🚀 go-pugleaf

In reply to Sean, message 23 

Sean, it�s disappointing that your message shows that you failed to grasp the substance of the proofs, and the tone of your reply indicates that your attitude was not conducive to clear thinking. 

As I showed in message 20, there are two proofs of the usefulness of multiple undo: one entails induction or iteration, while the other entails amalgamation. You attempted to criticize the inductive proof, so I�ll briefly discuss that proof here. 

The inductive proof is a proof by mathematical induction without the mathematical paraphernalia. You don�t need the mathematical paraphernalia to see why it is correct. 

I can restate the proof in even less technical terms as follows. Multiple undo consists in nothing more than the iteration of single undo. Consequently, if single undo is useful, of logical necessity each possible iteration of single undo is useful, thereby implying that multiple undo is useful. 

To make this more concrete. Suppose you execute single undo and the undo list hasn�t been exhausted. Under the assumption that single undo is useful, single undo is now useful. 

For additional perspective consider the following. We assume the usefulness of single undo, which means that if we execute a command X, we wish to have the possibility of undoing it. Now suppose we then execute and undo a command Y. We�re back where we were before, namely, in the position of wishing to have the possibility of undoing command X. 

Hopefully you can now see that the usefulness of multiple undo reduces to the usefulness of single undo. If you find that this is still not clear to you, then please talk to a friend who is mathematically conversant, and ask them to explain mathematical induction to you. I think that I�ve gone as far as is appropriate for this venue. 

Your analogy of multiple undo to multiple engines, brains, etc. is irrelevant and shows that you didn�t take the time to understand the inductive proof or, if you prefer, you didn�t bother to think clearly about the nature of multiple undo. Had you taken time to think clearly, you would have seen that undo is an instance of backtracking, so you would have devised an analogy that involves backtracking, such as the following. 

Suppose there�s a maze for a person to make their way through, and to make backtracking easier they can take rope that comes in links and is connected to the floor. They can use as many links they want, but once these links, connected together, are fully extended, the chain of links slips ahead to the next connection point on the floor, thereby moving one link further from the entrance. 

Now consider an argument that FM has tools that make multiple undo unnecessary. In the analogy, this is equivalent to an argument that the person in the maze has tools that make multiple backtrack links unnecessary. But if there are tools that make multiple backtrack links unnecessary, they should also render a single backtrack link unnecessary. This analogy could be fleshed out in greater detail, but I decline to do so because I�m not using the analogy to prove the usefulness of multiple undo, but only to show that an accurate analogy can be devised if one wishes to put their mind to it. 

Regarding the amalgamative proof, you said nothing about it. But the amalgamative proof proves the same conclusion as the inductive proof, so even if you were successful in showing that the inductive proof is incorrect, the amalgamative proof still remains. If you had taken the time to think through the amalgamative proof, you would have seen from yet another perspective how absurd the concept is that single undo is useful but multiple undo isn�t � or to put it differently, single undo is an important tool but multiple undo isn�t. 

In closing, may I offer some advice that I�ve found helpful? If possible, do not reply in the heat of emotion. If possible, do not reply to a controversial issue without allowing at least one night�s sleep to pass between framing the reply and refining it before presenting it. If possible, refine a reply over a period of days until, for several days, you find that you have only minor refinements to make. This indicates that the reply has stabilized over the short term. 

Refining a reply gives the writer an opportunity to weed out bad ideas so, hopefully, just good ideas remain. Refining a reply also gives the writer an opportunity to identify more good ideas, to hone good ideas, making them even better, and to hone clarity of expression. Accordingly, if we spend concerted effort refining a reply, we show respect for readers by conveying just our best ideas and by doing so in a manner that is easier for them to understand. The alternative is to affront readers with bad ideas and poorly expressed ideas, engendering ill feelings in the readers and creating a correspondingly poor reputation for our name.  

I think that if you follow the foregoing advice, Sean, you�ll find that your replies will be much more beneficial to the readers and, hence, much more appreciated. 

In reply to Sean, message 25 

As I showed in message 21, complexity is not an issue once single undo has been implemented. All that�s left is iterating the saving of undo state within the virtual memory space of the program. If you�re using a computer that�s 10 years old, this might be a problem, but it�s no problem for a recent computer. 

In reply to Joel Benson, message 26 

The probability of usefulness becomes zero only when the undo list is exhausted, a boundary condition that is cited in the proof. 

Regarding reverting to a saved file, normally I can�t remember the state of a saved file because I save many times at arbitrary points as I write, in order to guard against a crash. 

In reply to many messages 

From message 20, we can see that the usefulness of single undo implies the usefulness of multiple undo. This means that there is no point arguing about the usefulness of multiple undo as such. If controversy remains, what we should be doing is arguing about the usefulness of single undo. 

I repeat the closing statement of message 20, this time in italics for emphasis: 

Unless someone wishes to argue against the usefulness of single undo, we may assume that the usefulness of multiple undo is established.  

I hope that this restatement of the conclusion of the proofs will elicit the best arguments against the usefulness of single undo so that we can focus on the fundamental, underlying issue, namely, the usefulness of single undo. In this light, I wish to pose the question that we should address: 

Does FM have features that render single undo not useful? 

I don�t expect anyone to argue against the usefulness of single undo in FM, but it will be interesting to see if someone does since doing so is the logical implication of arguing against the usefulness of multiple undo. 

In conclusion, since no one has to-date argued against the usefulness of single undo in FM, it�s a reasonable expectation that no one will. Consequently, we can assume that the answer to the foregoing question is no. That is, until someone argues otherwise, we can assume that single undo is useful in FM, in which case, of logical necessity multiple undo is useful in FM.