On the Origins of -1
rjo__
Posts: 2,114
I can't really say that I think that we (as a species) are doomed.
But I can say that if we ever join our great demise,
it will most probably not be due to global warming, reversal of the Earth's poles or because of the toxic effects of the metals that the aliens use to construct their spaceships (which then crash and are hidden away from us just north
of Las Vegas: History Channel, Discovery Channel, DisneyFamilies, BBC, ABC, NBC etc.)
NO!
If anything encodes our demise, then it will surely come from the way that we use numbers.
Not some of us, not the ignorant few... all of us.
The use of negative numbers implies(or enforces) the use of an incorrect origin, just as
the use of imaginary numbers implies the presence of a missing transform. Perhaps,
if we took a little more care in our constructs of mathematical equality neither would exist.
BUT... they do exist.
We must suffer with them and from them, and we should be just a little frightened by
them.
We integrate the infinitely small into tangible equalities, and decimate our numbers as
though the process doesn't fracture reality. Imagine buying a ticket to see a man shoot
negative numbers out of a cannon... only to be told afterwards that the reason that you couldn't
see the negative numbers is because they are "imaginary negative numbers" and you need a
college education to see them.
But that isn't why I have created this thread.
I have created this thread... because of a single "negative number,"
-1.
I will tell you where I found this "number"...and then I will tell you why I think it happened to be there.
After that, you can be the judge.
Right now I'm going to sleep... more later
The only hint I can give at this time is that the "number" in question came out of a Parallax Propeller... not a real Parallax Propeller... one of those emulated Parallax Propellers:)
But I can say that if we ever join our great demise,
it will most probably not be due to global warming, reversal of the Earth's poles or because of the toxic effects of the metals that the aliens use to construct their spaceships (which then crash and are hidden away from us just north
of Las Vegas: History Channel, Discovery Channel, DisneyFamilies, BBC, ABC, NBC etc.)
NO!
If anything encodes our demise, then it will surely come from the way that we use numbers.
Not some of us, not the ignorant few... all of us.
The use of negative numbers implies(or enforces) the use of an incorrect origin, just as
the use of imaginary numbers implies the presence of a missing transform. Perhaps,
if we took a little more care in our constructs of mathematical equality neither would exist.
BUT... they do exist.
We must suffer with them and from them, and we should be just a little frightened by
them.
We integrate the infinitely small into tangible equalities, and decimate our numbers as
though the process doesn't fracture reality. Imagine buying a ticket to see a man shoot
negative numbers out of a cannon... only to be told afterwards that the reason that you couldn't
see the negative numbers is because they are "imaginary negative numbers" and you need a
college education to see them.
But that isn't why I have created this thread.
I have created this thread... because of a single "negative number,"
-1.
I will tell you where I found this "number"...and then I will tell you why I think it happened to be there.
After that, you can be the judge.
Right now I'm going to sleep... more later
The only hint I can give at this time is that the "number" in question came out of a Parallax Propeller... not a real Parallax Propeller... one of those emulated Parallax Propellers:)
Comments
I should say that when they write those "...books for Dummies," I one of the dummies they have in mind. That's important to keep in mind as I relate just how magnificent my experience has been so far. AND just how much fun the process has been. I can't thank Parallax enough for what they have done or relate how much I respect the work of the guys and gals at Altera in producing a set of tools and work environment that is just plain sexy.
The Propeller image is basically written in Verilog. If you haven't heard of Verilog it is the work of a group of people, whose only previous work experience was translating a Mayan Codex into Egyptian hieroglyphs for Richard Feynman. It takes the work os such geniuses to make something as powerful as Verilog and companies like Altera to put such things safely in the hands of people like me.
Where in the translation from Mayan to Egyption does the Parallax Propeller fit?
If you are comfortable with the Propeller then you are comfortable with the concept of parallelism...Verilog stretches you one step further... and asks you to imagine nearly unlimited parallelism... as many instructions as you like all operating in perfect parallelsim, syncronized by one or a series of clocks.
Once you have that concept, which I had never considered until I heard Phil talk about it and never really understood it until I started looking at the Verilog sources. Until then I would never have thought that it was even possible...swear to God.
... that's it. more later. I have to go to bed, I have the rugrat for the next three weeks.
I mean, you would have to go through 0 to get to it and that obviously does not exist. Ask the Romans. We don't need a symbol for nothing. Just leave a blank space on the page. Mind you people tend to draw a boarder round that blank space so you know where it is. That looks a bit like a 0.
There is no 2 either. The second one there is, well, just another 1. Right.
Like wise, by induction, we see there is no 3 or all those other loony tunes numbers people talk about.
No, there is only 1. And a bunch of operators on oneness.
By the way, did you know, that if you add up all the positive integers from 1 to infinity, 1 + 2 + 3 + 4 +5 +...., the result is -1/12, yes minus a twelfth.
This might seem surprising but given the fairy tail nature of anything other than 1, should not be.
