Decision Channeling Calculator
Created by David@TechForText.com © 2010
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You should closely examine the structure and function of the Decision Channeling Calculator, and its green and yellow pathways, before reading the following. This will make the material presented below easier to understand.
When the user enters a number into the input box of the Decision Channeling Calculator, the Calculator performs a series of computations to determine if the number is even or non-even. (Non-even is defined here as odd numbers, and numbers with a decimal, that is greater than or less than zero, such as 3, 85, 2.4, 4.21) If the number is non-even the Calculator will channel it through a yellow path, but if the number is even it will channel it through a green path. This is a simple form of decision-making, which consists of deciding which path to channel a number through.
The calculations that take place in the green and yellow boxes consist of a sequence based on the number the user entered in the input box. If the user entered a number, designated by X, the sequence would be X, 2X, 3X, 4X, 5X, etc. For example, if you enter an even number, such as 2, the Calculator will put a number in each green box, with the following sequence of, 2, 4, 6, 8, 10, 12, 14, etc. In addition, the Calculator will calculate the square root of each of these numbers, and place them in an adjacent green box. When a non-even number is entered, all of the above takes place in the yellow boxes.
The following material is somewhat technical. Readers who do not have an adequate background in spreadsheet formulas and mathematics might find this section difficult. Even if you have an adequate background, portions of this material should be read at a slow pace, step-by-step.
Basically, the decision-making capability of the Calculator is based on an evaluation of the mathematical properties of two sets of numbers. Some examples of number sets are represented by the following mathematical expressions: N=X, N>X, N<X, N+X=Y, N/X=Y, N-X=Y, etc. The two number sets used for the Decision Channeling Calculator are even and non-even numbers. Non-even numbers are defined here as either odd numbers, or numbers that are not integers (numbers with a decimal that is greater than or less than zero).
Almost everyone can easily identify an even and non-even number; it's common sense. However, a computer does NOT have common sense. It is necessary to delineate everything in a step-by-step way for a computer, which often must be done in the form of mathematics. To do this, I devised the following theorem, and translated it into computer instructions for the Decision Channeling Calculator.
N represents a real number, and N/2=n, and if n is rounded down to an integer, the result is represented by I.
If 2I=N or 2I-N=0 then N is an even number, if not, N is a non-even number.
This theorem can be restated with less mathematical symbols as follows:
I will use a number for this example called N. The number N is divided by two, and then it is rounded down to an integer, which we will call I. If the number I is multiplied by two, and if it is equal to the number N, then N is an even number, if not N is a non-even number.
I will present some examples of the above theorem, with numbers, in a series of steps.
N/2=n In words this means: 43 divided by 2 equals 21.5, which means n=21.5
When n=21.5 is rounded down to an integer, it equals 21, which means 21=I
Based on the theorem, 2I=N or 2I-N=0 indicates an even number. If we substitute our numbers (21, and 43) into the above formulas, we get 21 multiplied by 2, does not equal 43. Or 2(21)-43=-1 This proves, based on the theorem presented above, that 43 is a non-even number.
Another example is presented below:
(N/2=n) In words this means: 44 divided by 2 equals 22, which means n=22
When n=22 is rounded down to an integer, nothing is changed; it is still equal to 22, which means 22=I
Based on the theorem, 2I=N or 2I-N=0 indicates an even number. If we substitute our numbers (22, and 44) into the above formulas, we get 22 multiplied by 2, equals 44. Or 2(22)-44=0 This proves, based on the theorem presented above, that 44 is an even number.
. The theorem, discussed above, and the concepts of even and non-even, and the channeling of numbers through specific pathways, had to be presented in mathematical terms, using symbols that the computer would understand. To do this, two sets of computer instructions were created for the Decision Channeling Calculator.
One set of computer instructions blocks even numbers from passing through the yellow path, but it allows non-even numbers to pass through. The other set of instructions blocks non-even numbers from passing through the green path, but it allows even numbers to pass through.
=IF((ROUNDDOWN((E8/2), 0)*2)-E8=0, "", E8)
Computer instructions, in the form of a spreadsheet formula
This expression blocks even numbers, and allows non-even numbers to pass through the yellow path of the Decision Channeling Calculator.
