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AUTHORS:

TED COOPERTRC

CATEGORIES:

BREAKING THE CONSTITUTION

CALL FOR ACTION

CHEATING & FRAUD

CONSPIRACY, DEEP STATE

CORRUPTION

ECONOMY

HAPPY DAYS

HISTORY

HYPOCRISY

INJUSTICE

NEGLIGENCE, DERELICTION OF DUTY

PERSECUTION

PROPAGANDA, DISTORTIONS, SLANDER & LIES

SCIENCE

SOLUTIONS

STUPIDITY

THE TRUTH

TREASON

VIOLENCE

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Categories
CORRUPTION INJUSTICE PERSECUTION

NY TRUMP TRIAL DISGRACE

The NY Trump Trial had
no appearance of impartiality and FLAGRANTLY VIOLATED

1. The 7Th Amendment-Right to a Jury Trial

2. The 8th Amendment-Cruel and Unusual Punishment.

3. The 14th Amendment-Due Process

Plus
Title 18 Section 242

Categories
COMMON SENSE THE TRUTH

HOW TRUTH GETS DESTROYED


Due to my age, what is historical to me is probably ancient to you,
which makes me “conservative” and you probably a “progressive”. Many “progressives” and cultural bigots of today want to rewrite history & discard ancient things, such as the Bible, statutes of our founding fathers and maybe even the Constitution, in a manner similar to the ISIS idiots who destroyed the ancient Syrian city of Palmyra. Claims of advancing forward frequently involve the destruction of the past, either deliberately or unintentionally. But how can you claim to have advanced forward if you don’t know how you got there in the first place or what promoted another culture to excel? And so the truth gets lost.

Of course, the collection of too many things also tends to bury the really important points. This is where breakpoints to compartmentalize information become essential in maintaining the whole enchilada. And hierarchical filing structure helps to collect related breakpoints.

These are not new ideas as evidenced by the National Archives (NAR). It is merely common sense. BUT SUCH RECORDS SHOULD NOT BE ACCESSIBLE TO ONLY THE PRIVILEGED FEW, as has occurred with the recent findings of Joe Biden’s emails proving his criminal activity. Secrecy, censoring and non transparency can be just as destructive of the truth.

Consider this. Just think of how much better off we would have been had the historical library in Alexandria not been deliberately destroyed.

https://www.mymcpl.org/blogs/historical-libraries-library-alexandria

Maybe there might have been proof or disproof of the existence of ufo’s and et’s. I use this as an example , not as a sarcasm, because there are today real questions regarding ufo’s, which might have been answered by documents in the Alexandria Library. But for the lack of that library, we can only assume the answer to be “NO”.

By the same token, we are destroying our own libraries by proliferating them with the nonsense of WOKEISM. Is not the proliferation of self evident garbage to bury important findings the same as burning down the library?

Categories
COMMON SENSE

MY ELECTRIC BILL & BIDEN

My electric bill for January is $180 for 655 KWH.
It has been a cold cold month. I have one computer on at all times with two electric utility heaters that kick in and out depending on thermostat settings. Plus, I have two air filtration devices of which I run only one for no more than 8 hours a day. My water heater is all electric. I never use stove or oven. I only use a microwave very minimally. No dishwasher or wash machine. One refrig.

Without changing habits, summer usage is like half. So I have to figure the water heater and two heaters account for the difference, ie, 300 KWH.

I’m sorry Biden, BUT I AIN’T GOING TO FREEZE MY ASS OFF FOR YOU AND YOUR DUMB POLICIES. NOR DO I EXPECT ANYONE TO FREEZE THEIR ASS OFF FOR ME.

As far is Biden is concerned, we can all eat bugs, ride electric bicycles and huddle together to prevent hypothermia. Meanwhile,  he will enrich our lives with drag queen story hour. And if you object, he will have you thrown in jail for a lifetime.

Categories
COMMON SENSE

RESTRICT BORDER ACCESS

Why Is It Important To Restrict Access To This Country?

Three Words:
Portable Nuclear Bombs

Over the years we have witness an increase in a mentality that is willing to blow itself up along with its preceived adversaries in an act of alleged justice. This makes it imperative that access to dangerous technology be highly guarded from falling into the wrong hands. This is the real problem facing humanity today. And we must not forget that fact.

Joe Biden appears to have forgotten that by allowing anybody and everybody into this country without proper vetting. In so doing, he has increased the probability of some nutjob acquiring access to dangerous technology.

