The “Squaring” or “Doubling” Effect (“Power of Two”)

Frequently, some Confederation sources refer to the idea that the collective power of intention is greater than the sum of the individual intentions of the group members, because it is the result of the doubling effect, or as Ra originally called it, the “squaring” mechanism. This effect results in the phenomenon that each additional person who joins a like-minded group exponentially increases the overall strength of the collective intention, call, desire, etc.

This idea is interesting enough to explore the underlying mathematics. For those interested in a mathematical analysis of this “squaring”/doubling effect, here is the text below. If math is not your forte, then you may prefer to skip the formulas and look at the simple logical explanation of how this mechanism works and where the name “squaring” may have come from (because mathematically this calculation is known to us as “doubling” or “power of two”).

When I started translating Session 7 of “The Ra Contact”, I almost immediately stumbled upon a mathematical problem that was not easy to figure out right away. So instead of continuing with the translation, I spent the next two weeks searching and reviving my ancient knowledge of higher mathematics, and to my delight, it turned out to be quite useful 🙂 Let’s try to understand this math, which is not too difficult, but very interesting.

The example used in the Law of One books is quite simple. The math problem goes like this:

Given: 10 people calling for help.
Find: What is the value of their total call?

After hearing about the rule of “squaring” the call, Don (the questioner in the dialog with Ra) logically assumed that it was about finding the square of 10, so the answer would be 10²=100.

However, Ra gave a different result: 1,012. They also said that this number is slightly lower because of the correction for the statistical loss that occurs during the period of call. Ra didn’t say how to calculate this statistical correction (probably because they weren’t asked), but they did explain how “squaring” is done: “the square is sequential — one, two, three, four, each squared by the next number.”

It is noteworthy that in explaining this mechanism of squaring, Ra spoke of working with a sequence, i.e., a mathematical series in which each successive member “squares” the previous one. Ra said that this information and the approximate value of the result should be sufficient to understand this mechanism.

At first I tried to write these calculations step by step, based on the understanding of the term “squaring” as Don understood it, i.e. as “raising to the power of two”. In doing so, I approached these calculations in terms of working with a sequence, or a mathematical series, and got what can be summarized by this formula:

The result of this calculation seemed to be satisfactory, with 1330 slightly exceeding Ra’s result of 1012, which could be attributed to a statistical correction.

In subsequent sessions, however, Ra returned to this issue, eventually explaining that what they call “squaring” is what we prefer to call “doubling”. Of course, this clarification of terminology changes the way we look at this calculation. Here’s how Ra described it in session 10:

“The call begins with one. This call is equal to infinity and is not, as you would say, counted. It is the cornerstone. The second call is added. The third call empowers or doubles the second, and so forth, each additional caller doubling or granting power to all the preceding call.” (10.13)

Based on this description, we can write the following calculations, step by step, for a group of ten people (note that since there is no eleventh person in the group, the last doubling is done by the tenth member of the group, but not for him):

Obviously, the result of this calculation (512) is almost 2 times smaller than the one proposed by Ra (1012), therefore it confirms that we should work with this algorithm in the sense of a mathematical sequence or series whose value is the sum of the terms (and not the value of the last component).

On this basis, we obtain the following formula for calculating the effect of “squaring” or doubling:

This value of 1,022 is much closer to the one suggested by Ra [1,012], and it turns out that the statistical loss of 10 people calling is 1,022-1,012=10. Does this mean that calculating this loss is a matter of counting the number of callers? I don’t think it’s that simple. But I am not going to look for an algorithm to calculate this statistical correction because there is not enough information about it and, to be honest, I do not want to delve too deeply into mathematics, the knowledge of which is in my very distant past.

This formula does allow for methodical, step-by-step doubling and summing, but it is rather difficult to use casually, as it requires many intermediate calculations. Is there another way to do this “squaring”?

Let’s look at the following explanation given by Ra:

Questioner: If ten, only ten, entities on earth required your services how would you compute their call using this square rule?
Ra: We would square one ten sequential times, raising the number to the tenth square. (7.4)

Those who are familiar with the texts of the Law of One will not be surprised by this answer, which at first glance is not at all clear: what is “one” and “the tenth square” they are talking about, why did Ra use the word “square” and not say “doubling” from the beginning so that we wouldn’t be confused?

From the above calculations [2 x 2 x 2…] we see that when Ra said “squaring” they weren’t talking about raising the argument [N, which represents the size of the group] to the second power [N²] (which is how we normally understand “squaring” – as raising a number to the second power). As it turned out, what Ra meant by squaring was raising 2 to the power of the argument [2^N]. Despite the similarity, these are different operations: N² and 2^N. And it’s obviously the latter (2^N or the power of two) that represents the “squaring mechanism” in Ra’s terminology.

