental concepts to be worked out. Not because of some magical ease of calculation using the Arabic system, since many of them don't involve numerical calculations, but because they're fundamentally weird things to wrap one's head around and people don't bother until they start to see a use for them.

Sure, place notation simplifies dealing with huge stacks of numbers, but that Safehold wasn't well down the road to modern math has far more to do with the Church's view on doing _anything_ differently, and the fact that the socio-economic matrix didn't raise or actively discouraged asking the questions that more complex maths helps so elegantly to answer, than it does with how time-consuming cranking through the calculation was.

n7axw wrote:No. Numerals are not proscribed. But the point is that what is proscibed and what is not depends on who is interpreting the proscriptions. There are intendants out there for whom change is proscribed. Clyntahn himself tends to be in that category. One of the things he had against Charis in the beginning was its readiness to adapt to change. And numerals would fall into that category.

Don

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Louis R wrote:What amuses me about the whole sub-subject is how readily people seem to embrace Langhorne's gross delusion.

Numerals are a calculation method. They have nothing much to do even with the development of number theory, never mind the _rest_ of advanced mathematics, the foundations of which were primarily laid by people who didn't even have the advantage of the relatively systematic Roman numerals. Rational vs. irrational numbers, the peculiar properties of 0 and 1 [the numbers, not the symbols for the numbers] and the operations that manifest those properties, quadratic, cubic and Diophantine [even special cases of biquadratic] equations, trigonometry, plane and elements of spherical geometry, even an early notion of limits, all these things predate Arabic numerals by as much as - or more than - a thousand years. And it took another thousand years or more _after_ that for many equally fundamental concepts to be worked out. Not because of some magical ease of calculation using the Arabic system, since many of them don't involve numerical calculations, but because they're fundamentally weird things to wrap one's head around and people don't bother until they start to see a use for them.

Sure, place notation simplifies dealing with huge stacks of numbers, but that Safehold wasn't well down the road to modern math has far more to do with the Church's view on doing _anything_ differently, and the fact that the socio-economic matrix didn't raise or actively discouraged asking the questions that more complex maths helps so elegantly to answer, than it does with how time-consuming cranking through the calculation was.

That the biggest barrier was the Church's bone-deep conservatism seems to have been Don's point, at least.

I wonder too if some of it may be not having any positive example of Archangelic mathematical interest, along with no order with any business with it. The closest I can see would be the survey tools the Order of Hastings had to use, but if you've got no tradition of pursuit of wide-eyed wonder, if your almanacs are all already perfectly composed for you, if your rule-of-thumb building techniques were provided for you by the same Archangels who built the damn Temple... so many avenues for bothering with the development of mathematics may be technically open but they're certainly not cleared, posted, or apparently going anywhere you need to go. And none of them seem to have an Archangel's blessing for following them.

That's it in a nutshell.

The fun part is that I don't doubt that Langhorne _thought_ that imposing Roman numerals would help to cripple the advancement of science and technology. He's not likely, on the evidence, to have paid attention to the history of the field beyond the highly-romanticised pap he picked up in grade school - and most professionals don't know what they think they do about it. [You should see a professional historian go to town on Kuehn some time ]

JeffEngel wrote:

Louis R wrote:What amuses me about the whole sub-subject is how readily people seem to embrace Langhorne's gross delusion.

Numerals are a calculation method. They have nothing much to do even with the development of number theory, never mind the _rest_ of advanced mathematics, the foundations of which were primarily laid by people who didn't even have the advantage of the relatively systematic Roman numerals. Rational vs. irrational numbers, the peculiar properties of 0 and 1 [the numbers, not the symbols for the numbers] and the operations that manifest those properties, quadratic, cubic and Diophantine [even special cases of biquadratic] equations, trigonometry, plane and elements of spherical geometry, even an early notion of limits, all these things predate Arabic numerals by as much as - or more than - a thousand years. And it took another thousand years or more _after_ that for many equally fundamental concepts to be worked out. Not because of some magical ease of calculation using the Arabic system, since many of them don't involve numerical calculations, but because they're fundamentally weird things to wrap one's head around and people don't bother until they start to see a use for them.

Sure, place notation simplifies dealing with huge stacks of numbers, but that Safehold wasn't well down the road to modern math has far more to do with the Church's view on doing _anything_ differently, and the fact that the socio-economic matrix didn't raise or actively discouraged asking the questions that more complex maths helps so elegantly to answer, than it does with how time-consuming cranking through the calculation was.

That the biggest barrier was the Church's bone-deep conservatism seems to have been Don's point, at least.

I wonder too if some of it may be not having any positive example of Archangelic mathematical interest, along with no order with any business with it. The closest I can see would be the survey tools the Order of Hastings had to use, but if you've got no tradition of pursuit of wide-eyed wonder, if your almanacs are all already perfectly composed for you, if your rule-of-thumb building techniques were provided for you by the same Archangels who built the damn Temple... so many avenues for bothering with the development of mathematics may be technically open but they're certainly not cleared, posted, or apparently going anywhere you need to go. And none of them seem to have an Archangel's blessing for following them.

Michae wrote:Just curious but would Hydro-electric power "violate the Proscriptions",as they appear to be allowed power generated by water,which is basically the concept of Hydro-electric. The only problem I can see is the possibility of the dam being a prime target for sabotage.