It always amazes me that the aliens were smart enough to get themselves into space and transport themselves billions and billions of miles...
...but not smart enough to handle the last mile, thus crashing into the New Mexico desert?
Walter
P.S. I used to live in Roswell. Never saw any real aliens, just a lot of weird people doing "research".
No surprise there. Pilot's often say "flying is the easy part, it's the landing that's hard."
Those weird people were the aliens
Also 1 is quite often true.
The all knowing Parallax Serial Terminal.
I started my professional life on Univac 1100 mainframes. They are 36 bit, ONE'S compliment machines. They have +0 and -0. That might explain a lot about my professional life.
http://www.fourmilab.ch/documents/univac/minuszero.html
And +0 and -0 still exist, at least in the Delphi floating-point world. Most compilers handle these values as equal. Delphi doesn't, as it does FP equality by directly comparing memory, rather than via the FPU.
I've been burned by this more than once.
Also, I'm old enough to have learned with punched cards and overpunched signs... which also allowed for +0 and -0.
Walter
You will be glad to find that +0 and -0 are alive and well in the modern world.
Never mind Delphi, pretty much all programming languages today use the IEEE 754 standard for floating-point arithmetic. Which has a separate representation of + and - zero.
Now, it is possible that many languages, except Delphi, take care of this little issue. For example JavaScript: BUT wmosscrop, please consider. When using floating point one should never, ever use "==". For example, let's compare +zero to -zero in JavaScript a slightly different way: Or perhaps +zero with +zero: Hmmm...
This is a problem no matter what language you are using, never mind if they fiddle with + and - zero or not.
Don't do that!
This made me laugh out loud!
:thumb:
Whilst we are here, what on Earth has the mystery of -1 got to to do with any Propeller or Propeller Verilog?
We need to know...
Then I found that it was j^^2 = -1 and all was used in capacitors and inductors. So now we have an imaginary imaginative electronics.
So why can't we imagine we can travel above the speed of light and just imagine we have arrived in another start system, and just take a look around.
Maybe after all, we are just imagine being here in the first place - just a thought
Not entirely numeric but:
LOLOAQICI82QB4IP
There is nothing odd about imaginary numbers (a really bad name for them by the way). They are just pairs of numbers (x, y) with some odd rules about how to do addition and multiplication with them. You don't need i at all.
Same as there is no -1. There is just 1 with some weird operation you can do on it.
Firstly an imaginary number is not the same as a complex number, and secondly you confuse the number
with its representation - the number is defined by its properties, its algebraic structure(s), the representation
is arbitrary (although its wise to choose a simple one which has no redundancy if possible). I agree about
"imaginary" though - perhaps "imaginative" and "complete" for "imaginary" and "complex"?
"Complete" since all polynomial equations have a full set of roots in the complex domain.
A complex number is of the form a + bi where a and b are real an i is defined above.
Clearly all imaginary numbers are in the set of complex numbers. We can always write them as ai + 0. They all lie on the vertical axis of the complex plain.
So technically imaginary and complex numbers are not the same thing. Colloquially it's quibbling over detail.
No confusion here.
Complex numbers numbers have two components often seen as a + ib. This is convenient as we can do arithmetic on them using the "normal" rules of arithmetic. Just remember that i squared is -1 and it all comes out in the wash.
Or they could be seen as a vector (a, b). In which case there is no i to be seen anywhere and the rules of their arithmetic are a bit odd. This is clearly true because we can create computer programs for performing arithmetic on such complex numbers. The computer has no idea about i.
No doubt one could dream up other representations for complex numbers. In software they are often represented as structures with real and imaginary fields.
Personally I'm with a lot of mathematicians who say that "imaginary" is an unfortunate name for these things. All numbers are figments of our imagination anyway. Singling these out as being somehow extra mystical tends to be a bit hairy scary and intimidating when people are learning these things.
Turns out that it's the non-rational numbers that are imaginary. That is to say most numbers. The ones that fill in the gaps between the rationals. The ones we can't write down accurately in anyway. We can only identify them indirectly, like sqrt(2).
Then we have all those infinities, clearly imaginary.
Heater, agreed.
But, I'm dealing with 15+ year old legacy code... by someone who was not primarily a developer. So we fix these issues as we find them.
My point was more that Delphi doesn't use the FP processor for comparisons in all cases.
BTW, the equality test in Delphi is "=".
Walter
Ahhhgg...!
God I feel terrible. My plan had been-->get the tyke on the plane--> get the tyke off the plane--> get to the pool--> take pictures of octogenarians in bikinis-->log in to wifi--> continue thread with proof of presence at pool at Del Webb...
Problem... tyke not 40 inches tall. Grandma got grandpa Black Velvet.
More later;)
That would be "Javascript === true" unless you are happy to be left open to type errors.
Aren't we on the wrong thread for that?
I did not understand any of the rest of the post:)