Based on all this information, it can be assumed that the total call of a group of N people is calculated by one of the following formulas:

The variations are the result of subtracting (or “not counting”) one or even two first “squares”, due to the fact that the first two steps of the calculation aren’t performed in the same way as all the subsequent ones (according to the algorithm described by Ra in 10.13). However, as the number of calling entities increases, the differences between these formulas become insignificant due to the fast growth of the exponential function. But I’ll leave the elaboration of this idea to those who wish to explore it further; and in the following paragraphs I’ll talk about the simple version of this formula – the one presented as 2^N (which is called “the power of two”).

Actually, it’s not too surprising that Ra referred to the power of two, since this concept is not only known in science, but also in philosophy. In our modern world, of course, it’s the field of computer science where the power of two plays a fundamental role. We are talking about binary code, which plays an essential role in communicating with electronics, which only understands the language of two states of electric current: on and off. Therefore, there are two basic numbers used in binary coding: 1 (on) and 0 (off).

The parallel between computer science and the nature of this reality may be too far for some to imagine, but the common fact is that the greatest mathematicians are also very enthusiastic philosophers. The inherent aspect of duality of this reality has been studied in many different cultures for eons (i.e., māyā, an illusionary nature of this reality is not something shockingly new, and Leibniz’s invention of the binary numeral system in the 17th century was in very close correlation with the ancient Chinese “I Ching’s” diagrams of Yin and Yang, that corresponded to a zero and a one).

Existing knowledge of working with binary units will help us understand how the power of two (2^N) reflects the dynamics of interaction between entities in the group. In other words, we’ll try to explain the logic behind the squaring formula F(N)=2^N in an almost visual way.

The origin of this formula can be found in the field of mathematics called Combinatorics. In this particular case, by calculating the power of two [2^N], we are trying to find the number of ways in which binary digits (1 and 0) can be combined together in the N-size group. This is easy to demonstrate with an example.

Let’s take the following unit/entity: the well-known 1 bit of information [“bit” means a binary digit; it’s also a play on words: bit – piece, part]. A bit is a symbol or signal that can have one of two values: on or off, yes or no, high or low, charged or uncharged, etc.; in the binary numeral system, it is 1 (one) or 0 (zero).

Let’s look at the different sizes of groups of bits. This is how bits in a group can be combined:

For a group of two bits (i.e., N=2)
00, 01, 10, 11 (4 combinations in total, or 2²)

For a group of three bits:
000, 001, 010, 100, 011, 110, 101, 111 (8 combinations or 2³)

For a group of four bits:
0000, 0001, 0010, 0100, 1000, 0011, 0110, 1100, 1001, 0101, 1010, 0111, 1110, 1011, 1101, 1111 (16 possible combinations or 2⁴).

And so on.

For a group of 10 bits, the number of possible combinations is 2¹⁰=1024.

In the example above, we looked at the combinations of bits of information. So the question is, how does this mechanism apply to the living entities – what kind of individual dualities/polarities are combined in the group when we talk about collective calling (seeking, intending, etc.)? The simplest suggestion, I think, would be “agree-disagree” with the matter of calling/intention. Or something to do with “unification” – the term Ra used when they talked about “statistical loss over a period of call” (“the entities who call are sometimes not totally unified in their calling and, thus, the squaring is slightly less”). Another Confederation source, Q’uo (of which Ra is a part), recently expanded on the subject of unified/disunified calling (here’s the link).

I would imagine that when we use binary characteristics for people in the group, we are looking at them as possibly being in two states: “yes” or “no”, “agree” or “not agree”, “light” or “no light”, “on” or “off”, expressed digitally as either “1” or “0”. So if we imagine the simplest situation of two people, the combinations of their states of being can be:

yes (agreement, mutual desire) – “11”,
no (lack of mutual/unified desire) – “00”,
and these two situations where only one person desires something – “01” and “10”.

This example of the dynamics between two people brings us to an understanding of the statistical loss caused by people being “not totally unified in their calling” as Ra spoke of it. If there are only two people in the group, and only one of them says “yes” to an intention/desire/calling and “turns on her light” (digitally expressed as “1”), such situations (“01” or “10”) can’t be counted as an indicator of existing agreement between different entities in the group, can they?

But if there are 3 entities in a group and, again, one of them doesn’t have his “yes” to something (digitally expressed as “0”) while others have their light “on” and are blending it together (“11”), then we can say that this indicates the existence of some mutual agreement/unity within a group (digitally expressed as “011” or “110” or “101,” for example).

So when we estimate the value of a unified call, we are looking at probabilities. In other words, we ask: What is the level of confidence (probability) that a group of this size has a unified calling/intention?