Series fans should remember that electricity has been, and is in, daily use on Safehold to power the artifacts Merlin has given the inner circle, as well as his contact with Owl, manufacturing of items by Owl, etc. This being the case, it is unlikely that such use would trigger a Rakuri strike. In fact, the defensive force around the Rakuri array would depend on electricity.

SciFi90 wrote:Series fans should remember that electricity has been, and is in, daily use on Safehold to power the artifacts Merlin has given the inner circle, as well as his contact with Owl, manufacturing of items by Owl, etc. This being the case, it is unlikely that such use would trigger a Rakuri strike. In fact, the defensive force around the Rakuri array would depend on electricity.

There is a big difference between a couple dozen Terran Federation electronics and a Hydro-Electric grid and thousands or millions of late 19th or early 20th century equivalent electric motors.

Also, "unlikely" is not sufficient to bet your entire civilization on; especially when guessing wrong might get you bombed back to the stone age.

Weird Harold wrote:There is a big difference between a couple dozen Terran Federation electronics and a Hydro-Electric grid and thousands or millions of late 19th or early 20th century equivalent electric motors.

Especially since everything Merlin hands out will be stealthed against long range detection. Minimal current due to superconductive circuits and tiny charges. Radio emissions will be using frequency hopping and encryption to mask their existence against natural background noise.

And that's just the techniques known today.

Also, "unlikely" is not sufficient to bet your entire civilization on; especially when guessing wrong might get you bombed back to the stone age.

Worse than Stone Age. "Stone age" implies that there's survivors.

SciFi90 wrote:

Michae wrote:Just curious but would Hydro-electric power "violate the Proscriptions",as they appear to be allowed power generated by water,which is basically the concept of Hydro-electric. The only problem I can see is the possibility of the dam being a prime target for sabotage.

Series fans should remember that electricity has been, and is in, daily use on Safehold to power the artifacts Merlin has given the inner circle, as well as his contact with Owl, manufacturing of items by Owl, etc. This being the case, it is unlikely that such use would trigger a Rakuri strike. In fact, the defensive force around the Rakuri array would depend on electricity.

Merlin's tech is stealthed. That says nothing about the effect of unshielded electricity.

Louis R wrote:What amuses me about the whole sub-subject is how readily people seem to embrace Langhorne's gross delusion.

Numerals are a calculation method. They have nothing much to do even with the development of number theory, never mind the _rest_ of advanced mathematics, the foundations of which were primarily laid by people who didn't even have the advantage of the relatively systematic Roman numerals. Rational vs. irrational numbers, the peculiar properties of 0 and 1 [the numbers, not the symbols for the numbers] and the operations that manifest those properties, quadratic, cubic and Diophantine [even special cases of biquadratic] equations, trigonometry, plane and elements of spherical geometry, even an early notion of limits, all these things predate Arabic numerals by as much as - or more than - a thousand years. And it took another thousand years or more _after_ that for many equally fundamental concepts to be worked out. Not because of some magical ease of calculation using the Arabic system, since many of them don't involve numerical calculations, but because they're fundamentally weird things to wrap one's head around and people don't bother until they start to see a use for them.

Sure, place notation simplifies dealing with huge stacks of numbers, but that Safehold wasn't well down the road to modern math has far more to do with the Church's view on doing _anything_ differently, and the fact that the socio-economic matrix didn't raise or actively discouraged asking the questions that more complex maths helps so elegantly to answer, than it does with how time-consuming cranking through the calculation was.

What Arabic numerals (as imported from India...) permit is the concept of logarithms. This leads to slide rules and accurate (five figure and beyond) trigonometric tables. This then leads to precise mathematically based navigation and astronomy.
Hindu-Arabic numerals had a massive impact that is not immediately visible compared to a number system that breaks down at 1000 and has easily confused (and non standardized) characters above that number.

Sorry, but... No.

Logarithms derive from two separate streams: one the application of trigonometric identities to the calculation of tables of ephemerides for celestial navigation starting in the sixteenth century, the other an application of algebra to a problem of geometry that goes back at least to Archimedes [who solved a related problem with the techniques on hand in the 3rd century BCE] The move to logarithms _is_ dependent on understanding exponentiation, but like all of algebra is indifferent to the way in which the numbers are written down. The problem they were invented to solve isn't really _that_ much more tractable in Arabic numbers than Roman, which, come to think of it, is why people were giving it so much attention. Napier's insight was that a property of exponentials can be applied to directly do the work the older trig technique approximates, while the solution of the quadrature of a hyperbola leads directly to the natural logarithm. Relating natural and common logarithms is then a fairly trivial exercise.

I'll try to remember to check my references and see if I can lay out the sequence in proper detail for you, but the key point here is that Safeholders weren't _doing_ celestial navigation - which, BTW, would have led them very, very quickly to the problems of maintaining numerical accuracy in the Ptolemaic system that led to its downfall - nor were they rummaging around in the back end of geometry and algebra for obscure problems to sink their teeth into. With no need for Rudolfine Tables of their own there's no incentive to invent the techniques needed to _calculate_ those tables quickly, accurately and economically.

AirTech wrote:What Arabic numerals (as imported from India...) permit is the concept of logarithms. This leads to slide rules and accurate (five figure and beyond) trigonometric tables. This then leads to precise mathematically based navigation and astronomy.
Hindu-Arabic numerals had a massive impact that is not immediately visible compared to a number system that breaks down at 1000 and has easily confused (and non standardized) characters above that number.