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The Limits of the Singularity

Will there be a never-ending intelligence explosion? or not?

The Universe's Limits. Material Limits, Architectural Limits and Design Space.

What are many futurologists missing or omitting from their views? Have some of them actually thought about the hindering factors?

Singularity, AI, Essay, Design Space

May 14th, 2015



Things are limited by the qualities of its parts. No good knife can be made out of bad steel, and certainly no boat either (i.e. the Titanic).

Things exist within the many limits of our Universe. These limits determine when something changes and under which exact mathematical conditions. Bones break, metals bend or melt, liquids change phase. Everything has limits, and everything changes.

Even the design of the Universe has caps, the speed of light has a boundary, and so do space and time at Planck scale. Science has allowed us to define a specific amount of time since the Big Bang, not infinite; specific, and measureable.

Just as biological minds are physically limited by the speed of its chemical processes, mechanical minds are physically limited by the possibilities of its constituents.


Brains are the things behind intelligence and, while complex, their workings are not magical. They have parts, and these parts have limits. There's a limit to the speed of neurotransmitters, there's caps to their working conditions whether they are temperature, acidity or else.

In the same way a building is limited by the strength of concrete, so is the architecture of a brain limited by the characteristics of its parts. There are design trade-offs everywhere. Nerve tissue can only grow so long, or transmit so fast. A building can only be so tall before it collapses, the transport of materials to its highest levels must have drawbacks and unique engineering challenges which must be solved in an economically optimal fashion.


It is undeniable that power laws exist throughout nature. One particular example is that of allometric scaling laws in living creatures. These laws pair different sets of variables and how they scale relevant to each other, the pairing is mostly done against body mass. Knowing body mass, one can reliably predict how much energy a creature consumes, its metabolic rate, speed, wingspan and more.

These power laws seem to exist, mainly because of limits and the resulting architectures that build on those boundaries, bringing forth solutions to the problems that nature faces when building its living beings.

Similarly, there should be power laws related to the architecture of intelligence; and artificial brains should be no exception to the rule.


Let's carry on to biology. The length of a muscle depends on its underlying bone structure, which gives it the support it needs. Bones themselves depend on their mineral constituents and their architecture for strength. These constituents' values were written arbitrarily in math by the Universe (I'm a Pantheist). Those mathematical values determine at which values they transform, and how. Their arrangements and combinations bring forth more possibilities, and that is the realm of architecture: Organization.

Muscles are mostly levers. Levers are math, and they are constrained by Archimedes "Law of the Lever".

M1 * A = M2 * B

In all its beautiful simplicity this equation relates strength, speed and range of motion. You can't have all three.

A lever with a small amount of B (the distance to M2 from the fulcrum) acquires speed, since its load will travel more, also gaining range. But it will lose strength, as M2 will have to be larger to compensate.

Viceversa, the same lever grappled from M1 has much more strength, since A is larger; but lacks range and speed, since B is short.

If the equations behind the simple physics of these constructs have trade-offs by themselves. It is not admissible to think that up in the chain these limits will disappear.

Muscles inherit all the limitations of physical levers and their mathematical principles, and then those of the resistance of their materials and the intrinsic architecture of those materials.

The fact that all possible levers share the "Law of the Lever" is the architectural limit of every lever... ever. (Sorry, I had to make that pun)


There is however, one big caveat about the "bones" of artificial intelligence: they keep getting better, exponentially.

AI depends on computing, and computing speed depends on computer hardware, whose transistor count has been observed to be doubling every two years.

If bone and muscle strength improved at the rate of Moore's "law", we would all be superheroes by now; and our anatomies and sizes would be much different.

Take for instance big mammals, whose legs need to be much stouter to hold their weights, the materials remain the same but their arquitecture is different. This characteristic is not only a consequence of weight, but also of the limits of bone; if those legs' arquitecture were any thinner they would break by weight alone. Stronger bone moves the kilograms per leg-bone cross-section surface area needed to a new value.

The material limits of AI are currently being pushed at the rate of Moore's "law", this is not sustainable. No exponential growth is sustainable in nature.

Sooner or later the material limit of computing hardware will be reached, and then, the architectural limit of computing performance will have to be found through painful design.


I have come to believe that what we understand as human intelligence is mostly an architectural issue. The variations of the qualities or structure of the proteins that live in living creatures' brains are not as marked as we would be led to estimate. Neurons, and their sub-types, are mostly the same in all living creatures.

Back to the computer comparison, this would be the same to say that every computer on earth is stuck with the same microprocessor model; one that is individually un-improvable. All you Intel fans, enjoy the Core i9000, or for AMD folks the FX 1/X X->0.

Then every "brain computer" would only vary in the depth, configuration and arrangements of these microprocessors. Making an "intelligence" rely not only on a single microprocessor, but rather a network of them.

It is then that the architecture of this network defines what that intelligence can do or cannot.

Take for instance a "modern" regular desktop computer. We have two big specializations here, two big different architectural layouts. We have Graphics Processing Units (GPUs) and Central Processing Units (CPUs), both of which are roughly analogous to the right, and left sides of the human brain respectively. GPUs are highly parallel and specialized, CPUs are serial and much more general purpose.

The material limits of both are just the same, it is their different architectural configuration that gives them their specialized properties.

While material limits are deeply rooted in the mathematical layout of the Universe, architectural limits are exclusively abstract and absolutely defined by design space. In a theological sense, every limit in the Universe is an architectural limit.


There's so much that nature has already explored of design space in building the human brain, but she's really hampered in that has really big material drawbacks in the sense of brains being built on neurons and all the systems required for them to live.

An artificial brain, living in the abstract "bit-space" of a computer's innards has no need for glia and other structures. It needs to pump no nutrients to those cells. Therefore, the design space of an artificial brain is so much more unbounded than that of organic brains.

If nature were as unbounded as computers, a brain of a hundred cubic kilometers in size could be a reality. What would such a gargantuan machine be capable of?

Not only that, the speed of those digital neurons would only be limited to how fast those microprocessors can update the value in software. Which is legions faster than a nerve cell can.

This is why Artificial Intelligence has the potential of being almost Alien-like to us. We don't know where in design space will it fall, or how is that design space shaped. We don't know and we can't possibly fathom where it will go once it has the potential of rebuilding itself.


All we know is that the Universe has built-in mathematical boundaries and that these boundaries are insurmountable. Given this train of thought it is very likely that Intelligence, in itself, has a material and architectural upper-bound.

The Singularity is a jump towards a plateau.