Then there are those who say “Well, nuclear bomb technology has become so proliferated that it makes no difference what we do. So we might as well give up and let the nutjobs have their way.” WRONG. As long as there is one ounce of rationality left in the world, that glimmer of hope needs to be maintained.

One thing is for certain. To make “global warming” the central theme in global politics rather than protecting the world from nuclear proliferation is completely irresponsible. And what does DEI have to do with protecting the world? NOT ONE DAMN THING. DEI = Divisive Efforts and Injustice. It is interesting to note that DEI spelled backwards is IED, Improvised Explosive Device.

The RIGHT STRATEGY to defend against nuclear attacks from the air is Reagan’s STRATEGIC DEFENSE INITIATIVE. But to protect against nulear IED attacks, the border must be highly restricted with RBA, not open borders. And you cant have either protections if you persist in pursuing green energy, electric cars, and DEI to the exclusion of all else.

Categories
SOLUTIONS

SECURING CHECK WRITING

Before the advent of electronic banking, the use of a paper iou in the form of a check with the payor’s checking account number and hand written signature was sufficient for the bank to diminish the funds in the payor’s checking account. The only danger to the owner of a checking account came from the possibility of another person being able to to perfectly copy the hand written owner’s signature, something very improbable and easy to protect against occurring.

Then came the computer with its ability to perfectly copy the signature of a person. With a picture of the signature of a checking account owner and knowledge of the account number, it became much easier for thieves to do electronic forgery. The question now is, how to minimize this threat. And the answer would appear to be simple.

First, we nust realiaze that in order for the computer to copy a signature it can only do so in graphic mode. So what we need is a non-displayable text mode signature. And with online banking, we already have that non-displayable text mode signature in the form of a password. Therefore, any electronic transaction authorizing a bank to diminsh the funds in a checking account should require the password of the checking account owner. Should a bank fail in providing this security, then it should be held laible for any losses due to its negligence.

Categories
COMMON SENSE PROPAGANDA, DISTORTIONS, SLANDER & LIES

FAR LEFT OR FAR RIGHT

In political jargon, people like to use the linear terminology of “far left” or “far right” to condemn the opposite side. They go so far as to label the opposite side as “radical extremists” or “dangerous cult”. They tend to see “communism” as “far left” verses “nazism” as “far right” How convenient for them…. and HOW STUPID.

Such thinking is myopic, unintelligent and nepharious. It is flat earth thinking that fails to see that in the end both directions eventually meet in an irrational mode of behavior and accusation, as if completing a full circle where one direction is indistiguishable from the other. In mathematics it is well known that, given a rational radius, there is at least one irrational point around the circumference of a circle. So it is with political directions.

Categories
ECONOMY

FIAT CURRENCY

THE IDEA BEHIND FIAT CURRENCY.

We begin with the idea of “value of currency” and the factors that
contribute to its inflation or deflation.  But what is ‘inflation”?
Quite simply, “inflation” is
. . THE RISING COST OF GOODS AND SERVICES
. . DUE TO THE OVER ABUNDANCE OF MONEY.
And “deflation” is just the opposite.

A. THINGS THAT CONTIBUTE TO INFLATION:

1. INCREASED ACCESS TO MONEY.

. . a. PRINTING MORE MONEY.

. . . It should be noted that it is not necessary to physically print more
. . . money. All that needs happen is for the Federal Reserve to buy
. . . government ious and make a book-keeping entry crediting their
. . . own account with a phoney deposit & then debiting their account
. . . for the amount of the purchase of  those government iuos.
. . . He who does the book-keeping controls the economy.

. . b. LOW INTEREST RATES.

. . c. LOW TAX RATES.

. . d. DECREASED
. . .  POPULATION. MORE
. . . MONEY PER PERSON.

2. INCREASED COST OF
. . . PRODUCTION DUE TO
. . . SCARCITY OF RAW
. . . MATERIAL AND/OR
. . . LABOR.  INCREASED
. . . WAGES OR INCREASED
. . . ENERGY COST.

3. EXCESSIVE SPENDING.
. . MONEY TOSSING.
. . TOO MUCH MONEY CHASING
. . GOODS AND  SERVICES. ESPECIALLY PERTAINS
. . TO GOVERNMENT.

B. CURBS AGAINST. MONEY HOARDING

1. DECREASED ACCESS TO MONEY.

. . a. HIGH INTETEST RATES.