=IF((ROUNDDOWN((E8/2), 0)*2)-E8=0, E8, "" )
Computer instructions, in the form of a spreadsheet formula
This expression blocks non-even numbers, and allows even numbers to pass through the green path of the Decision Channeling Calculator.
The meaning of the symbols in the green and yellow expressions, above, are explained below. This will be followed by a discussion of how these formulas function, and how they instruct the computer.
The E8 is a cell reference for the pink input box on top of the calculator. This acts as if it was a transmission wire that sends data from the input box to any cell that has =E8 in it.
The / with the 2 means divide by 2.
The * means multiply, and the *2 means multiply by 2.
The word ROUNDDOWN and the 0, means to remove all decimals. That is numbers are rounded down to zero decimal places, which is the same as rounding down to an integer.
The two quotation marks " " in each expression means do not display anything. More precisely, this means display the symbols between the quotation marks, but in this case, there is nothing between the quotation marks, so nothing is displayed.
The IF( ) means if something is true, (or if a condition exists) perform a specified set of computations, but if it is false (or if a condition does NOT exist) perform an alternative set of computations. The computations can involve displaying a specific set of words or numbers if true, and if false displaying an alternative set of symbols.
The Calculator's two sets of decision-making computer instructions are explained in the following paragraphs. Both sets of instructions are highlighted, one in yellow, and the other in green, which corresponds to the pathway they control on the Decision Channeling Calculator.
=IF((ROUNDDOWN((E8/2), 0)*2)-E8=0, "", E8) To make this explanation clear, I will present it in terms of the actual steps it carries out in the Decision Channeling Calculator. This will be presented along with an example, in red type, using the number 3. That is, assume the user entered 3 in the pink input box of the Calculator.
Step one) Divide the number that the user entered into the input box by 2 This is done by (E8/2). Assuming the user entered 3, the result is: 3/2=1.5
Step two) Round the result from step one down to zero decimal places (Round down to an integer) This is done by (ROUNDDOWN( , 0). The result from step one is 1.5, and when it is rounded down to zero decimal places it is equal to 1.
Step three) Multiply the result from step two by 2 This is done by *2 Thus, from step two we obtained 1, and when 1 is multiplied by two, the result is 2
Step four) Subtract the number the user entered in the input box, from the result obtained in step three This is done by -E8 The result from step three is 2, and the user entered 3, which is 2-3=-1
Step five) If the result from step four is 0 (zero), the number the user entered is even, and it will be blocked from the yellow path. (The blocking is done by “” ) However, if the result from step four is NOT 0 (zero), the number is non-even, and it will be allowed to pass through the yellow path. This passage, is done by the E8 at the end of the expression. With our example, the result from step four is -1, so the number entered by the user is non-even, and thus it will pass through the yellow path.
=IF((ROUNDDOWN((E8/2), 0)*2)-E8=0, " ", E8)
Interesting note: The location of the quotation marks, in this expression mean do not display even numbers, which results in blocking even numbers from passing through the yellow path. The location of E8 at the end of the expression allows non-even numbers to pass through the yellow path. The green expression does just the opposite of the yellow expression. The green expression, blocks non-even numbers and it allows even numbers to pass through the green path. Thus, in the green expression the location of the quotation marks and the E8 are reversed. That is the E8 was placed before the quotation marks, and the quotation marks was placed at the end of the green expression. See the following, and compare it with the yellow expression above:
=IF((ROUNDDOWN((E8/2), 0)*2)-E8=0, E8, “” )
This green expression involves the same principle (as explained above) for the yellow pathway. The actual steps it carries out in the Calculator are explained below, along with an example presented in red type, using the number 3. (Assume the user entered 3) Note all of the following calculations are the same as for the yellow path, except for the last step.
Step one) Divide the number the user entered by 2 This is done by E8/2 Assuming the user entered 3, the result is: 3/2=1.5
Step two) Round down the result from step one to zero decimal places. (Round down to an integer) This is done by (ROUNDDOWN( ,0) The Result from step one is 1.5, and when it is rounded down to zero decimal places it is equal to 1.
