Can random mutations cause an increase in information in the genome?

Are you saying that the general pattern of mutations is highly predictable but just random per individual occurence, as with rolling of dice, or something larger?

Actually, dice rolling is a guided process.

Actually, dice rolling is a guided process. Dice don't roll by themselves generally.

Definition of random process. A (one-dimensional) random process is a (scalar) function y(t), where t is usually time, for which the future evolution is not determined uniquely by any set of initial dataor at least by any set that is knowable to you and me. In other words, random process is just a fancy phrase that means unpredictable function. Throughout this chapter we shall insist for simplicity that our random processes y take on a continuum of values ranging over some interval, often but not always -8 to +8. The generalization to ys with discrete (e.g., integral) values is straightforward. Examples of random processes are: (i) the total energy E(t) in a cell of gas that is in contact with a heat bath; (ii) the temperature T(t) at the corner of Main Street and Center Street in Logan, Utah; (iii) the earth-longitude f(t) of a specific oxygen molecule in the earths atmosphere. One can also deal with random processes that are vector or tensor functions of time, but in this chapters brief introduction we shall refrain from doing so; the generalization to multidimensional random processes is straightforward. Ensembles of random processes. Since the precise time evolution of a random process is not predictable, if one wishes to make predictions one can do so only probablistically. The foundation for probablistic predictions is an ensemble of random processesi.e., a collection of a huge number of random processes each of which behaves in its own, unpredictable way. In the next section we will use the ergodic hypothesis to construct, from a single random process that interests us, a conceptual ensemble whose statistical properties carry information about the time evolution of the interesting process. However, until then we will assume that someone else has given us an ensemble; and we shall develop a probablistic characterization of it.

I think the significance in ToE of the claim of random mutations is to assert that it is an unguided process; that life is not designed, and that is indeed what some prominent evos have stated.But it's wrong. Just because there is a random factor, perhaps and maybe not, that doesn't mean that the overall process is unguided. Keep in mind I am not saying that I think mutations can even create macroevolution, but just getting into the claim of random mutations in general.

Of course, I have problems with evolutionary models as I don't think they match the facts.

Still, as far as us mortals go, it is not possible to predict what mutation will happen next.

If random is based on our mere lack of knowledge, then it is not inherently random, but random more describes our perspective than an absolute quality.

Are you sure? I would think that we could under certain conditions predict with a high degree of accuracy the mutations that will occur in certain situations, and with more knowledge, we should be able to predict with even more accuracy.But let's say we have complete knowledge of how genes work, the exact conditions, etc,...are you saying even then we could not predict the mutations would occur under certain sequences under certain conditions?

In terms of mutations, the entire process is clearly not so random as evos have suggested, and in fact, may not even be random at all since we really have no way to know, as far as science, what the Intelligent Cause of the universe planned and knew about evolution, except that it is logical to consider that an Intelligence that advanced could predict what would occur with considerable accuracy, and perhaps even governs what occurs moment to moment.

To illustrate this idea. Think of a card counter in Vegas. He can beat the house if not caught because the cards are predicatable even if random per hand. There is a control that governs what is likely to occur. So he uses a "random process" to get a particular result because the entire process is not random at all, but very predictable.