Humans have 46 chromasomes and roosters have 78. Why the disparity? Are roosters smarter than us? Are there dormant genes on rooster chromasomes?

You are confusing numbers of chromosomes with total number of coding genes in an organism which are not the same thing at all. Think of the genome as a book - you can have 40 longer chapters or 80 smaller ones - the content is very similar if not the same.

The number of chromosomes is NOT related to numbers of genes nor how "smart" an animal is (however one defines that). Similarly the total size of the genome is not related to the number of genes.

I concur - the number of chromosomes has nothing to do with the number of genes, and while the greater number of genes generally corresponds to greater complexity (for example, humans have more genes than yeast), this does not have anything to do with being smart. We have a lot of genes that are responsible for our highly developed brains and our intelligence; but another organism - say, a bee - has other genes that allow it to develop wings, and to digest sugary food to make honey.

What is surprising, is that the increase in genome size from less to more evolved organisms, is much greater than the increase in the numbers of genes. This is because in advanced organisms (such as humans and roosters), most of the genome is not coding; that is, it does not contain genes with information to make proteins. Instead, these regions may perform regulatory functions - they control when a gene is active and when it is repressed. We believe that this increase in the flexibility of regulation of gene activation was very important for evolution.

Even more interestingly, we have not yet been able to find a function for a very large fraction of the genome. This is a very complex topic, and you can read more about it here:

As for dormant genes, this is a very interesting point to bring up. While they have little to do with genome size, such genes do really exist. This is crucial to avoid the making of unnecessary, or even harmful proteins - for example, you would not want the cells in your skin to make haemoglobin (the dye that red blood cells use to carry oxygen). So, in skin cells, the genes used to make haemoglobin are silenced ('dormant').