Step three) Then, multiply the result from step two by 2. This is done by *2 The result from step two is 1, thus 1 x 2=2
Step four) Subtract the number the user entered from the result from step three. This is done by -E8 With our example, the result from step three is 2. The user entered 3, which is 2-3=-1
Step five) If the result from step four is 0 (zero), then the user entered an even number. Then it will be transmitted through the green path. If the result from step four does not equal 0 (zero), the original number is non-even, and it will be blocked from the green path. The result from step four is -1, so the number entered by the user is non-even, and thus it will be blocked from the green path.
It is quite likely, that many other sets of computer instructions can be created, to do the decision-making and channeling process described in the previous paragraphs. In general, there are usually many alternative ways of creating computer instructions to achieve an objective. This applies to computer instructions in just about any format, including spreadsheet formulas.
The computer instructions discussed above, in the form of two spreadsheet formulas, are the instructions I derived on the first attempt. I did not try to create alternatives, or more efficient set of instructions, because the first set I created worked perfectly.
The calculations involved with the decision-making and channeling process involve less than a dozen calculations, but the calculations at the end of the pathways involve over 100 to 200, relatively simple calculations, involving, adding, and taking square roots.
The programming concepts involved with the calculations, at the end of the green and yellow paths of the Calculator, are much simpler than the two formulas created for the decision channeling process. However, they require OVER 100 formulas, and many more computations, then the decision channeling process.
The concept of difficulty, as human beings experience it is NOT the same for the computer. That is problems that are very difficult for humans, sometimes require very little computer resources. However, a task that is not very difficult for a human might consume a large amount of computer resources. An extreme example involves turning large high quality photographs upside down. A five-year-old child can quickly and easily perform this task. However, it is relatively difficult for a computer, in terms of computer resources, and the huge amount of required computations. Most calculus problems would be easier to solve for the computer then the above.
Note the words: easier, difficult, difficulty when applied to the computer, in this text, refers to all of the following, (when the computer is solving a problem, or carrying out a task): the number of computations required; the number of processor cycles required; the amount of random access memory required; the use of any other computer resources, the tendency for the computer to crash. When the above factors are relatively large, the task is difficult, and when they are small, the task is easy, based on the way I am using the terminology.
In the green boxes at the end of the green path, on the left, a chain like sequence of adding the number the user entered takes place. This involves accessing the number the user entered, and placing it in the first green box. For example, if the user entered 2 in the pink input box of the calculator the following sequence will result. 2 will be placed in the first green box, by way of the green path. Then the calculation for the second box, involves adding the number the user entered 2 with the result in the first green box, which is 2+2=4. The third green box will access the number in the second box, which is 4, and add 2 resulting in 6. The fourth box will be 6+2=8. The fifth box is 8+2=10. The sixth box is 10+2=12, etc.
The computer code for the above, in the form of spreadsheet formulas, is as follows:
In the first green box (which is cell N32) the formula is =$O$30. (This formula accesses cell O30, which contains the number the user entered, as a result of the channeling process through the green pathway.
Second green box is cell N34, and it contains =N32+$O$30. ($O$30 access the number the user entered, and the it is added to the quantity in the first green box, which is cell N32)
Third box is cell N36, and it contains =N34+$O$30 ($O$30 access the number entered by user, and it is added to the quantity in the second box, which is cell N34)
Fourth box is cell N38 and it contains =N36+$O$30, ($O$30 access the number entered by user, and it is added to the quantity in the third box, which is cell N36)
Fifth box is cell N40 and it contains =N38+$O$30 ($O$30 access the number entered by user, and it is added to the quantity in the fourth green box, which is cell N38)
(Note, the $ does not mean dollar in these formulas. Basically, it means unconditionally link to a specific cell, which will maintain the cell linkage even if the configuration of the spreadsheet is changed. For example, $O$30 means an absolute linkage to cell O30.)
Formula in first box =N32^0.5, (This means access the number in cell N32 and take the square root of it.)
Formula in second box =N34^0.5, (Access the number in cell N34 and take the square root of it.)
Formula in third box =N36^0.5 (Access the number in cell N36 and take the square root of it.)
