**Abstract** With reference to bitcoin and cryptocurrencies, a theory of intellectual conservatism is outlined.

There is a logical-mathematical structure to our beliefs such that simpler -deeper- beliefs, underlie more complex and superficial beliefs. Quine made use of this structure to argue that there is no clear cut distinction between analytic (true by definition) and synthetic statements (true on the basis of experience) (1):

*The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a manmade fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occasions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements… But the total field is so undetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to re-evaluate in the light of any single contrary experience. No particular experiences are linked with any particular statements in the interior of the field, except indirectly through considerations of equilibrium affecting the field as a whole.*

A shift in beliefs near the surface need not have any effect on deep-lying beliefs, whereas a shift in beliefs of the latter type always has a profound impact on beliefs of the former type. The simpler and the deeper the belief, the more dramatic will be the impact of any shift. This is the basis of Thomas Kuhn’s notion of the “paradigm shift” (2). A paradigm shift we might say us is a change in a belief-structure so deep that, following this change, the identity of this structure itself can be considered to have changed, i.e. a new belief-structure is formed by a paradigm shift.

Paradigm shifts require a substantial re-thinking of the nature of our world, and this process tends to be difficult and uncomfortable. Temperament is a contributing cause of this difficulty/discomfort (temperaments may be divided into conservative and liberal, and the conservative temperament doesn’t like to change its ideas), but perhaps the most predominant cause is old age. Like the body, the mind becomes less dynamic with age. A significant reason for this loss of dynamism is that, as we age, the structure formed by our beliefs invariably becomes more complex, and any deep change to the belief structure of an older person will have a more dramatic impact than a deep change to the belief structure of a young person, and is harder to bring about. We can analogize this difference to the difference between moving the foundation stones of a cathedral in the process of building, and moving these same stones after the building is completed. This notion of a belief structure that grows in complexity over time can be applied to the belief-structures of individuals and to those of the social group of which individuals are a part: over time, individual belief-structures become more complex and less dynamic, and over time collective belief-structures become more complex and less dynamic.

These belief-structures can be analyzed according to their correspondence to more or less complex/superficial levels of reality, with mathematical beliefs lying at the simplest and the deepest level of all belief-structures. In turn, mathematical belief- structures themselves range from the simple and the deep to the complex and superficial. This means that deep changes to these mathematical structures tend to be very rare. The Pythagorean Theorem, for example, has stood unchallenged for millennia.

But as the successful challenge to Eucid’s plausible-seeming fifth postulate -the parallel postulate- indicates, no mathematical belief is so fundamental that it is immune to revision. The day may come therefore -nay the day certainly will come- when the venerable theorem thought to every school child as gospel truth is generally regarded as flawed and inadequate… The relative depth of mathematical belief structures means, not merely that deep changes to these structures are rare; it means also that conceiving of deep changes that are justifiable is difficult – it requires considerable mental agility to conceive of these changes. This no doubt is the reason for the high number of mathematical breakthroughs that are the work of younger, more dynamic, minds. Those working in other, shallower, disciplines are often creative into old age, but as G.H. Hardy observed (3), mathematics is a young person’s game:

*No mathematician should ever forget that mathematics, more than any other art or science, is a young man’s game. To take a simple illustration, the average age of election to the Royal Society is lowest in mathematics.*

It may also be the reason that those that claim that Satoshi Nakamoto’s revolutionary new currency, bitcoin, to be a passing fad – “bubble- are primarily old men. From the discussion above, we can expect resistance to Nakamoto’s revolutionary thinking to arise from two related but distinct quarters. Firstly resistance will come from the fact that his paper calls for a mathematical paradigm shift of sorts, and people resist paradigm shifts. Secondly, resistance will come from the fact that those in authority -academics, businessmen, politicians etc.- those that have the power to help or hinder the progress of the bitcoin paradigm shift are generally men well past their intellectual prime as far as mathematics is concerned. At root of bitcoin and cryptocurrencies is the notion of a one-way function, a mathematical operation that is easy in one direction but difficult in the inverse direction. It is by solving of one-way functions in the difficult direction that the bitcoin ledger is maintained and bitcoins are mined. Why is there an essential difference in difficulty between -say- multiplying primes to produce integers and factoring integers into their prime components? One of the most important questions in computer science and mathematics is the question of whether the class problems whose solutions are, for classical computers, verifiable in an efficient amount of time (called NP) is the same as the class of problems that, for classical computers, are solvable in an efficient amount of time (called P), where efficient means that as the size of the problem grows arithmetically the number of steps required by the computer to solve the problem doesn’t grow exponentially). Factorization is what is known as an NP-hard problem -there is no known efficient way to solve it- from which to follows that to answer this question about prime factorization it is first necessary to answer the P versus NP question, a question to which the Clay Mathematics Foundation have attached a million dollar prize. An old, inflexible, mind is bound to find this question far beyond it’s capacity.

**FACES OF THE THE OLD WORLD**

*“It’s like a Ponzi scheme in many ways where people are encouraged to put money in, and those at the top who know what they’re doing will take that money away at the top of the pile, and leave everybody else scrabbling around”.*

*Charlie Munger, the 94-year-old billionaire investor, is convinced that bitcoin is “noxious poison”*

**FACES OF THE NEW WORLD**

*I9 year old bitcoin millionaire says that if you don’t make a fortune over the next 10 years, it’s your own fault.*

*Meet the 28-year-old mathematician building a Bitcoin empire (with £10m of computers and a mind-boggling electricity bill)*

These two lines of resistance help explain the sense of Max Planck’s statement (5) that “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.” Bitcoin is at the center of a perennial duality between the historical tendency towards the decentralization of knowledge and power -the dis-unification and the consequent proliferation of sources of knowledge and power- and the contrary tendency reflected by political and intellectual conservatism, but over time the first trend will -without some kind of outside intervention- always prevail. Eventually bitcoin’s opponents will die (some of them sooner rather than later), and my expectation is that eventually cryptocurrencies will be the only currencies around.

The dogs bark, but the carriage nonetheless passes…

##### References

(1) Quine, W (1951), Two Dogmas of Empiricism

(2) Kuhn, T (1962), The Structure of Scientific Revolutions

(3) Hardy, G (1940), A Mathematician’s Apology

(4) Nakamoto, S (2009), Bitcoin: A Peer-to-Peer Electronic Cash System

(5) Planck, M (1949), Scientific Autobiography and Other Papers