Let’s review our previous combinatorics here. For example, for the group of two binary digits/entities, all possible combinations of their states of being are expressed as follows: 00, 01, 10, 11

Based on this, the probability of having the state of agreement/consensus in a group of two is ¼=25% (one out of four possible cases, highlighted by the bold style, i.e. 11). This is even less than the probability of a random event (50/50). Perhaps a group of two people (statistically speaking, in general, of course) is not very stable and can be easily swayed from agreement to disagreement (the odds are three against one).

However, with the addition of just one more self, the probability of agreement or mutual intention (between different selves) in the group increases twofold and is already 50%: 000, 001, 010, 100, 011, 110, 101, 111. And this seems to indicate the minimum level of unity in the group for its unified intention/calling to begin to have a squaring effect.

From this we can conclude that a group should consist of at least three members in order to have probable unity. This is also suggested by the way Ra described the mechanism of squaring, where the squaring itself begins only with the third call and not earlier. In addition, when talking about the optimum size of the group for conducting Ra’s channeling, Ra confirmed in 36.21 that a group of three is the minimum size for this type of working (and in the case of this particular group, consisting of Carla, Don, and Jim, it was the optimum size for them).

Let’s continue with this analysis of probable unity. As the number of members in the group increases, the probability of unity increases rapidly. For a group of 4 it is already 11/16=69%:

0000,
1000,
0100,
0010,
0001,
0011, 0110, 1100, 1001, 0101, 1010, 0111, 1110, 1011, 1101, 1111

(For those of you with a background in higher mathematics, please look at the series of numbers written in italics – this is the so-called Identity Matrix (I_N). If anyone can find its application in describing the squaring mechanism, that would be wonderful, as I think the whole process would be better described in terms of matrix algebra (but I can’t venture that deep into mathematics, the knowledge of which remains in my very distant past)).

Furthermore, for a group of 5 people, the probability of agreement between different members is 81%. And so on… For the above example of 10 people calling, their unified call will be present in 98.9% of all possible combinations of their states of vibration (regarding the matter of calling, of course).

And this is where we came to understand how the adjustment for statistical loss is calculated. Visually, it’s demonstrated above by not taking into account the combinations of digits that are not in bold (because they don’t represent a unified calling/intention). Mathematically, the general formula for measuring unified calling/intention would be as follows:

Let’s verify it. For a group of 10 people, the calculation would look like this: 2¹⁰ – (10 + 1) = 1,024 – 11 = 1,013. This value is almost identical to the one given by Ra (1,012). The difference of 1 probably has something to do with the unique properties of the first call: “the call begins with one. This call is equal to infinity and is not, as you would say, counted”. Or maybe it can be explained using matrix algebra.

But based on all my calculations and their logical explanations, I’d like to take the liberty of proposing the following formula for calculating the total calling/intention for a group of N people, adjusted for the statistical loss caused by the lack of unity:

This has been a rather long explanation, and I hope that it’s not too complicated for non-mathematicians, and provides enough inspiration for mathematicians to explore it further. But I don’t want to expand on this topic, as it can be discussed at length from many different perspectives. I will just mention an interesting method of calculating the power of two (or doubling/squaring) that has come down to us from ancient times, because it may shed some light on the origins of the term “squaring”.

It’s called the “Wheat and Chessboard Problem,” and it exists in the form of various legends from both the East and the West, but they all boil down to the same idea: if a chessboard were to have wheat placed on each square in such a way that one grain was placed on the first square (the “cornerstone” Ra spoke of!), two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), then the number of grains on the chessboard at the end would exceed the world’s current wheat production by a factor of thousands.

This is a very interesting legend, which you can easily find on the Internet (as well as its many variations) and read more about (as well as the origin of the phrase “the second half of the chessboard”).

Perhaps (and this is only my guess) the real origins of this legend go back to the distant past, when Ra or other Confederation members “walked among our peoples” and taught us rather complex concepts with simple and accessible means, such as a chessboard and seeds. In this case, the word “squaring” may have come from the connection of this mathematical procedure with the squares of the chessboard. And if you search the Internet for “ancient Egyptian multiplication”, you will find more interesting facts about ancient Egyptians using the power of two (“squaring”) in their math.

Another interesting observation about the graphical representation of the power of two in the form of “squares” is illustrated in the picture below, which shows how by duplicating squares/rectangles you can easily get the next values of the power of two.

In closing, I would like to say that what I find most inspiring about this Mechanism of Squaring is that when just seven (see chart below) awakened and calling people shine their unified collective light, it overpowers the twilight of 100 lonely sleeping souls who do not want their curtains opened. It inspires to continue to change the world, but not by trying to become a world leader or a guru, but simply by being ourselves and shining the light of our own being on those closest to us, for each additional person not only adds strength to the unified collective voice, but magnifies it exponentially!