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The weight of bits

According to a researchers’ publication the growing production of bits will have a physical impact on the planet, as more and more of the planet mass is “converted” into bits. The graphic represents, in a logarithmic scale, the number of years it will take for a growth of 50%, 20%, 5% and 1% a year for bits to reach a mass equivalent to the one of the Earth. Image credit: Melvin Vopson

Just three weeks ago an article was published on Phys.org reporting on a study by Melvin Vopson, Senior Lecturer in the School of Mathematics and Physics at the University of Portsmouth, and his reflection on the nature of bits, considering the mass energy equivalence (Einstein), the application of thermodynamics to information by Rolf Landauer, and the information theory of Claude Shannon. The reflections are interesting but the interpretations provided by the many articles that picked up on them are quite distorted, to say the least (starting with attributing the mass-energy equivalence to Einstein General Relativity whilst it is part of the special relativity – E=mc²).

I was surprised to receive a number of calls from friends telling me that bits have mass and that their growth is going to create an “increase” in the planet mass, to the point of doubling it in 200 years! Others were saying that the mass of our planet will be “converted” into bits in 200 years!

What surprised me was how news get distorted. At the same time, the research of Melvin opens up some “old” philosophical questions that are still fascinating today and that, in some way, can relate to the old dualism of soul versus matter, thoughts vs brains.

First of all. Bits are figment of our imagination, they are immaterial, massless. At the same time, when we want to have bits and operate on bits we need “stuff”. We need stuff to store them and stuff to manipulate them. A first interesting point is the prediction that at a growing rate of 50% a year we are going to have a number of bits that is equivalent to the number of atoms in about 150 years. Let’s start debunking this. Although mathematically speaking one could calculate the exponential progression and assuming a rough knowledge of the number of bits we have today (you won’t be able to find a single accepted estimate, but one can pick up one as good, just for the sake of discussion, like the production of 1 sextillion bits in 2020 – 1 sextillion  = 1,000,000,000,000,000,000,000) and growing at a 50% rate per year we can indeed state that in 150 years we could have as many bits as atoms in the Earth (133,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000). The problem here is two fold:

  • in any finite system, doesn’t matter how bit it is, any exponential growth can only go that far and than start to decrease and eventually stop;
  • the assumption that we need one atoms to store one bit is not (physically speaking) true. To get a sense of the physical limitations read the old, but still very interesting paper “Ultimate physical limits to computation” by Seth Lloyd.

Independently of the kind of support we are using, it will still be something that we have on the Planet so storing more information, and processing it, will not increase the planet “mass”. It is like saying that producing more cars does not increase the mass of the planet because. obviously, we are using material from the planet to build the cars. However, when producing cars we can attribute a weight to the cars produced and this weight plus the weight of what is left on the planet (quite a bit!) correspond to the total weight of the planet. In the case of information, bits, it gets trickier. Suppose that you store the bits on a magnetic disk. Storing a 1 or a 0 means polarising the magnetic particles in one or the opposite direction. The energy associated to the magnetic direction is the same so a magnetic disc full with 1s weighs the same as the same one full with 0s. Not so if we are using capacitors to store bits. In this case storing one value requires more electrons than storing the other value and this difference result in a different “weight”, for other medium this may require a different energy level and following the mass-energy equivalence it implies a different mass/weight. A 4 GB capacitive memory may increase its weight by a billionth of a billionth of a gram (0.000000000000000001g). By comparison, charging a Kindle (that has 4GB of storage capacity) increases its weight by 100 million times more (watch the clip).

Melvin is looking at the energy involved in the storage and manipulation of bits and estimates  in 100 billion billion the number of bits existing today translating the associated (estimated) energy (processing and storage) in mass and obtaining a value that compares to the mass of a single bacteria. That seems, and it is, insignificant. However, thanks to the power of exponentials, assuming the growth of bits remains the same, the amount of energy that will be required by 2245 will translate into 50% of the Earth mass. As I stated in the beginning these assumptions of constant (accelerated) growth and the use of the same technology for processing and storage over the next 250 years are not realistic.

There may be some very very futuristics scenarios where humankind will continue to create information at an accelerated rate supporting this with a capability to harvest more energy from the Sun. Currently Earthlings grab some 50% of the Sun’s energy hitting the planet. There is the theoretical possibility of harvesting at least part of the other 50% and that could be used in the future to power the information expansion and would indeed increase the “mass” of the planet over time.

The shift from bit to information involves semantic processing, done in our brains for millennia and now seeing the first tiny steps of artificial intelligence. This requires energy (our brain is a major user of our body metabolism) but it is a gray area as soon as we start discussing the weight of thoughts. We know that thinking requires less energy than walking, thinking smart thoughts looks like no more energy intensive than having foolish thoughts. Actually, smart behaviour, that one that gets encoded with experience, has been shown to require less energy than indecisive behaviour …

As for the weight of bits, the weight of thinking and souls remain a grey area better discussed by philosophers…

About Roberto Saracco

Roberto Saracco fell in love with technology and its implications long time ago. His background is in math and computer science. Until April 2017 he led the EIT Digital Italian Node and then was head of the Industrial Doctoral School of EIT Digital up to September 2018. Previously, up to December 2011 he was the Director of the Telecom Italia Future Centre in Venice, looking at the interplay of technology evolution, economics and society. At the turn of the century he led a World Bank-Infodev project to stimulate entrepreneurship in Latin America. He is a senior member of IEEE where he leads the Industry Advisory Board within the Future Directions Committee and co-chairs the Digital Reality Initiative. He teaches a Master course on Technology Forecasting and Market impact at the University of Trento. He has published over 100 papers in journals and magazines and 14 books.