In 1955 John Nash wrote a special letter to the NSA. At the he was merely in his 20's but had already put out 2 revolutionary papers on game theory establishing what is know as the Nash Equilibrium”, and a solution for the value of money in trade called “The Bargaining Problem”. At this time in his life Nash was already considered a “mathematical genius” and at this time viewed as being quite “sane”, whereas most people know him from his Hollywood biography/drama A Beautiful Mind starring Russel Crowe, and that over the next few years he would appear to fall quickly and deeply into a state of psychosis.

Of all of the material by Nash that I have read, this letter that was later released to the public by the NSA, is the most revealing in regard to the way that Nash thinks and solves problems.

I'm not capable of fully understanding the intricate mathematical and cryptographic solutions that Nash's puts forth in this writing, nor the design of the machine that he gives, however, with a careful examination of the points that he makes, and his style of presenting them, we can still gain interesting insight into how this man's life and works unfolded, starting from when he was just a young man.

Let us examine a few lines from the scrawling manner Nash used to communicate his ideas to the worlds leading intelligence and research agencies.

Dear Major Grosjean

Firstly we can note right away, and throughout the pages here, that it appears Nash took little time to formalize his thoughts. It almost seems like he literally had this insight and immediately began to write it down. Throughout his writing here he strikes out words and add words later with little arrows. The reader can almost feel the sense of urgency and excitement in both the discovery and the excitement of communicating it.

Nash lets the Major know he has sent the description of a machine to another agency, which in my opinion is somewhat peculiar for reasons I will explain at the end of this writing. He also notes that he is sending the letter in handwriting, which although computers and the internet were essentially not around at this time, still seems to speak to some form of security. He sent the machine to the Navy as well, and most noteworthy in this paragraph is where Nash finishes with “I think”. An awkward and halfhearted way of confirming the truth of what will be understood to be the presentation of a very powerful conjecture.

I'm Not Just a Circle Squarer

A circle squarer refers to someone that is trying to solve an unsolvable problem, and this is where this correspondence starts to get interesting. At the time it might not have been understood that Nash was a genius (see this declaration on his letter of recommendation on pg. 5 here, but if we can assume the truth of such a claim we should really note that Nash is admittedly affirming that he is presenting an unbelievable truth. He wants the reader to consider the validity of an otherwise unpalatable claim.

Dear Sirs

I'm not exactly clear on which agencies or people specifically each of these letters are addressed to, but it doesn't matter for the purpose of highlighting the significance of the content. Here Nash reiterates his point about sending his design to the RAND corporation. He closes this paragraph with an important line, the principle he describes is important to him and that he has reason to believe the people he is reaching out to don't know the truth or significant of it, although he doesn't directly say how or why he would know this.

A General Conjecture

The basic idea is in the last line:

...the mean key computation length increases exponentially with the length of the key....

We can also note here how scrawly and disorganized the presentation of his writing actually is, although his line of thought is actually quite direct and coherent.

The Significance of This General Conjecture

It's always fun when a genius states the significance of something (assuming its truth) is “easy to see”. In math, we sometime assume the validity of something and can work out certain solutions without ever proving the assumption. This is an approach that, in a non-mathematical implementation, can also useful, but doesn't always sit right with people. It's the beginning of where Nash's ability to solve problems from odd angles comes into play. He states it here:

...it is quite feasible to design ciphers that are effectively unbreakable.

The keywords here are “feasible” and “effectively”.

He then goes on to explain a world he foresees in which decryption will be ineffective in relation to the evolution of ciphers. This is the beginning of his realization and the world that his mind started to paint upon his discovery of this insight.

A Valuable Conjecture With No Expectation of Being Proven

Things get interesting here. Nash admits he can't prove it, and doesn't expect it CAN even be proved, yet he is adamant that it is still very significant. This is another realization or specification that wouldn't sit well with the average reader. He also basically explains that as time goes by we will begin to understand the validity of it.

We (the US) Can Not Afford to Not Make Use of It

He continues to gloss over the validity of it, which I think is probably standard among “geniuses”. Having no time to convince people, he wants to go on to the ramifications of such a conjecture actually holding. It's interesting that he writes to the governments and says “we” but also qualifies the pronoun with “(the US)”. It seems there is some paranoia here he is dealing with, or in other words, he wants to make sure the reader knows he is patriotic to his nation. The last line is significant and will come into play at the end of this article, “....we should try to keep track of the progress of foreign nations towards 'unbreakable' types of ciphers. Here Nash is explicate in what he proposes, the existence and evolution towards unbreakable ciphers as well as the implication of them.