. . b. HIGH TAXES.

. . c.. INCREASE IN POPULATION.
. . . LESS MONEY PER PERSON.

2.  OVER ABUNDANCE OF RAW MATERIAL
. . AND/OR LABOR.

3. OVER PRICING, HIGH COURT COSTS,
. . CHARGING MORE THAN THE MARKET WILL BARE.

This is why the gov is struggling to gain total control over crypto currency. It takes away their ability to control the market. But crypto does offer a way for the gov to control induviduals.

A FIAT currency is not based upon any commodity like gold. It is strickly a book keeping system maintained by the banking cartel. The world departed from a currency system bssed upon gold back with Nixon. It is probably better to have the value of gold determined by the free market rather than a government opinion. But the hazard of that is that it allows rogue nations to hoard it and possibly upset the existing fiat currencies in use. The same may even be possible with crypto currency since it is like an electronic commodity that has limited supply.

In the end, it would seem that any currency sysyem amounts to the old barttering system in the exchange of goods and services. The question is HOW MUCH DO YOU WANT A THIRD PARTY,
like the government, interfering in your exchanges. And if you really
want a third party interfering to the extent that it forgets its basic
function of securing the nation’s borders, then lots of luck with that,
because you wont even have a nation to live in or a government to
protect you from unfair trading.

In real estate, the driving priority is location, location, location.
In government, the driving priority must be
THE BORDER, THE BORDER, THE BORDER.

Categories
TECH

INTERNET BASICS

Rules For Securing Your Own Email:

1. You can’t secure your email if you use a cloud email service except via the tools provided by the email service

2. Your router and your firewall are all you need to secure your own email server. This requires a simple understanding of how internet addressing works.

First, understand that a domain name has no real significance in addressing. All addressing boils down to an IP NUMBER and a PORT NUMBER. The ip number, v.w.x.y, is the equivalent of a building address. The port number, z, is the equivalent of an apartment number. The two are expressed together as v.w.x.y :z.

With respect to email, the port numbers 25 and 587 are used to send email. The port numbers 143 and 993 are used to retrieve email in an IMAP fashion as opposed to 110 and 995 in a POP fashion.

So how do I block out unwanted hackers or spammers. First, my ROUTER must block out all unused ports, ie, empty apartment numbers. But it has to let through all traffic to the ports in use, ie, ports 25 and 587. This is accomplished via PORT FORWARDING, which is a function in your router to direct traffic addressing a port to its ultimate computer program, ie, destination.

Secondly, I have to use the firewall to block out the ip numbers (addresses) of unwanted visitors trying to hack my computer. These are found by inspecting the email server log. The hackers become quite obvious in the log.

Oh, wondering about my ip address? It is the ip assigned to me by my internet service provider. The isp forwards all internet traffic calling out this ip address to my router which begins sorting out what ports go to what computers I have on my local network.

What is my local network? That’s everything I have wifi-ed or physically attached to my router. And how do ports get connected to programs? Once the router directs a specific port to a specific computer, the programs (apps) have to be told what ports to “LISTEN” to.

So what has domain naming got to do with anything? First, we have to know that a domain is a fancy word to identify the digital hardware and software resources belonging to a specific owner. So I have two main domains that are identified as trcooper.com and aaarrrg.com. These names get resolved (translated) into the ip addresses where they reside(hosted) by an INTERNET DOMAIN NAME SERVER (DNS) which is nothing more than a lookup service, like a phone book or 411.

So, getting back to the actual residency of my domains, the trcooper.com main domain is on the GoDaddy computers, whereas aaarrrg.com is on my home computer. These are where my websites reside.

But what about my email server? Where does it reside? This is where SUB-DOMAIN naming comes in. My email server resides on my home computer which is identified as a sub-domain of trcooper.com and identified as mail.trcooper.com. The dns server will direct all traffic calling out mail.trcooper.com to my home computer and not the GoDaddy computer. So it’s all like a company that has multiple addresses.

The only thing I have not covered is encryption which provides the ultimate security in digital communication. Another word that goes flying around is the word “protocol”. I find this word being so widely abused that it has almost lost its meaning. Basically, it is a predefined way in which two communicants can verify they are speaking to the right person.  One of the first protocols was the “ack”- “nak” , acknowledge- no acknowledge. Different strokes for different folks. Ground control to major Tom. At the current time, it appears as though a protocol called TLS (transport layer security) is replacing SSL (secured socket layer) in two-way digital communications.

