Sagan’s Numbers

Whose and Truth: Or 5 letter words weighing the same. 

In 1974, Carl Sagan and other astronomers sent out an interstellar radio messages into deep space. The information in the radio message began with the integers 1 through 10 as best can be represented in binary units of data. The choice to send numbers into space reflects the notion that fundamental to the universe, the very fabric that holds it together, is the truth we find in their consistent nature; that 1 is a thing, and that 1 + 1 will always equal 2. But in this interstellar message is an assumption that whatever beings that might encounter the numbers are ones who perceive in a manner similar to us. What is perception, then? We find in the following line it’s boldest expression to date, “What is true is true absolutely, in itself; the truth is one, identical with itself, whatever may be the beings who perceive it – men, monsters, angels or gods,” as philosopher Husserl tells us.[1] There is a subtle conflation here between truth and perception lurking in Husserl’s words, one found in the way that perception and truth are only what they are because they are guaranteed against change regardless of who perceives something true, and even when it is that they perceive it. For now, it is only important to assume that between men and gods, alien life is to be situated, and that they must perceive numbers and truth in the same way we do. This radical statement framing the overall force and reach of our faith in logic and rationality is double edged – it is also the intellectual instinct that is responsible for Bertrand Russell’s Principia Mathematica. I won’t pretend to anyone that I’ve read the entire text, but instead I look at two aspects of it to inform the following opinions. The first is it’s anthem which claims that “from this proposition [consisting of entirely abstract symbols] it will follow, when arithmetical addition has been defined, that 1 + 1 = 2.”[2] The three volumes of Russells’ work aim at making this as a truth beyond doubt. This much is easily digestible without reading every word of the text. The second aspect informing my opinion is that Russell takes almost 2000 pages to establish this claim from beginning to end. 

            To send an alien race 1, and then 2, without providing them three volumes of argumentation that grounds the idea of 2, seems a cruel trick, like showing the human intellect while deliberately obscuring the powers by which we can accomplish such feats as the meaning of number 2. How can any being derive a meaningful connection between 1 and 2 without also having the necessity of their relationship proven to them by Russell? They may see 1 and also may see 2, but what will connect the two objects together, proving that 2 is the offspring of two 1s? Can we not still further imagine the horror and perplexity of our alien friends as they encounter the number 3?

            My concern here lends itself to a more basic question, one which should concern our astronomers a great deal more than it seems to have done so far. By sending out integers as though they represent our high intellectual capacity, we are making an assumption on what demographic of an alien race our message will reach. Sagan must imagine that an alien race is without distinctions, that whoever his message meets is of the mental caliber to also interpret numbers as the highest realization of thought, and not some off-world penal colony floating adrift towards us. Also, aside from Sagan’s assumption as to who he imagines will encounter his message, he seems to have overlooked, or entirely forgotten, the existence of civilizations on earth such as the Pirahã  people, who only have terms for 1, 2, and many. That is, if we are to believe those anthropologist who spend their careers attempting to prove the relativity thought along these lines. For the Pirahã , beyond 2 it would seem as though things obscure into a formlessness of many, and so not necessarily forming into 3. So, if we are to take seriously the attempt at communicating with an alien race through numbers as something universal to perceiving beings, shouldn’t we just as well have stopped at the number 2? Yet, still, wouldn’t 1 in itself present a puzzle that might act as a key for an alien race to unlock the secrets of the cosmos? Before considering these questions and what it would mean to attempt to send a message intelligible to any creature with the capacity for understanding “truth,” we must take one step further into considering whose universality we have sent into space. 

