Assembly Theory in Chemistry

In chemistry, molecular AT Historical Evolution (HE) treats bonds as the elementary operations that creates molecules.

The shortest path for a molecule is found by:

1. breaking its bonds
2. ordering its motifs in order of size

Given a motif generated on the path, the motif remains available for reuse.

The recursivity allows identifying the shortest construction path with parts already built on that path. This lets us quantify the minimum number of constraints, or memory size, to construct the molecule.

The HE index can be estimated from any complex discrete living thing with well-defined building blocks, which can be broken apart.

At every step, the size of the living thing increases by at least one.

The number of total possible steps, although potentially large, is always finite for any finite living thing. Thus, the HE index is computable in finite time.

For molecules, the HE index can be determined experimentally.

A hallmark feature of life is how complex living thing are generated by selection wich many functional results.

For example, a DNA molecule holds genetic information reliably and can be copied easily.

By contrast, a random string of letters requires much information to describe it. But is not normally very complex nor useful.

Thus, science has no measure that quantifies the complexity of functionality to distinguish these 2 cases.

We overcome this inherent problem by pointing out another feature of the evolutionary process. Natural selection:

• takes many steps to create complex and functional living things.
• allows many identical copies of these living things.

Therefore, an evolutionary process produces many identical, or near-identical, multistep living things.

The HE index on its own cannot detect selection. But copy number, combined with the assembly index, can.

This is our new way to measure complexity in terms of the hierarchy of causation stemming from selection at different levels.

We do not typically know the full assembly trajectory of a living thing.

So AT finds the minimal number of steps to produce the living thing.

We assume that every sub-livingthing, once available, can be used as often as needed to generate the living thing.

Our HE measures both:

• uses realistic dynamics for molecules, using bonds as building blocks,
• is computable for any molecule.

The main work for detecting evolution and memory is done here by combining the HE index and copy number of the living things.

AT aims to develop a new understanding of the evolution of complex matter that naturally accounts for selection and history in terms of what operations are physically possible in constructing an object.

For molecules, the HE index:

• has a clear physical interpretation
• has been validated as quantifying evidence of selection in detecting living molecular signatures.

However, it can be applied to polymers, cell morphology, graphs, images, computer programs, human languages and memes, etc.

The challenge in such cases will be to construct an HE that has a clear physical meaning in terms of what operations can be caused to occur to make the evolved non-living thing*.

AT has 2 important features of the context the living thing is found in.

1. There must be living things in its environment that can constrain the steps to assemble the living thing
2. These living things themselves have been selected because they must be retained over subsequent steps to physically instantiate the memory needed to build the target object.

Examples are enzyme catalysts in biochemistry.

• These permit the formation of many very unlikely molecules. This is because the enzymes themselves are also selected to exist with many copies.

We believe that the traditional notion of biological ‘individual’ and living things that are produced from natural selection is the same.

Thus, our approach naturally accounts for well-known phenomena, such as niche construction, whereby organisms and environment are co-constructed and co-selected.

Copy number is important because a single example of a highly complex molecule (with a very high HE index) could potentially be generated in a series of random events that become increasingly less likely with increasing HE index.

If we consider a forward-building assembly process without a specific evolutionary goal in mind, the number of possible living things that could be built at each recursive step grows super-exponentially in the absence of any constraints.

The likelihood of finding and measuring more than one copy of a living thing therefore decreases super-exponentially with increasing HE index in the absence of selection for a specified evolutionary goal.

Living things with high HE index, found in abundance, is evidence of natural selection because of the combinatorially growing space of possible living things at each recursive HE step (Fig. 2).

Finding more than one identical copy indicates the presence of a non-random process generating the living thing.

HE quantifies 2 competing effects:

1. The difficulty of discovering new objects
2. Once discovered, some objects become easier to make

This shows how selection was required to discover and make them.

The exponential growth of evolution with depth in HE, as quantified by the HE index, is derived by considering a linearly expanding evolutionary pool that has living things that combine at step whereby a living thing at the HE index combines with another living thing from the evolutionary pool.

Discovering new living things at increasing depth in a historical evolution gets increasingly harder with depth because the space of possibilities expands exponentially.

Once the pathway for a new living thing has been discovered, the production of a living thing (copy number greater than 1) gets easier as the copy number increases. This is because a high copy number implies that an object can be produced readily in a given context.

Thus, the hardest innovation is making a living thing for the first time. This is equivalent to its discovery*, followed by making the first copy [offspring] of that living thing.

*Superphysics Note: Duh. Thanks Captain Obvious. (Facepalm)

But once a living thing exists in great abundance, it must already be relatively easy to make.

Hence, evolution scales linearly with copy number for more than one object for a fixed cost per object once a process has been discovered.

The increase in evolution comes from increasing copy numbers and increasing HE indices.

If high values of evolution can be shown to capture cases in which selection has occurred, it implies that finding many high HE-index-living-things is a signature of selection.

In AT, the information required at each step to construct the object is ‘stored’ within the object (Fig. 2).

Each time 2 objects are combined from an evolutionary pool, the specificity of the combination process constitutes selection.

Randomly combining objects within the evolutionary pool at each step is not natural selection. This is because no combinations exist in memory to be used again for building the same object.

If, instead, certain combinations are preferentially used, it means that a mechanism* exists that selects:

• the specific evolutionary operations and
• the specific target living things to be generated.

*Superphysics Note: This mechanism is either consciousness or desire, depending on viewpoint. Assembly Theory is a philosophical theory.

Growth dynamics allows parameterizing selection in an empirically observable way by parameterizing reuses of specific sets of operations.