Categories
COMMON SENSE

WHAT PRICE FOR NON-INVOLVEMENT

The Biden Admin is doing everything it can to prevent Israel from accomplishing its task to wipe out Hamas. All in the name of protecting “innocent” Palestinian citizens. Well are those citizens really so innocent, since they freely elected Hamas to be their government?

One might argue that not all Palestinians voted for Hamas.
QUESTION: DID ANY OF THEM DO ANYTHING TO PREVENT HAMAS FROM MURDERING JEWS? It seems not. So it can be said they are complicit in the murder of jews, even though they had no part in it. Even Biden has said, “Silence is complicity”.

There are those who claim that by retaliating, Israel is a war criminal. That will not be determined until it is over. And if any such judgment of that is to occur, it must be within the same context as WWII in which Winston ChurchHill destroyed the French Navy after it had been acquired by Nazi Germany, killing hundreds of “innocent” French sailors. Is ChurchHill to be rendered a war criminal? I think not.

Certainly, those protesting and demonstrating on behalf of Palestinians DO BEAR RESPONSIBILTY FOR THE MURDER OF JEWS AND SHOULD BE HELD ACCOUNTABLE AS SUCH. But what about the silent Palestinian? Are they to be considered the same?

Unfortunately in war, it becomes a numbers game and the non-involved do become the victims of war. How many lives of non-combatants do you spare vs how many of your own do you spare. This becomes the over riding answer in war. Its called “colateral damage”, ie, unintended consequences.

Perhaps we need to ask ourselves
“WHAT IS THE PRICE OF OUR NON INVOLVEMENT?” Do we want to become the unspoken victims of war, as in the movie SHENANDOAH, or a combatant?

What ever the answer, we should be sure there is in fact a war going on before making a choice. And to answer that question, all we need do is ask ourselves, “Am I safe walking down the street alone at night in my country?”

BOTTOM LINE IS
TO CLAIM NON INVOLVEMENT IS TO ACCEPT ANY CONSEQUENCES.

For those who do become involved, the overriding objective should be winning the peace, not just the war itself. There is no glory in war. But winning the peace does not mean you surrender your principles. Nor does it mean surrendering or betraying your country as Biden has done.

Categories
COMMON SENSE SCIENCE SOLUTIONS TECH

The DIRECTION OF MULTIPLICATION

A. THE MEANING OF DIRECTION & SIGNAGE:

   We humans see ourselves in terms of position: vertical upright,
   horizontal on back, & horizontal on side.  These being our most
   common positions relative to Earth, they become the  3  basic
   dimensions that are seen as  3 linear axes orthogonal (at right
   angles) to each other. Furthermore, we think of measurable
   increments along each axis as being in the positive or negative
   direction depending upon their position relative to a zero point
   on the axis.   Such a concept gives us a 3-dimensional reference
   system that we see as absolute, albeit not necessarily so.    

   In mathematics unfortunately the plus and minus signs have two
   different meanings, depending upon the position relative to an
   operand. When touching an operand, it means the value of the
   operand is in the positive or negative direction along a linear axis.
   But it can also mean to add or subtract the operand in the absence
   of an explicit operator between two numbers.  And in the absence
   of a touching sign, the default is in the positive direction. When
   not touching an operand, it means addition or subtraction
   between two operands, ie,  it becomes an operator. So in an
   expression, there can be both directional signs and operational
   signs.

   As a side note & not relevant to this discussion, a minus sign in
   front of an exponent means to raise the reciprocal of the base to
   the power indicated by the exponent.

 

B. IMAGINARY NUMBERS:

   The imaginary number, i, is said to be the square root of -1 which
   is impossible, because according to current convention, there is no
   number multiplied by itself one time that yields a negative number.
   Lacking the ability to determine a numeric value, the square root
   of -1 is assigned the variable, “i” & complex numbers are
   mathematical expressions containing  “i”. A complex number is of
   the form (+or-)a +  (+or-)b * i, where “a” is the numerical offset,
   “b” is the numerical multiplicand, & “i” is the Multiplier. It is rare
   to see i * b, where “i”, as the Multiplier, precedes “b”, as the
   multiplicand. But that is going to change in this writing, as we
   shall soon see.