This Principle Should be Kept Secret

I think in a way this is where his writing gets fun in a sort of conspiracy type fashion. Nash proclaims an importance in keeping this conjecture secret, which he MUST of felt a rush from, when he came up with it. He also seems to take great caution in trying to convince the reader he has done his duty and due diligence in protecting it from others and especially from “enemies” or “foreign nations”. This is a theme he comes back to at various points in the letter. His use of the word “probably” is also curious as if he is being condescending.

Nash Believes the Machine he Invented Has This “Unbreakable” Property

I have read that, in today's crypto-science, Nash's proposed design is not actually as secure as he states here. I'm still unsure if that is true, or if those that claim this don't fully understand his proposal. Nonetheless it is quite the claim, and at this point it seems clear Nash felt he had a lot on his shoulders with this insight. Furthermore, as I understand his conjecture and its implications, whether his machine's encryption is unbreakable or not is not important, and I kind of suspect Nash would have felt this way as well.

This Conjecture is Suitable For Computers of the Future

This excerpt is very interesting when read in conjunction with this paper called Parallel Control, also written by Nash a year earlier for RAND. It is a design for a system of computers, that for all I can tell, we still haven't reached in our modern day age. The paper and proposal has the same feel as this letter. I feel like people today might suggest that his design is flawed, and that in many ways we have surpassed his insights, yet there is an implication by Nash that in 1955 he foresees technology that is beyond what we even have today. My basic point here is that he is thinking about a crude form of the internet in relation to his unbreakable encryption conjecture. Here, by crude, I mean to point to undeveloped ideas, rather than a lesser evolved version of internet technology.

Please Let Me Know if You Considered My Conjecture

This is where it seems to me Nash is playing with the authorities. He knows, whether his conjecture is seen as significant or not, for obvious security reasons he won't get much of a reply. In informal language he admits he expects and hopes to get confirmation that the content of his letters were considered. This is critical in relation to one of the paragraphs we covered from above:

...we should try to keep track of the progress of foreign nations towards “unbreakable” types of ciphers.

In a sense, this whole letter, and the designs he sent to RAND and the Navy, are really a backhanded way of checking on how informed Nash's government's agencies are on this “unbreakable” conjecture. In a way, it almost seems like he is taunting them and bragging about his knowledge and ability.

Secret Information Conveyed to the “Right People”

Nash closes by affirming the idea that he has been very careful with his insights but that he also realizes that he needs to express them to his own government. The response to his general sentiments I think is what is most interesting and ties the whole communication together.

Dear Mr. Nash 'Where is This Machine?'

I'm not exactly sure the truth of this, but at least as a conspiracy theory it is interesting to note that the receivers of Nash's letters were somewhat forced to reply and reveal their interest since they couldn't seem to find the designs he said he sent to the other agencies. We know this result is favorable to Nash because he stated “it would be nice to have some sort of answer.”

Dear Mr. Nash: 'Your System, Although Admittedly Ingenious, Isn't Ingenious, We Won't Be Using it, And We Cannot Discuss it'

This is a telling response, and to me puts the whole communication into perspective. I'm not entirely sure Nash meant to do anything more than to stoke a fire with his government. I think it would be foolish to assume that the receivers of these letters simply tossed his ideas aside, but what we can probably agree to is that if the conjecture Nash proposed was as significant as he seemed to think, he would have received a reply identical to this one.

Conclusion

I have my own thoughts on the implications of Nash's insights, but they are very related to many other papers and insights that Nash had at this time, and so it is very difficult to explain in a succinct manner, especially to those not very familiar with Nash's works. In other papers Nash showed all finite games have a solution, the value of money in trade, a design for an AI computer system, and this conjecture that eventually the encryptor outpaces the decryptor. It was shortly after these insights that Nash apparently had a mental breakdown. He subsequently fled to Europe where he says he was trying to exchange his US dollars for the Swiss currency which he believed was of a stronger value. He was going around saying he was going to free the people from the colluding governments and that the anticommunist and communist governments were on the same side. It was at this time he came up with the basic concept for what he dubbed “Ideal Money” which is the levation of a standard of money that no governments or group of people can control. In the Hollywood story of him, it is correctly portrayed that Nash fought for his freedom from asylum, yet his true life biography shows that he never actually fully admits he was insane and that he never actually used medication to bring his mind back into order. It is said that after this time Nash spent many years as the “Phantom of Fine Hall” scribbling on chalk boards all through the night at Princeton university, and in the last 20 or so years of his life he spent about how the advent of an electronic currency with a stably issued supply will asymptotically take the power out of the hands of central banks and authorities to arbitrarily control the money supplies and their respective values.