Formula in fourth box =N38^0.5 (Access the number in cell N38 and take the square root of it.)
Formula in fifth box N40^0.5, etc. (Access the number in cell N40 and take the square root of it.)
I created the above formulas based on the following notation and concepts. The ^ in these formulas means take a to number to specific power. For example, 2^2 means two to the second power, or 2 squared, or 2 multiply by 2, which equals 4. Another example is 4^3, which is four to the third power, or 4 multiplied by 4, multiplied by 4 equals 64. Another example is 4^1 =4. Thus, to take the square root of a number, you simply take the number to the one-half power. In my formulas I used 0.5 which equal to one-half. For example, 4^0.5 means the number four to the one half power, which is the same as saying the square root of four, which equals 2.
The graphic below is a copy of a few of the green boxes, from the bottom of the Decision Channeling Calculator. The formulas on the left, create a sequence based on the number the user entered. If the user entered X the sequence is X, 2X, 3X. 4X, 5X, etc. The formulas in the boxes on the right take the square root of each number in the above sequence. For example, user enters X. then the calculations on the left are (X^0.5), (2X^0.5), (3X^0.5), (4X^0.5), (5X^0.5), etc.
The decision-making, and related channeling of numbers through pathways, is relatively simple decision-making. However, the complexity and utility of this type of decision-making could be increased by designing software with more IF programming functions, and more pathways. In theory, this can be coupled with other programming concepts, including advanced mathematics, and artificial intelligence.
In the simplest sense, the decision-making carried out by the Calculator, essentially involves sorting out numbers according to specific criteria, and channeling them to designated locations. This might have some practical application for calculations that are generally done with conventional spreadsheets, or calculation devices created from spreadsheets. Of course, the concept and the related formulas would have to be greatly modified, to fulfill specific needs.
Probably the most useful concept demonstrated by the Decision Channeling Calculator is multiple calculations performed simultaneously. I have used this concept in many of the calculation devices I have created. When applied to the design of dedicated mathematical software, (including spreadsheets) it can save hours of work for the ultimate user. That is several, dozens, or even hundreds of calculations can be performed simultaneously, even if they are very complex, with out any special skill, with little time and effort, and with a minimum of data entry. Of course, this can only be achieved with sets of calculations that use the same data. However, it does not matter, if different calculations, and related formulas, use the data in very different ways. Two examples are presented in the following two paragraphs, with the needed data in red type.
A simple example is, with the length of the radius of a sphere you can calculate a sphere’s surface area, its volume, the surface to volume ratio, the volume to surface ratio, its perimeter, its diameter, the dimensions and volume of a box big enough to enclose the sphere. That is with properly designed software, you can obtain all of the above, just by entering the length of the radius.
An example related to business, involves the monthly expenditures and monthly Revenue obtained from sales. With this data all of the following can be calculated, profits and losses, acceleration or deceleration in the rate of profits, the rate of return based on the monthly profits and expenditures, the average rate of profits or losses, the optimistic, realistic (most likely), and pessimistic forecast of profits and losses, for three months, six months, nine months, a year, two years, three years.
Are there other programs, besides the Decision Channeling Calculator, that make decisions? Of course, there are many types of software available on the market that make decisions, of one type or another, based on the way I am using the terminology. Decision-making is deciding between two or more choices or possibilities, and responding in some way. For software, the response is always based on some type of computation.
One of the simplest examples of software making a decision is when to display an error message, and which error message to display. At a far more complex level, speech to text software, (such as Dragon NaturallySpeaking) enters text into a computer, based on spoken words from the user. In this process, this software often has to make decisions, when there is some uncertainty of one or more words that the user verbalized. This might involve, the software selecting a word from several possibilities, which can be based on the probability of occurrence, in terms of other words that were verbalized along with it. However, the decision-making carried out by speech to text software is sometimes incorrect, and the user must make the final correction. However, most speech to text software programs, also have the capability of learning from experience, to make better, or more accurate, decisions. (Incidentally, this is a form of artificial intelligence.)
Even the IF( ) function from spreadsheet software (Excel and OpenOffice) involves a simple form of decision-making. This usually involves a decision on what to display, in response to a mathematical result. For example, this can be words that relate to statistics, such as above average, average, below average.