 

C. THE RULES OF MULTIPLICATION:

   The aforementioned indeterminate problem of not being able to
   evaluate “i” arises from the fact that mathematicians established
   long ago that A MINUS NUMBER TIMES A MINUS
   NUMBER SHOULD BE POSITIVE.  Furthermore, they
   established that THE PRODUCT OF TWO OPPOSITELY
   SIGNED VALUES SHOULD BE NEGATIVE. These
   conclusions arose due to the distributive law of mathematics.
   Let me state here my belief that when it comes to groupings
   via ( ..), the order of operations should dictate that expressions
   within a group should be evaluated first. But I will not quibble
   over the distributive law.

 

D. CURRENT MULTIPLY OPERATIONS IN USE:

   These current-day conventions affecting a change in value
   resulting from multiplication can be expressed as follows:

   Let:
            M = multiplier/operator

             m = multiplicand/operand

              “*” means times,
              (not to be confused with “**” which means exponent of)

             R = resulting product

 

   1. THE  PRODUCTS OF ACCUMULATIVE
       MULTIPLICATION:

      Accumulation Of Positives:
         Plus times Plus = Plus
             +M * +m  =  +R
              Interpretation:
                     Add +m  to the current value  M times.
                  OR GRAPHICALLY,
                     Relative to the current point,
                     go right M times in increments of |m|.  
               Example:
                   +3 * +2 =  +2 + 2 + 2 = 6

      Accumulation Of Negatives:
         Plus times Minus = Minus
            +M * -m  =  -R   
            Interpretation:
                   Add -m  to current value M times.
                OR GRAPHICALLY,
                   Relative to the current point,
                    go left M times in increments of |m|.  
             Example:
                +3  *  -2  =   0  + ( –  2  – 2  – 2)
                                =  0 + – ( 2 + 2   + 2)   =   -6

 

   2. THE  PRODUCTS OF DECUMULATIVE
       MULTIPLICATION:

      Decumulation Of Positives:
         Minus times Plus = Minus  
            -M * +m   =  -R
            Interpretation:
                Subtract +m  from the current value  M  times..
             OR GRAPHICALLY,
                Relative to the current point,
                go left M times in increments of |m|.  
             Example:
                 -3 * +2  =   0  +   -( 2 + 2 + 2)   =    – 6

      Decumulation Of Negatives:
          Minus times Minus = Plus
             -M * -m  =  +R
             Interpretation:
                  Subtract -m  from current value  M  times.
               OR GRAPHICALLY,
                  Relative to the current point,
                  go right M times in increments of |m|.
            Example:
               -3 * -2  = – ( -2) – (-2) – (-2 ) 
                           =  + 2 + 2 +2 = +6 

   Observe that I have identified two different types of multiplication,
   “accumulative” and “decumulative”. I make this distinction
   because accumulative  multiplication requires repetitive addition,
   where decumulative multiplication requires repetitive subtraction.

   Also, we note that the sign of the product resulting from the
   repetitive multiplication of a negative multiplicand  alternates
   between + on even repetitions & – on odd repetitions.  In other
   words, a successive number of subtractions of a negative number
   from itself ALTERNATES BETWEEN + & -.  This alternation
   does not appear anywhere else.  So this behavior is seen as
   unusual. 

 

E. RECONSTRUCTING THE PICTURE OF MULTIPLICATION:

   By insisting that the Multiplier always occurs in front of the
   multiplicand, we can clearly see that, among other things, a
   negative Multiplier means decumulation, whereas a positive
   Multiplier means accumulation. Aside from this fact, we might
   speculate that there could be other meanings in addition. What
   those could be, we are about to find out. 

   Moving on, we might assert that the Multiplier,M, reside on an
   M-axis different from the multiplicand,m, on a separate m-axis,
   with the two axes intersecting each other orthogonally at right
   angles. So the visual graphic of the Multiplier in relation to the
   multiplicand becomes a 2-dimensional planar picture with each
   axis having its own set of + & – directions, rather than just a
   simple 1-dimensional linear graphic.

             THIS                                  NOT JUST THIS

             m-axis
                  |  +                                                                              
       – ——0——- + M-axis        –  ———0———+ M & m
                  | –                              (We are not just talking candy here)

   Given this distinction, we can now begin to think in terms of:

      VECTOR CROSS-MULTIPLICATION,
          (aka, CROSS-MULTIPLICATION
               or
               CROSS-COMPUTATION 
               or
               X-MULTIPLICATION) ,

   versus

      VECTOR DOT-MULTIPLICATION,
          (aka, DOT-MULTIPLICATION
                or
                DOT-COMPUTATION   
                or
                *-MULTIPLICATION
                 or
                 SCALAR-MULTIPLICATION) .

