Jerry said:
I came across another piece of that complex pattern the other night. I was listening to an interview of Scott Flansburg (a.k.a. The Human Calculator) on Coast to Coast AM. Long story short, this was the piece: i=0
As I understood it, -1 is an operation, not an actual number, thus it can not have a square root. Scott points out that the human mind is is not "wired" to naturally count "0". If I were to ask you to count to ten on your fingers, you would likely count "1-2-3-4-5-6-7-8-9-10", disregarding 0.
I'm pretty sure you are misunderstanding it. In human social systems, one of the first things we learn to do is to count money. A matter of self-interest, eh? And a negative amount of money is a debt. Its magnitude is as real for the debtor as it is for the person owed. Perhaps you should reconsider a thing known as "the number line". Can you offer any reason why, if a sequence of numbers can increase endlessly in one direction of that line, a decreasing sequence of numbers should not decrease endlessly? Thus zero and the negatives become as completely valid as the positives. Also, regarding zero, since we have a
word (more than one, such as "none") for "an empty quantity", it is perfectly rational to also have a numerical symbol for it.
But, just because dudes like ancient Romans and Mayans didn't have such a symbol, that doesn't mean they should have had it.
Their systems of numerical notation did not require a zero. (About the only rational place for it would have been as the result of a subtraction of two identical values --and even then, just leaving the result-space empty would have signified zero, right?)
Our "Arabic" notation system (called that though invented in India)
requires zero. It is also not an "intuitive" notation system (else ancient peoples would have devised it, see?). And after you see the detailed explanation, perhaps it will be obvious why it is not intuitive. What Arabic notation is, is a shorthand way of describing a complicated calculation. That is, the number 2857 equals (2x10x10x10)+(8x10x10)+(5x10)+(7). The
positions of the digits are critical to specifying what the
implied multipliers are. And zero is required as a "place holder": I cannot write 287 and have you think, just by looking at it, (2x10x10x10)+(8x10x10)+(7); I must write 2807 to be sure you know what I mean -- and that works simply because the long form, (2x10x10x10)+(8x10x10)+(0x10)+(7), is perfectly correct, mathematically. (And almost-as-obviously, if a blank was used for zero, then something like 28 7 could be confusing --is it one number or two?)
Regarding the imaginary number
i, it was
called "imaginary" because, even though mathematics could manipulate it in a perfectly rational way, it didn't seem to correspond to anything in the physical world. Well, times change, and for more than a century imaginary numbers have found a lot of practical use in the field of electromagnetic engineering. That's because of something of a coincidence; in mathematics the imaginary numbers are given their own "number line" which is oriented at right angles (like the Y-axis of a graph, compared to the X-axis) to the ordinary number line, intersecting at zero, of course (while 1
i does not equal 1, 0
i does equal 0) -- and in electromagnetics, electric fields and magnetic fields are always present at right-angles to each other. Using ordinary numbers for one field, and imaginary numbers for the other field, allows data on both field strengths to be presented together, without their becoming confused (or added when they shouldn't be added).
Jerry said:
Scott explains that the number 9 is a built in error correcter. Take any number, add the value of the didgets together and subtract them from said number, and the added value of the result will always = 9. If your answer doesn't = 9, you have made a miscalculation.
For example: 2598; 2+5+9+8=24; 2598-24=2574; 2+5+7+4=18; 1+8=9
I actually think this is a coincidence, and am going to conduct an experiment right here in this Message,
which I've never tried before. See, one thing about Arabic numerals is that the use of (x10) as a multiplier is
arbitrary. We call it "Base Ten" because of that multiplier, but surely you have heard about Base Two (binary) that computers use? It works just like Base Ten, except that the multiplier is (x2) instead of (x10) --and that only two numerals are needed, not ten. So, the number 100101=(1x2x2x2x2x2)+(0x2x2x2x2)+(0x2x2x2)+(1x2x2)+(0x2)+(1), which is 37 in Base Ten. So, what I suspect is that error-correction thing also works in other Bases, and so what looks like a special property of Base Ten isn't really. For this experiment I will take exactly that number
you used above and process it in Base Eleven, not Ten; if the error-correction is not a special propery, then the final result should be ten and not nine (one less than the Base). SO: 2589=(2x11x11x11)+(5x11x11)+(8x11)+(9), but we can ignore than since we are just adding the digits and they still total to 24 --
but in Base Eleven this is written as 22=(2x11)+(2). Subtract 2598-22 and the result is 2576 (that much math still works ordinarily; I'm glad we didn't need to use the eleventh numerical digit that Base Eleven requires, a symbol that represents the quantity of "ten"). Next, the sum of the digits 2576 is twenty, which is written in Base Eleven as 19=(1x11)+(9), and the sum of those digits is indeed ten, just as predicted. And yes, that is something I've never tried before. I've
thought about the interesting properties of "nines" in Base Ten, and wondered about other Bases on occasion, but never had a reason to test it to be sure. (Not to mention, this particular error-correction trick is one I don't recall seeing before.)
Mathematics is very consistent. Remember that. No faith is required; its consistency is as factual as 1+1=10 (in binary --are you ready for a nerd joke? "There are 10 kinds of people in the world: those who understand binary, and those who don't."

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Jerry said:
By including 0, Scott has created a "perfect calender" of 13 months, each having 28 days.
Nothing new there. You should be able to find plenty of references on the Web to old calendar-reform suggestions, with that one proposed fairly frequently. Note that it only does 364 days a year, and so an extra day or two is needed to match the true annual cycle of 365.2422... days per year.