If you don&#x27;t understand what I&#x27;m saying -- and that could be entirely my fault -- you can just ask. If you (mistakenly) assume that by 2 + 2 I mean the <i>expression</i> &quot;2 + 2&quot; rather than the <i>computation</i> 2 + 2, why not assume that you may have missed something (which is the actual case) rather than assume that I don&#x27;t understand the basics (which is not)?<p>Since I don&#x27;t wish to discuss this topic further with rude people, but I do wish to explain my point to other readers, I&#x27;ll note that the entire concept of computational complexity, which is probably the most important concept in all of computer science (and is at the very core of computation itself -- there can be no computation without computational complexity), is predicated on the axiom that in computation 2+2 does not <i>equal</i> 4 (in the sense that they are &quot;the same&quot;), but is <i>computed</i> to be 4. If 2+2 were actually 4, there would be no computational complexity (and so no computation).<p>As a matter of fact, an entire model, or definition of computation (another is the Turing Machine) called lambda calculus is entirely based on the concept that substitution is not equality in the theory of computation, by defining computation to be <i>the process of substitution</i> (which is what  lambda calculus calls <i>reductions</i>). If 4 and 2+2 were the same (as they are in classical math), there would be no process, and the lambda calculus would not have been a model of computation but simply a bunch of trivial (classical) mathematical formulas.<p>Indeed, some people confuse the LC <i>notation</i> with classical mathematical notation (which it resembles), and mistakenly believe that 2+2 equals 4 in LC in the same sense that it does in math (I assume because the same reductions preserve equality in math). This is wrong (in LC reductions do not preserve &quot;sameness&quot; but induce -- or rather, are -- computation). To their defense, LC does make this fundamental distinction easy to miss in hiding 100% of what it is meant to define -- namely, computation -- in operations that classical mathematicians associate with equality[1], and in itself does not have a useful formulation of complexity[2]. Nevertheless, those people might ignore computational complexity, which is the same as ignoring computation itself, and while they may turn out to be great mathematicians, you would not want them specifying or writing your traffic signal or air-traffic control software.<p>[1]: Although I believe most notations take care to not separate consecutive reductions with the equal sign but with an arrow or a new line, precisely to signify that reduction is not equality. Also, unlike in math, LC reductions are directional, and some substitutions can&#x27;t be reversed. In this way, LC <i>does</i> directly represent one property of time: it&#x27;s directionality.<p>[2]: The challenge complexity poses to LC is great, and only in 2014 was it proven that it is not just a model of computation but one of a &quot;reasonable machine&quot;: <a href="http:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1405.3311" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1405.3311</a>