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<h2 class="hd hd-2 unit-title">Map of Lecture 5</h2>
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<p>In this and the next lecture, we continue with Minds and Computers, but move to a different sub-topic: Turing Machines and the Turing test. Turing Machines are a simple form of computer. The Turing test figures in a proposal concerning whether a particular individual (e.g. a person, a computer) can think. Roughly (refinements will come later): if an individual can pass the Turing test, then the individual can think. If the proposal is correct, then a computer could think, at least in principle.</p>
<p>Reading: Turing’s 1950 paper, “<a href="/assets/courseware/v1/0c0db957c39184b538869f8d9e9a3b56/asset-v1:MITx+24.09x+3T2019+type@asset+block/5_turing_computing_machinery_and_intelligence.pdf" target="_blank">Computing Machinery and Intelligence</a>”. It's mostly about the Turing test, but he does also talk about “digital computers”, of which Turing machines are a simple example.</p>
<p>First, Turing Machines. That will take up most of this lecture. At the end we’ll start our discussion of the Turing test by having one in class.</p>
<ul>
<ul>
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<li><span style="line-height: 1.6;"><a href="/courses/course-v1:MITx+24.09x+3T2019/jump_to_id/b16b52f12ae640de81f2e8f5bea55f25" target="_blank">Turing on Multiple Realizability</a>: In which, before the main topic is introduced, I highlight a point Turing makes that we’ve already </span>seen in Searle.</li>
<li>Turing Machines: </li>
<ul>
<ul>
<ul>
<li><a href="/courses/course-v1:MITx+24.09x+3T2019/jump_to_id/a0a07b652580426f903b3b392321052d" target="_blank">Introducing Turing Machines</a>: So what are they?</li>
<li><a href="/courses/course-v1:MITx+24.09x+3T2019/jump_to_id/7802129c6eaa485684f26b19c37fef17" target="_blank">Computing a Function</a>: Turing Machines are things which can “compute functions”. Let me tell you what that means.</li>
<li><a href="/courses/course-v1:MITx+24.09x+3T2019/jump_to_id/c13c11bef6d14883bb0f92fdee08f3f7" target="_blank">Computability</a>: In which I tell you a surprising fact (at least, it is widely-regarded as such): if a function is computable at all, it’s computable by a Turing Machine.</li>
<li><a href="/courses/course-v1:MITx+24.09x+3T2019/jump_to_id/9a16cd46a3824829a0fc7d6c675fd85f" target="_blank">Aside: Some Interesting Facts About Turing Machines</a>: a digression, but Turing Machines are remarkable things.</li>
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</ul>
<li>Searle in Turing Machine Terms: To see the connection between Turing Machines and our previous discussion of Searle, we restate Searle’s points in terms of Turing Machines.</li>
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<ul>
<ul>
<li><a href="/courses/course-v1:MITx+24.09x+3T2019/jump_to_id/1f94348be1294e56ba461f2107b18a96" target="_blank">The Chinese Room, in the Key of Turing Machines</a>: Strong AI<em><strong> </strong></em>restated in terms of Turing Machines, and the Chinese Room argument given again in those terms.</li>
<li><a href="/courses/course-v1:MITx+24.09x+3T2019/jump_to_id/ae28d8780fee4818a9e19a59e192f4c4" target="_blank">Turing Machines and Axiom 3</a>: In which some observations about Turing Machines are found to support Searle’s Axiom 3.</li>
</ul>
</ul>
</ul>
<li><a href="/courses/course-v1:MITx+24.09x+3T2019/jump_to_id/e015ed7dcad943e2bd885b8013199746" target="_blank">A Turing test</a>: Enough talk: let’s do it!</li>
</ul>
</ul>
</ul>
<p></p>
<p>You can download the Lecture 5 slides <a href="/assets/courseware/v1/6c7048300085fdb2376959c1ac97fae2/asset-v1:MITx+24.09x+3T2019+type@asset+block/24.09x_Lecture_5_Slides.pdf" target="_blank">here</a>.</p>
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<h2 class="hd hd-2 unit-title">Turing on Multiple Realizability</h2>
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<h1>Turing on Multiple Realizability</h1>
<p></p>
<p>Before getting to the main subject, we’ll start by noting something interesting from the reading: Turing made essentially the same point as Searle concerning <em>multiple realizability</em>. That point is vital for what follows. By the end of this part of the lecture, you should understand Turing’s way of putting the point.</p>
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Problem: beer cans, string and a windmill
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<p>Searle&#8217;s point when he says that a computer could be built out of beer cans, string and a windmill is that</p>
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<h2 class="hd hd-2 unit-title">Turing Machines: Introducing Turing Machines</h2>
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<h1>Turing Machines</h1>