   The difference is as follows.

   Vector dot multiplication results in a simple 1-dimensional product
   (called the dot-product) that resides on the same axis as the
   Multiplier & multiplicand. Up to now, current conventional
   multiplication has always been equivalent to vector dot
   multiplication for both accumulative and decumulative
   multiplication. But that is about to change, as we are about to
   change decumulative multiplication from vector dot to vector
   cross multiplication. The mathematical expression for computing
   the vector cross product is given as:

    R = M * m

   Vector cross multiplication results in a  product (called the
   cross-product) that is uniquely identified with a direction which
   is orthogonal to directions identified by the M-axis & the m-axis.,
   & whose numerical value is the simple product of the two
   numerical values further multiplied by the sine of the smallest
   angle, @, between the two vectors, M and m.  The mathematical
   expression for computing the vector cross product is given as:

   R = M X m = M * m*  sine(@) .

   So we now have two methods of multiplication, with
   cross-multiplication giving us a clearer 3-dimensional/directional
   picture shown as follows.

                   + m-axis              + R-axis  = CROSS PRODUCT AXIS 
                            ^                        /\
                             |                      ‘ 
                             |                  ‘             
                             |            R1 = (M1 X m1) * sine(90) /
                           m1       ‘     
                              |    ‘
      -M————–0———— M1 ——–> + M-axis
                        ‘     |    @ = -90   
                    ‘         |
                ‘             |
            ‘                 |
      -R                  -m   

   We now proceed to examine the deeper meanings of the
   cross-multiplication method.  

 

F. ABOUT THE ANGLE, @,  BETWEEN M & m.

   We’ve started out saying that M-axis was orthogonal to
   m-axis for the sake of simplicity. But the cross-product
   approach says that such is not always the case when it comes
   to vectors, because @ can take on any value between +90
   degrees and -90 degrees as the shortest path between the
   sides of the angle. And this has consequences for both the
   numerical value of the resultant, R, its dimension & its
   positive versus negative directions.        

   Before we go any further, we need to have a clear understanding 
   of how we view angles from a fixed observation point. Then we
   need to know what the sine of an angle is. And finally, we can
   discuss what role the of the angle between the Multiplier &
   multiplicand might be.     

   1. ABOUT PLUS & MINUS ANGLES:

       Envision the face of your clock where the M-axis is a straight
       line running from 12 to 6 in a negative direction & the m-axis
       is a straight line running from 9 to 3 in a positive direction.
       Progressing clockwise, we consider 12 o’clock to be +0
       degrees, & relative to it we recon 3 o’clock to be +90 degrees,
       6 o’clock to be +180 degrees, & 9 o’clock to be  +270 degrees.
       But progressing counter-clockwise from 12 o’clock, we
       consider +270 degrees to be -90 degrees & +180 degrees
       to be -0 degrees. So in this scenario, 12 o’clock is the reference
       side of any angle from it. And because we have aligned the 
       M-axis with 12 o’clock, the M-axis is also the reference side
       of any angle at which the m-axis intersects it.  Furthermore,
       should the M-axis be in a direction other than 12  o’clock,
       then the M-axis should remain the reference side of the 
       angle, @.  

       Therefore, the plus or minus direction of the angle,@,  between
       the M-axis and the m-axis depends upon whether or not we go
       clockwise or counterclockwise from the M-axis to the m-axis.
       And the shortest path from M to m will dictate whether we 
       proceed clockwise or counterclockwise from M.

   2. ABOUT THE SINE OF AN ANGLE:
       Now what about the sine of @? Without going into too much
      detail about what is meant by the sine of an angle, it is enough
       to say that the sine( +0  degrees) is +0, the sine(+90 degrees) is
      +1, the  sine(-0 degrees) is -0, & the sine(-90 degrees) is -1.
      So the sine of an angle acquires the same sign as the sign of the
      angle. If the angle is negative,  its sine is negative. If the angle is
      positive, its sine is positive.

   3. WHICH WAY JOSE, PLUS OR MINUS?:
       We now have to determine in what direction the product
       points, plus or minus, along  the resulting orthogonal axis. 

