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Langhorns deadliest blow - Killing Zero

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Re: Langhorns deadliest blow - Killing Zero
Post by phillies   » Wed Oct 17, 2018 9:20 pm

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Randomiser wrote:I see the argument about the concept of zero. Negative numbers however are less likely to have been lost. Any banker making loans or any merchant giving credit has an entirely functional grasp of negative numbers or something very like them in order to keep track of business. There were certainly plenty of both on Safehold well before Merlin.


A banker might also have debt and asset numbers, which cancel each other one to one, no subtraction being needed. With paper and no abacus, subtraction becomes crossing out matching pairs of letters.
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Re: Langhorns deadliest blow - Killing Zero
Post by dobriennm   » Wed Oct 17, 2018 11:13 pm

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phillies wrote:
Randomiser wrote:I see the argument about the concept of zero. Negative numbers however are less likely to have been lost. Any banker making loans or any merchant giving credit has an entirely functional grasp of negative numbers or something very like them in order to keep track of business. There were certainly plenty of both on Safehold well before Merlin.


A banker might also have debt and asset numbers, which cancel each other one to one, no subtraction being needed. With paper and no abacus, subtraction becomes crossing out matching pairs of letters.



And zero (and negative numbers) are really needed to start thinking of numbers as a continuum. Zero fills in the "hole" between negative numbers and positive numbers. You need to start thinking of numbers not as discret numbers of things (or fraction of things).


It's hard to take a limit of a function F(x) as x approaches 2 if you can't think of x~1.9, then 1.99, then 1.9999, then 1.999999999............… or x~2.1, 2.01, 2.0001, 2.0000.....1 which is kinda the basis of calculus.
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Re: Langhorns deadliest blow - Killing Zero
Post by evilauthor   » Thu Oct 18, 2018 9:56 am

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dobriennm wrote:It's hard to take a limit of a function F(x) as x approaches 2 if you can't think of x~1.9, then 1.99, then 1.9999, then 1.999999999............… or x~2.1, 2.01, 2.0001, 2.0000.....1 which is kinda the basis of calculus.


I believe fractions already existed on Safehold.

Hell, a tenth mark coin (aka, currency whose value is only one tenth of a mark) is a thing that exists on Safehold. When you break the value of your currency up into parts smaller than your common unit of denomination, you have an entirely functional grasp of fractions.

Fractions might not be as good as decimals, but they're functional even with Roman numerals.
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Re: Langhorns deadliest blow - Killing Zero
Post by dobriennm   » Thu Oct 18, 2018 1:10 pm

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evilauthor wrote:
dobriennm wrote:It's hard to take a limit of a function F(x) as x approaches 2 if you can't think of x~1.9, then 1.99, then 1.9999, then 1.999999999............… or x~2.1, 2.01, 2.0001, 2.0000.....1 which is kinda the basis of calculus.


I believe fractions already existed on Safehold.

Hell, a tenth mark coin (aka, currency whose value is only one tenth of a mark) is a thing that exists on Safehold. When you break the value of your currency up into parts smaller than your common unit of denomination, you have an entirely functional grasp of fractions.

Fractions might not be as good as decimals, but they're functional even with Roman numerals.


Yeah, but it's still thinking of numbers as discrete things. Even thinking of 1/10 instead of 0.1000 means you are thinking of dividing one "object" into 10 "smaller objects". It's functionally useful in ordinary society as it exists on Safehold, but it's not useful in higher mathematics.

After all, thinking of numbers as being a continuum means irrational numbers aren't really "irrational", they're just another number on the continuum of numbers (think number line). It's a very abstract way to look at numbers which means you can do so much more with them and with mathematics in general.

Note: An Irrational Number is a real number that cannot be written as a simple fraction. Think Pi or the square root of 2
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Re: Langhorns deadliest blow - Killing Zero
Post by evilauthor   » Thu Oct 18, 2018 1:33 pm

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dobriennm wrote:Yeah, but it's still thinking of numbers as discrete things. Even thinking of 1/10 instead of 0.1000 means you are thinking of dividing one "object" into 10 "smaller objects". It's functionally useful in ordinary society as it exists on Safehold, but it's not useful in higher mathematics.


Oh well, if higher math is what you're going for, then AFAICT, no, higher math did not exist prior to Merlin reintroducing Arabic numerals. It's questionable if even geometry existed prior to Merlin even though RL Earth has had geometry since the Bronze Age (and possibly even before).

Once Merlin introduced Arabic numerals though, we see Doctor Macwhatshisname working with it and gaining new insights into the meaning behind random comments that various angels had made. This suggests that he was already working out the beginnings of higher math even before he got inducted into the Inner Circle and started feeding him higher math.
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Re: Langhorns deadliest blow - Killing Zero
Post by Silverwall   » Thu Oct 18, 2018 2:01 pm

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evilauthor wrote:
dobriennm wrote:Yeah, but it's still thinking of numbers as discrete things. Even thinking of 1/10 instead of 0.1000 means you are thinking of dividing one "object" into 10 "smaller objects". It's functionally useful in ordinary society as it exists on Safehold, but it's not useful in higher mathematics.


Oh well, if higher math is what you're going for, then AFAICT, no, higher math did not exist prior to Merlin reintroducing Arabic numerals. It's questionable if even geometry existed prior to Merlin even though RL Earth has had geometry since the Bronze Age (and possibly even before).

Once Merlin introduced Arabic numerals though, we see Doctor Macwhatshisname working with it and gaining new insights into the meaning behind random comments that various angels had made. This suggests that he was already working out the beginnings of higher math even before he got inducted into the Inner Circle and started feeding him higher math.


