Maybe very very short (single-gene) sequences. The thing with DNA is it's the product of evolution. The DNA guides the synthesis of proteins, then the proteins fold into a 3D shape, and they interact with chemicals in their environment based on their shape.
In the context of a living being, different genes interact with each other as well. For example, you have certain cells that secrete hormones (many genes needed to do that), then you have genes that encode for hormone receptors, and those receptors trigger other actions encoded by other genes. There's probably too much complexity to ask an AI system to synthesize the entire genetic code for a living being. That would be kind of like if I asked you to draw the exact blueprints for a fighter get, and write all the code, and synthesize all the hardware all at once, and you only get one shot. You would likely fail to predict some of the interactions and the resulting system wouldn't work. You could only achieve this through an iterative process that would involve years of extensive testing.
Could you use a deep learning system to synthesize genetic code? Maybe just single genes that do fairly basic things, and you would need a massive dataset. Hard to say what that would look like. Is it really enough to textually describe what a gene does?
This is all true, but it doesn't preclude the possibility of generating DNA. Human share a lot of DNA sequences with other animals, and the genetic differences between individual humans are even smaller. You might have trouble generating a human with horns or something, but a taller one is probably mostly an engineering problem.
What GPT-3 and DALL-E shows is that you can infer a lot based on the latent structure of data, even without understanding the underlying physical process.
Deep learning is probably not the right tool to generate a taller human. We've mapped the human genome. You could probably create a statistical model that pretty accurately maps different versions of genes to height. Then it would mostly be a question of swapping different versions of genes to get the result you want. With a statistical model, you would need a relatively small dataset (hundreds, or thousands of human genomes), and you wouldn't have to worry about errors being introduced.
In the context of a living being, different genes interact with each other as well. For example, you have certain cells that secrete hormones (many genes needed to do that), then you have genes that encode for hormone receptors, and those receptors trigger other actions encoded by other genes. There's probably too much complexity to ask an AI system to synthesize the entire genetic code for a living being. That would be kind of like if I asked you to draw the exact blueprints for a fighter get, and write all the code, and synthesize all the hardware all at once, and you only get one shot. You would likely fail to predict some of the interactions and the resulting system wouldn't work. You could only achieve this through an iterative process that would involve years of extensive testing.
Could you use a deep learning system to synthesize genetic code? Maybe just single genes that do fairly basic things, and you would need a massive dataset. Hard to say what that would look like. Is it really enough to textually describe what a gene does?