Nevertheless, the Decision Channeling Calculator, makes the decision, and takes action based on the decision. This action involves channeling numbers through the green or yellow pathways, and carrying out over 100 calculations, in the green or yellow boxes. This is to some degree different than all of the above.
However, the point here is it is
not uncommon for software to make decisions, with varying degrees of
For most purposes, humans are better decision-makers then any available computer technology, because most decision-making involves a large number of human values and goals. Computers can perhaps help humans make better decisions, such as by retrieving relevant information, and carrying out logical and mathematical processes.
However, when there is a massive amount of data that must be processed to make a decision in a fraction of a second, computers are superior to humans. For example to prevent collisions and crashes of airplanes during emergency situations, computer technology can provide an advantage over human judgment and reactions. Computer technology, with appropriate sensing equipment, could probably also be employed to prevent collisions in automobiles.
Yes; computer technology with sensing and control equipment, could be used to override reckless decisions, judgments, and behaviors, in some cases, such as with automobile drivers and airplane pilots by preventing speeding, excessively sharp turns, and any dangerous maneuver. For example, the 9/11 World Trade Center disaster, at least in theory, could have been prevented, with computer technology designed to sense and override, pilot maneuvers that can result in dangerously low altitudes and collisions with buildings.
When numbers are excessively large, (more than 15 digits) the Decision Channeling Calculator cannot distinguish between even and non-even numbers. There is a mathematical reason for this, which is, the difference between even and non-even numbers diminish (in terms of a ratio or percentage) as numbers increase in magnitude.* For example, the difference between 100 and 101 is 1/100 or 1%, but the difference between 100000 and 100001 is 1/100000 or 0.001%. When we use even larger numbers such as 100,000,000,000,000 and 100,000,000,000,001 the difference becomes extremely small, 1/100,000,000,000,000 or 0.000000000001%.
The Decision Channeling Calculator can still distinguish the very tiny difference mentioned above (0.000000000001%.), but when the difference becomes even smaller, the Calculator cannot distinguish between even and non-even numbers. For example, if you put this even number 100,000,000,000,000,000, or this non-even number 100,000,000,000,000,001 into the Calculator's pink input box, it will treat them as if they were both even, and they will both be channeled through the green path.
In addition, when numbers are very large they are likely to be rounded down to an even number, by the software. For example, 100,000,000,000,000,001 is non-even (odd), and it is round downed to an even number, in the Excel version, which is 100,000,000,000,000,000.
*Note: In terms of numbers, as opposed to a ratio or percentage, the difference in magnitude between an even and non-even number is always 1 or less than 1 but greater than 0 (zero). The difference in magnitude between an even and odd number is always 1.
The Decision Channeling Calculator can handle negative numbers, and all of the material covered in this section, applies to both positive and negative numbers. However, with negative numbers there are no square roots, in terms of real numbers. (That is the square root of a negative number is imaginary. For example, the square root of -4 is 2i.) Thus, when negative numbers are entered into the calculator, the yellow and green boxes with the words Square Root of Number will have no calculated results. You will see an error message in these boxes, but the yellow and green boxes that calculate the number sequence, X, 2X, 3X, 4X, 5X, etc., will provide calculated results.
1000000000000000000000 is displayed as 1E+21. The 21, with a plus sign, (+) represents the number of decimal places after the first digit. This can be clarified by counting the 21 red highlighted digits in the following: 1000000000000000000000
Another example is: 1456789666666890000000 is displayed as 1.45678966666689E+21. The 21 represents the number of decimal places after the first digit. This can be seen by counting the digits highlighted in red as follows: 1456789666666890000000
0.000000000000000000001 is displayed as 1E-21. With this example, 21 with the minus sign represent the number of decimal places after the decimal point, as indicated by the 21 digits highlighted in red as follows: 0.000000000000000000001
Another example is: the number 0.0000000000000000000067987 is displayed as 6.7987E-21. Note the 21 with the minus sign (-) represent the number of decimal places after the decimal point. This becomes clear by counting the digits highlighted in red as follows: 0.0000000000000000000067987
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