Not really, we have an equally compelling theory that is based on the needs of the author to tell a story so forcing development along for story reasons. There is no indication that they are being poked along by Merlin so he would have to be a genius greater than Newton and Leibowitz combined to make that much progress so fast. I also dispute that these ideas were already there as I don't believe that you could even comprehend the queston when you don't have a place-based number system, the concepts literally make no sense. You MUST have a place based number system for all this higher math to even begin to make sense.

At best they would be considered unsolvable problems of philosophy just like they were here on earth in similar situations. Just look at how many years people tried to square the circle becasue they didn't understand the concept of irrational numbers. https://en.wikipedia.org/wiki/Squaring_the_circle it was not proved impossible until 1882! They just don't have the tools to even ask the right questions and wandered off down mathematical dead ends. This does not lead iteslf to radically fast innovation once modern numbers and zero arrive because they don't know what is true (Very little) and what is false (a lot).

EDIT: Unlike other discussions where we have to rely on RFCs word outside of the books that there is other knowledge/capability present but not shown I feel that RFC has gone to great lengths to show just how badly mangled safeholdian maths is. Assuming anything beyond the Math shown in the first book is very unwise because of the incredible limitations RFC placed on safehold by eliminating arabic numbers, all traces of the place based maths systems and removing even abacusus which are truely ancient devices that far predate zero. Even a cursory look at how math evolved/works shows that these actions PREVENT most modern maths being conceived of.
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Re: Langhorns deadliest blow - Killing Zero
Post by evilauthor   » Thu Oct 18, 2018 4:16 pm

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Silverwall wrote:Not really, we have an equally compelling theory that is based on the needs of the author to tell a story so forcing development along for story reasons. There is no indication that they are being poked along by Merlin so he would have to be a genius greater than Newton and Leibowitz combined to make that much progress so fast. I also dispute that these ideas were already there as I don't believe that you could even comprehend the queston when you don't have a place-based number system, the concepts literally make no sense. You MUST have a place based number system for all this higher math to even begin to make sense.

At best they would be considered unsolvable problems of philosophy just like they were here on earth in similar situations. Just look at how many years people tried to square the circle becasue they didn't understand the concept of irrational numbers. https://en.wikipedia.org/wiki/Squaring_the_circle it was not proved impossible until 1882! They just don't have the tools to even ask the right questions and wandered off down mathematical dead ends. This does not lead iteslf to radically fast innovation once modern numbers and zero arrive because they don't know what is true (Very little) and what is false (a lot).

EDIT: Unlike other discussions where we have to rely on RFCs word outside of the books that there is other knowledge/capability present but not shown I feel that RFC has gone to great lengths to show just how badly mangled safeholdian maths is. Assuming anything beyond the Math shown in the first book is very unwise because of the incredible limitations RFC placed on safehold by eliminating arabic numbers, all traces of the place based maths systems and removing even abacusus which are truely ancient devices that far predate zero. Even a cursory look at how math evolved/works shows that these actions PREVENT most modern maths being conceived of.


I said that Doctor Mac was working out the BEGINNINGS of higher math, not that he had already done so. And that was only after Merlin had introduced Arabic numerals to him, NOT before.

And my first paragraph said that Safehold almost certainly did NOT have even geometry even though RL Earth has had geometry since the Bronze Age. And just because we didn't work out squaring the circle until the 19th century doesn't mean geometry didn't exist; you don't need to square the circle to build the Great Pyramids or to calculate how many bricks the Great Wall of China needed. Basic Pythagorean math will suffice and that long predates Arabic numerals.

And let me repeat, prior to Merlin, I don't believe Safeholdians had knew as much math as Pythagoras or Euclid had.

AFTER Merlin however, Safeholdians took to Arabic numerals extremely quickly, to the point that Duchairn and his entire branch of the Church were using it to manage the Jihad's logistics. I think there was even a comment in one of the books by a Churchman that there was an irony in the new number systems; people couldn't even THINK in terms of such huge numbers that the Jihad's logistics required without the number system the Charisians had introduced.
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Re: Langhorns deadliest blow - Killing Zero
Post by Annachie   » Thu Oct 18, 2018 5:09 pm

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Do we think he would have allowed the Knotted Rope?
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You are so going to die. :p ~~~~ runsforcelery
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Re: Langhorns deadliest blow - Killing Zero
Post by evilauthor   » Thu Oct 18, 2018 5:59 pm

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Annachie wrote:Do we think he would have allowed the Knotted Rope?


He had to. Safeholdian sailors have been using it since Creation AFAICT. It's explicitly noted that Langhorne changed things so that nautical knots equal landbound miles, aka, 1 knot = 1 mph.

Which is weird because that REDUCED unnecessary complexity that he was using to strangle any kind of scientific thinking.
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Re: Langhorns deadliest blow - Killing Zero
Post by Silverwall   » Thu Oct 18, 2018 9:55 pm

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To help those who are not well versed in the history of Math you may find the following essay on the history of zero interesting.
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Zero.html

It differentiates between the two uses of zero, being a placeholder in the number system and being a number in it's own right.

P.s. one thing you can't do without zero? Graphing and map making using cartesian co-ordinates, which as the name suggest was invented the famous french mathematician René Descartes in the 1600s. This makes me wonder makes you wonder if the maps in the holy books had lines of latitude and longitude on them :-) If they did I assume zero longitude would run through Zion as the prime meridian.
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