I recently came across a reference to a famous quote by supercomputing pioneer Danny Hillis: “Memory locations are wires turned sideways in time”. When first hearing this, it sounds a bit mind-bending— how can you turn something sideways in time? But once you recall the idea of time as a fourth dimension, the quote is pretty clever. Normally, you think of an ideal wire as transferring a bit, the simplest piece of computer data, from one point of space to another. And an ideal memory location stores a bit in a particular place now, so you can access it in the future. Thus, if you could turn things sideways in time, transferring a movement along a line in space to a movement to a future point in time through a rotation in the fourth dimension, you could indeed transform a wire into a memory by simply carrying out such a rotation. So many things in modern computing would be simpler if we could do this easily.
On the other hand, on closer scrutiny, the idea of memories as sideways wires in time doesn’t really seem that useful. In practice, we must base computer memories on very different applications of physics than wires— simple dimensional rotations are just not in our current bag of manufacturing tricks. And if you look more closely at wires, while they do carry bits to another point in space, they also carry them to a future point in time, due to propagation delay. The fact that wires are not instantaneous, but have real delays, has become more and more significant as computing technology advanced; due to the infinitesimally sized components of current processors, they are a constant consideration for every designer. So the conceptual rotation in time of a wire, to translate it to a memory, would be something less than 90 degrees, as wires already are turned a bit in the time direction.
Another interesting thing about this concept of rotating in time is that, once you think about it, it’s not really a statement about modern computing technology, just about thinking of converting a transfer in space to one in time as a dimension. You can apply it in a lot of other cases. How about this one: “Podcasts are just radio shows turned sideways in time”. That kind of applies, right? But we don’t even need to constrain ourselves to modern high-tech. Couldn’t we just as easily say “Cassette tapes are concerts turned sideways in time?” Or “Government laws are king’s proclamations turned sideways in time?” In some sense, the evolution of modern life fits in here too— can’t we say that “Genes are biological mutations turned sideways in time”? Even the ancient Greeks could have gotten into the act, by saying “Papyrus scrolls are Plato’s lectures, turned sideways in time.” Sure, all of them do sound profound to some degree on first hearing, but are really just clever restatements of the idea of time as a dimension.
Another interesting aspect of this quotation is Hillis’s concern with “deep time”, the idea that he wants to somehow be able to communicate information about our current society long distances along the time dimension. Already we barely know what our predecessors 3000 or so years ago thought about and how they lived. We may seem to have generated a lot of information in our current civilization, but if there was some major disaster and we spent a few years without power to refresh our computer memories, hardly any of it would survive. Our mass-produced physical books are much less hardy, for the most part, than the ones created by ancient Greeks and Romans, so even written information would disintegrate very quickly. And what about 10,000 years from now? We know basically nothing about any human civilization that may have existed that long ago.
To address this problem, Hillis became involved in the Long Now Foundation, an organization that attempts to look at long-term problems facing humanity in the 10,000 year range. One of their key projects is to create the Clock of the Long Now, which you may recall me mentioning in an earlier podcast: it’s a clock that is built to last at least 10,000 years, by being put in a sheltered location and not requiring any external source of power. They are even trying to take human factors into account, for example by not allowing any expensive materials in the construction, so there will be no incentive for future thieves to destroy and loot it. And it is only allowed to use materials available during the Bronze Age, so it will still be repairable after a general societal collapse if needed. Though if society has collapsed to the point where Math Mutation podcasts are gone, will there really be a point to our race continuing to survive? In any case, Jeff Bezos seems to think so, since he has spent over 40 million dollars funding this clock’s construction.
And this has been your math mutation for today.