            There is a bright, unnerving glimmer on numbers as universal ideas, an irritating light reflecting out of the ivory towers where such thoughts are produced and taken most seriously. The irritation is found in this: numbers are seen as the most fundamental object in our conception of the cosmos. If there is anything such as an ideal object (existing outside space and time and therefore not subject to change) in existence, such an object needs a champion that can defend them. We find the champion in the alleged sovereignty of 1 as indubitably real, therefore 1 + 1 = 2 is real, too. Yet simultaneously, there is a revealing insecurity to this claim as the champion of the possibility of ideal objects. We can find this in Russel’s 2000 page treatise about 1 + 1, but even more so in the 2000 years of philosophical debating that goes back to Plato. To claim that numbers and their existence are real in a universal way – as if these ideas were golden statues cast before the creation of anything at all – while also spending millennium didactically polishing clean these golden objects to protect them from rust in thousands of philosophical proofs, is a mixed message to say the least. Either we should not fear that a number can be subjected to decay, and so spend our efforts elsewhere, or we must question the purity of the gold before us. This confusion is glossed over by the sole fact of the authority which is behind the invention of the problem. The rational instinct responsible for ever having first posited numbers as universal, ideal objects is the same one which also acknowledges the equivocation of the claim of their realness.

            If we are to admit that Russell’s Principeia Mathematica  is humanity’s best attempt at proving 1, or 1 + 1 = 2, then are we not also admitting that arithmetic and numbers are not beyond doubt? That they are in need of proving? This immediately brings into question whose proof we are to use to conceive of numbers as universal. To go one step further along this tract, we can even ask whose concept of universality we ought to consider as truly universal. For the question to be taken seriously – ‘whose universal’ means appealing not to the internal coherence of an idea, nor to any philosophical proof, but rather an appeal towards taste for determining which proof suits an individual best. After all, if any proof was indubitably correct, the others would not exist, and a false proof is no better than any other given their only validity resides in the fact of their internal coherence. The fact that we can imagine numbers existing as ‘whose numbers’ or as ‘whose truth’ shows us a seam in numbers as ideal objects, revealing the patchwork of their creation. It is precisely at this seam we see the point at which a careful observer can pry open the golden statue and see hidden inside these objects the finger prints of the humans who molded the metal before it had solidified. For anyone doubting this proposition, take some of the interpretations of Hippasus’ life, a Greek man who was drowned at sea for taking too far his opinion that irrational numbers were just as real as their rational counterparts. And so any projection of numbers into space as the ideal matter of perception would be nothing more than the most sophisticated idolatry of man’s best idea’s being the measure of all things. When Sagan sent out his integers 1 – 10 into deep space, he was acting like a zealous muezzin calling out from the highest ivory tower for the entire cosmos, including us, to accept his truth as the supreme one.

            Considering the element of taste which cannot be denied as having a considerable pull in the matter, for human kind to send out any universal in hopes of signaling our existence and our identity, it would be wise to not attempt to remove the truths relative to humans in whatever ideas we transmit. Rather than sending what we interpret as universal to the cosmos, it makes more sense to send out that which is most universal to mankind. This also solves one of the problems I previously proposed that we must not assume our message will reach the most educated members of another race and furthermore raises the question of the nature of truth. We cannot transmit universal human experiences such as familial relationships, or clothing, which seem definitely human across most cultures, because these are not tangible enough to send out – we need an image. Instead, we ought send out that which has the most weight in symbolic terms, which humans of the 20th century would recognize. Where previously our goal was to send out proof of intelligent life existing on earth, our new goal is to send out whatever would  make it easiest for another race who receives the transmission to pick humanity out of a line up if all the creatures of the universe were placed side by side. Images with the most weight are easily measurable given developments in advertising which took place in the 1920’s through to today. We can turn to corporations and their systematic self-branding across the globe, and their ability to find a common thread among billions. And so, rather than sending out numbers encoded in binary bits of data that could hopefully be mapped into logical coherence, we should instead send the image of two arches side by side, and the word for golden in every language known to man. 

[1]. Logical Investigations – §36, “Critique of specific relativism and, in particular, of anthropologism.”

[2]. Principia Mathematica – *54.43.


Alan Verbembalmer