<div dir="auto"><div dir="auto"><br></div><div dir="auto">Lee, Surely someone has developed probabilistic Turing Machines which can, very rarely, make errors. I am ignorant of the field since 1972 when I took a course which used Hopcroft and Ullman as a text.</div><div dir="auto"><br></div><div dir="auto">Nick, I agree that your questions are charming. Your humanity is clearly seen. By the way, it occurred to me this morning that the motto of behaviorists should be, "If it talks like a duck\U0001f986...etc"</div><div dir="auto"><br></div><div dir="auto">Frank<br><br><div data-smartmail="gmail_signature" dir="auto">-----------------------------------<br>Frank Wimberly<br><br>My memoir:<br><a href="https://www.amazon.com/author/frankwimberly">https://www.amazon.com/author/frankwimberly</a><br><br>My scientific publications:<br><a href="https://www.researchgate.net/profile/Frank_Wimberly2">https://www.researchgate.net/profile/Frank_Wimberly2</a><br><br>Phone (505) 670-9918</div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Apr 27, 2019, 10:59 AM Russ Abbott <<a href="mailto:russ.abbott@gmail.com">russ.abbott@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;font-size:small;color:#000000">Nick,</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;font-size:small;color:#000000"><br></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;font-size:small;color:#000000">One of the most attractive things about your posts is how charming they are. They are so well written! Thank you for keeping the discussion at such a civilized and enjoyable level -- even when I don't agree with you.</div><div><div dir="ltr" class="m_5740626307822649245gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><font><u style="color:rgb(33,33,33);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16.5px;line-height:20px"><br></u></font></div><div dir="ltr"><font><u style="color:rgb(33,33,33);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16.5px;line-height:20px"> </u></font><span style="color:rgb(33,33,33);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16.5px;line-height:24.75px"> </span>-- Russ Abbott <br>Professor, Computer Science<br>California State University, Los Angeles<br></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Apr 27, 2019 at 9:44 AM <<a href="mailto:lrudolph@meganet.net" target="_blank" rel="noreferrer">lrudolph@meganet.net</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Frank writes:<br>
> I would hate to have to demonstrate that a modern computer is an instance<br>
> of a Turing Machine. Among other things they usually have multiple<br>
> processors as well as memory hierarchies. But I suppose it could be done,<br>
> theoretically.<br>
<br>
First a passage from a chapter I contributed to a book edited by a<br>
graduate student Nick knows (Zack Beckstead); I have cut out a bit in the<br>
middle which aims at a different point not under consideration here.<br>
===begin===<br>
If talk of \u201cmachines\u201d in the context of the human sciences seems out of<br>
place, note that Turing (1936) actually introduces his \u201cautomatic machine\u201d<br>
as a formalization (thoroughly mathematical, though described in<br>
suggestive mechanistic terms like \u201ctape\u201d and \u201cscanning\u201d) of \u201can idealized<br>
*human* calculating agent\u201d (Soare, 1996, p. 291; italics in the original),<br>
called by Turing a \u201ccomputer\u201d. [...] As Turing remarks, \u201cIt is always<br>
possible for the computer to break off from his work, to go away and<br>
forget all about it, and later to come back and go on with it\u201d (1936, p.<br>
253). It seems to me that then it must also be \u201calways possible for the<br>
computer to break off\u201d and never \u201ccome back\u201d (in fact, this often happens<br>
in the lives, and invariably upon the deaths, of non-idealized human<br>
calculating agents).<br>
===end===<br>
Of course Turing's idealization of "an idealized *human* calculating<br>
agent" also idealizes away the fact that human computers sometimes make<br>
errors. A Turing machine doesn't make errors. But both the processors and<br>
the memory of a modern computer can, and *must* make errors (however<br>
rarely, and however good the error-detection). To at least that extent,<br>
then, they are not *perfect* instantiations of Turing machines. On the<br>
other hand, that very fact about them makes them (in some sense) *more*<br>
like (actual) human calculating agents.<br>
<br>
So, Nick, why are you asking what Turing machines think, instead of what<br>
modern computers think? (Be careful how you answer that...)<br>
<br>
<br>
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