<p>One of the things for which Alan Turing is famous is the <em>Turing Machine</em>. A Turing Machine can either be thought of as an abstract mathematical blueprint of a computer, or else some physical device built according to that blueprint. Computers like the one you are looking at now are not (physical) Turing Machines but, in a sense we will make precise, are no more powerful than Turing Machines.</p>
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<h3 class="hd hd-2">Video: Introducing Turing Machines</h3>
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<p> Consider the Turing Machine characterized by these quadruples: &lt;S1,1,R,S1&gt;, &lt;S1,0,1,S1&gt;, &lt;S2,1,H,S2&gt;, &lt;S2,0,H,S2&gt;. When the corresponding Turing Machine is in state 2 and scans a &#8220;0&#8221;, it </p>
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<p>If the above Turing Machine is started in S1 on the leftmost &#8220;1&#8221; of a block of five &#8220;1&#8221;s, it will:</p>
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<h2 class="hd hd-2 unit-title">Turing Machines: Computing a Function</h2>
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Problem: function
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<p>Consider the Turing Machine characterized by the quadruples: &lt;S1,1,R,S1&gt;, &lt;S1,0,L,S2&gt;, &lt;S2,0,H,S2&gt;, &lt;S2,1,0,S2&gt;. Assuming the definition of &#8220;computing a function&#8221; given in the segment, what function on the natural numbers does it compute? </p>
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<h2 class="hd hd-2 unit-title">Turing Machines: Computability</h2>
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<p>So, for any fancy computing machine anyone has yet thought of, if a function is fancy-computable, it<span style="line-height: 25.6000003814697px;">’s Turing-computable. That motivates the thesis that if a function is computable <em>at all</em>, it’s Turing-computable. That’s one way of putting the <em>Church-Turing Thesis…</em></span></p>
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<legend id="2c8e88faeae24b089a1b2452e904dd6d_2_1-legend" class="response-fieldset-legend field-group-hd">In what sense are Turing Machines the most powerful computers there are?</legend>
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<h2 class="hd hd-2 unit-title">Turing Machines: Aside</h2>
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Problem: halting
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<h2 class="hd hd-2 unit-title">Searle in Turing Machine Terms: The Chinese Room, In the Key of Turing Machines</h2>
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<h1>Searle in Turing Machine Terms</h1>
<p>To see the connection between what we’ve already discussed and this Turing Machine stuff, we can put Searle’s arguments against Strong AI in terms of Turing Machines. We’ll do that in this part of the lecture; by the end, the connection should be clear.</p>
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Problem: mathematical ignoramus
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<legend id="52d52759f9f345c4b8329e276b44eb31_2_1-legend" class="response-fieldset-legend field-group-hd">Even a mathematical ignoramus could act as the scanning head of a Turing Machine. Does this conclusively show that Turing Machines don&#8217;t have mathematical beliefs?</legend>
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<h2 class="hd hd-2 unit-title">Searle in Turing Machine Terms: Turing Machines and Axiom 3</h2>
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Problem: observations about Turing Machines
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<legend id="95a5ed4526184dc1b9edf927eae7baf0_2_1-legend" class="response-fieldset-legend field-group-hd">Searle&#8217;s Axiom 3 states that syntax by itself is not sufficient for semantics. It is best supported by which of the following observations about Turing Machines?</legend>
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<h2 class="hd hd-2 unit-title">A Turing Test</h2>
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<h1>A Turing Test</h1>
<p>Now that we know something about Turing Machines, we can talk about the Turing test. We will do that properly in the next lecture; in the meantime, by way of introduction to the Turing test, let’s just do one.</p>
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<p>We’ve only just scratched the surface of Turing machines. If you want to delve deeper, a good place to start is my colleague Agustín Rayo’s MITx course, <a href="https://www.edx.org/course/paradox-infinity-mitx-24-118x">Paradox and Infinity</a>.</p>
<p>Next time, we’ll discuss the Turing test in more detail. Please read part I of Ned Block’s “<a href="/assets/courseware/v1/527c84abeb46068a76933e5aeb688070/asset-v1:MITx+24.09x+3T2019+type@asset+block/4_block_mind_as_software_of_brain.pdf" target="_blank">The Mind as the Software of the Brain</a>”. S<span style="font-size: 1em;">ee you there!</span></p>
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