So in this paper (https://arxiv.org/pdf/1707.02389.pdf https://arxiv.org/pdf/1707.02389.pdf), (If I'm groking it correctly) Terrance Tao seems to embed a Turing

So in this paper (https://arxiv.org/pdf/1707.02389.pdf https://arxiv.org/pdf/1707.02389.pdf), (If I'm groking it correctly) Terrance Tao seems to embed a Turing Machine in a vector space. So is using a single vector not a real problem, or am I just not getting it?