       Traditional vector math calls for the application of the RIGHT
       HAND THUMB RULE.  Finding this to be a little too
       nebulous to explain, I will only mention that the index
       finger should be the multiplicand. I leave it there.

       As an option, I would suggest discounting the sign of the
       Multiplier and applying the sign arising from the sine(@) 
       to the sign of the multiplicand to determine the sign of the
       resultant.  

 

G. REDEFINING ACCUMULATIVE  VS DECUMULATIVE
   CROSS-MULTIPLICATION:

   Having identified two different, but similar forms of
   multiplication, we now ask,”Are we using the correct form
   of multiplication for each?”. After all, we see some unexplainable
   differences between decumulative & accumulative operations.
   So let’s try applying vector cross-computation to multiplication
   instead of dot-computation. 

   We can now see that cross-multiplication not only results
   in a product pointing in an orthogonal direction away from 
   the directions of the Multiplier & multiplicand, but can
   yield an absolute value entirely different from today’s
   conventional multiplication, especially if the sine(@) is
    other than +1 or -1. Therefore, we ask “Which value(s)
   +1 or -1  would yield the same results as todays
   multiplication”.

   The answer(s) are clear. For accumulative
   multiplication, we need a sine(@) = +1, ie, @ = +90.
   For decumulative multiplication we need sine(@) = -1,
   ie. @ = -90. With this understanding,  we now modify the
   current conventions by simply replacing  the * operator with
   the X operator and adding the (sine @),   making @ = +90
   for  accumulative  & @ = -90 for decunulative
   multiplication. 

   Let:
            M = multiplier/operator

            m = multiplicand/operand

            “*” means times,
            (not to be confused with “**” which means exponent of)

            “X” means vector cross multiplication,
            (not to be confused with  variable “x” )

            “@” is the smallest angle between the M-axis & m-axis.
                    It is plus (+) if the shortest distance
                    from the M-axis to the m-axis is clockwise.
                    It is minus (-) if counterclockwise.   

             R = resulting product

 

   1. ACCUMULATIVE CROSS-MULTIPLICATION:
       For accumulative multiplication, +90 degrees is appropriate.
       In order for the resultant product, R, to become the same
       value as determined by vector dot multiplication, the value
       of sine(@) must equal +1, which means the angle, @, between
       the +M-axis and +m-axis must be  +90  degrees.
        @ = +90,   sine(+90) = +1 

      Accumulation Of Positives: 
         Plus times Plus = Plus 
         R =  +M X (+m)
              = |+M| * (+m) * sine(@) 
              = |+M| * (+m) * sine (+90) 
              = |+M| * (+m) * (+1)
              =  |+M| * (+m)
              = + (M * m)

      Accumulation Of Negatives:
         Plus times Minus = Minus 
         R =  +M X (-m)
              = |+M| * (-m) * sine(@) 
              = |+M| * (-m) * sine (+90) 
              = |+M| * (-m) * (+1)
              = |+M| * (-m)
              = – (M * m) 

   2. DECUMULATIVE CROSS-MULTIPLICATION:
      For decumulative multiplication, -90 degrees works.
      In order for the resultant product, R, to become the same
      value as determined by vector dot multiplication, the value
      of sine(@) must equal -1, which means the angle, @, between
      the +M-axis and +m-axis must be  -90. 
      @ = -90,   sine(-90) = -1

      Decumulation Of Positives: 
         Minus times Plus = Minus 
         R =  -M X (+m)
              = |-M| * (+m) * sine(@) 
              = |-M| * (+m) * sine (-90) 
              = |-M| * (+m) * (-1)
              =  |-M| * (-m)
              = – (M * m)

      Decumulation Of Negatives:
         Minus times Minlus = Plus 
         R =  -M X (-m)
              = |-M| * (-m) * sine(@) 
              = |-M| * (-m) * sine (-90) 
              = |-M| * (-m) * (-1)
              = |-M| * (+m)
              = + (M * m)

 

   Note that I did not recognize or apply the sign of the Multiplier. It
   was unnecessary when the sine(@) was included. Of course, I
   could have made @ = +90 for the decumulative operation. But
   then there still needed to be some explanation for the differences
   from accumulative cross-multiplication.

