So called higher capacities, like abstraction, are highly hyped. Look:
What happens when you apply the Church number 3 to a busy beaver? You get 3 busy beavers on the same tape.
Details will be added into the article Turing machines, chemlambda style.
If you want tot experiment, then click on “fork me on github” and copy the gh-pages branch of the repo. Then look in the dynamic folder for the script moving_random_metabo_bb.sh. In a terminal type “bash moving_random_metabo_bb.sh”, then type “church3bb.mol”. You shall get the file church3bb.html which you can see by using a js enabled browser.
The sh script calls an awk script, which produces the html file. The awk script is check_1_mov2_rand_metabo_bb.awk. Open it with a text editor and you shall see at the beginning all kinds of parameters which you can change (before calling the sh script), so that you may alter the duration, the speed, change between deterministic and random algorithms.
Finally, you also need a mol file to play. For this demo has been used the mol file church3bb.mol. You can also open it with a text editor and play with it.
UPDATE: Will tweak it more the next days, but the idea which I want to communicate is that TM can be seen as chemistry, like in chemlambda, and it can interact very well with the rest of the formalism. So you have these two pillars of computation on the same footing, together, despite the impression that they are somehow very different, one like hardware and the other like software.