 

H. THE MYSTERY OF THE FLIP-FLOPPING RESULTANT: 

   1. ABOUT  SUCCESSIVE MULTIPLICATIONS.: 
       The fact that the resultant product of M1 X m1, R1, always
       resides in the direction orthogonal to the plane of the M-axis/
       m-axis, only one possible direction is left in which  R may
       reside, that direction being identified as the R-axis. And if that
       resultant  product, R1, now becomes the multiplicand, m2, of
       a 2nd such computation involving a new M2, then the direction
       of the new resultant  product, R2, must be on the same  axis as
       the previous multiplicand, m1. And  if that product, R2,
       becomes the next multiplicand  m3, on a 3rd such computation,
       then the direction of the new resultant product, R3, must be in
       the same direction as R1.  In other words, given a succession
       of repetitive vector cross-multiplications & where the
       resulting product becomes the next multiplicand, the R-axis
       switches positions with the m-axis & reverses its negative &
       positive directions.          

   2. REPETITIVE
       DECUMULATIVE CROSS-MULTIPLICATION 
       OF NEGATIVE  REAL NUMBERS:

       The placement of the product appears as a positive on the 
       R-axis & as a negative on the m-axis  in alternating order
       due to the right-hand thumb rule flip-flopping with each
       iteration of computing the cross-product.

       This explains why a repetitious negative times a negative 
       equals a positive R1 on the R-axis, followed by a negative
       R2  on the m-axis,  followed by a positive R3  back on the 
       R-axis. It gives the appearance of a pulsating R-axis
       acting as a binary switch between + & -. 

   3. RAISING IMAGINARY  -i TO THE Pth POWER.

       If we conduct a succession of decumulative-cross 
       multiplications of -i , assuming @ = 90 degrees, we get:

        (Cycle begins)

       (-i)**2 = -i  X -i   =  +i**2  =  -1   ( R1 to the R-axis)
                              ______________|                    
                              V
       (-i)**3 = -i X -1  =  -1 X -i  = +i     (R2 to the m-axis)
                               ______________|                    
                               V
        (-i)**4 = -i X +i  =                   +1   (R3 to the R-axis?)
                               ______________|                    
                               V
        (-i)**5 = -i X +1  =                    -i   ( R4 to the m-axis?)
                                                             |
        (Cycle starts over)                       |               
                               _______________|                    
                               V
        (-i)**6 = -i X  -i   =                    -1  (R5 to the R-axis?)                                                             

        Powers of (-i) confirmed by internet.

        Of great interest here is the observation that the successive 
        multiplications oscillate between real rational numbers and
        imaginary irrational + & – i.  We must ask, ” is i the basic 
        unit of measure in the world of irrational numbers?”. 

        NOTE:  e**i*pi = -1     where e is Eulers irrational constant.

 

I. CONCLUSIONS:

   1. We have identified two distinct forms of multiplication, ie,
       accumulative vs decumulative multiplication, the difference
       being the accumulative form is a series of additions whereas
       the decumulative form is a series of subtractions. 
       The sign of the Multiplier, M, identifies which form it is.

   2. We have identified two methods of multiplication, dot-product
        multiplication and cross-product multiplication, We have
        adopted  cross-product as the proper method to be used in both
        accumulative and decumulative multiplication. In doing so,
        we recognize the angle between  between the Multiplier &
        multiplicand to be +90 degrees for accumulative multiplication
        as opposed to -90 degrees for decumulative multiplication. 
        As a result, the sign of the Multiplier does not enter into the 
        computation of the product. 

    3. The angle, @, from the Multiplier to the multiplicand is
           normally +90 degrees in order to make the sine(@) = +1,
           thereby confirming that the M-axis is normally orthogonal
           to the m–axis, albeit not eliminating other possibilities for
           values of angle @, resulting in a wide variety of product
           values and plus or minus direction.

   4. The fact that both operands, M & m,  reside on a different axis
       as vectors means that the communitive law no longer applies,
       disproving the idea that a minus times a plus is the same as
       a plus times a ninus. It becomes like saying
       6 cats are the same as 6 dogs.

   Nothing has been done to change anything outside the realm of
   conventional arithmetic & mathematics.  Rather we have found
   old precepts to be applied in new ways to open the door to
   understanding some areas that left us perplexed. As a result, we
   have uncovered a new way of perceiving multiplication, resulting
   in the identification of decumulative multiplication as distinct
   from traditional accumulative multiplication. We have  uncovered
   some interesting details about how we can graphically interpret
   multiplication that involves what we call “direction” Finally, we
   have shed important new light on an entity that has kept its
   meaning hidden from us for so long,
   ie, the imaginary number,  “i”.