<div dir="ltr"><div class="gmail-group gmail-w-full gmail-text-gray-800 gmail-dark:text-gray-100 gmail-border-b gmail-border-black/10 gmail-dark:border-gray-900/50 gmail-bg-gray-50 gmail-dark:bg-[#444654]" style="border-width:0px 0px 1px;border-style:solid;border-color:rgba(0,0,0,0.1);box-sizing:border-box;width:1344.47px;font-family:Söhne,ui-sans-serif,system-ui,-apple-system,"Segoe UI",Roboto,Ubuntu,Cantarell,"Noto Sans",sans-serif,"Helvetica Neue",Arial,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-size:14px"><div class="gmail-text-base gmail-gap-4 gmail-md:gap-6 gmail-md:max-w-2xl gmail-lg:max-w-2xl gmail-xl:max-w-3xl gmail-p-4 gmail-md:py-6 gmail-flex gmail-lg:px-0 gmail-m-auto" style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin:auto;display:flex;padding:1.5rem 0px;font-size:1rem;line-height:1.5rem;max-width:48rem"><div class="gmail-relative gmail-flex gmail-w-[calc(100%-50px)] gmail-flex-col gmail-gap-1 gmail-md:gap-3 gmail-lg:w-[calc(100%-115px)]" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex"><div class="gmail-flex gmail-flex-grow gmail-flex-col gmail-gap-3" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex"><div class="gmail-min-h-[20px] gmail-flex gmail-flex-col gmail-items-start gmail-gap-4 gmail-whitespace-pre-wrap" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex;min-height:20px;white-space:pre-wrap"><div class="gmail-markdown gmail-prose gmail-w-full gmail-break-words gmail-dark:prose-invert gmail-light" style="border:0px solid rgb(217,217,227);box-sizing:border-box;max-width:none;font-size:1rem;line-height:1.75;width:652.997px">

<span style="color:rgb(52,53,65)">What about math, it is a language but it has no referent.</span>

<p style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin:0px 0px 1.25em">Mathematics can be thought of as a language, but it is fundamentally different from natural languages like English or Spanish. While natural languages primarily rely on referents to convey meaning, mathematics is an abstract and formal system used to represent relationships, quantities, and patterns.</p><p style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin:1.25em 0px">However, it's not accurate to say that mathematics has no referents at all. In mathematics, symbols and expressions serve as a means of representing abstract concepts and relationships, and these symbols can be seen as having referents, albeit abstract ones. For example, the number "2" is a symbol that represents the abstract concept of "two of something." Similarly, variables like "x" or "y" serve as placeholders for unknown or varying quantities, and they can also be thought of as having referents within the context of a specific problem or equation.</p><p style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin:1.25em 0px 0px">In this sense, the referents in mathematics are more abstract and generalized compared to those in natural languages, which are often tied to concrete objects, experiences, or ideas. The power of mathematics comes from its ability to represent and manipulate these abstract concepts and relationships in a precise and logical way, allowing us to model and solve problems across a wide range of disciplines.</p></div></div></div><div class="gmail-flex gmail-justify-between" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex"><div class="gmail-text-gray-400 gmail-flex gmail-self-end gmail-lg:self-center gmail-justify-center gmail-mt-2 gmail-gap-3 gmail-md:gap-4 gmail-lg:gap-1 gmail-lg:absolute gmail-lg:top-0 gmail-lg:translate-x-full gmail-lg:right-0 gmail-lg:mt-0 gmail-lg:pl-2 gmail-visible" style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin-top:0px;display:flex;padding-left:0.5rem"><button class="gmail-p-1 gmail-rounded-md gmail-hover:bg-gray-100 gmail-hover:text-gray-700 gmail-dark:text-gray-400 gmail-dark:hover:bg-gray-700 gmail-dark:hover:text-gray-200 gmail-disabled:dark:hover:text-gray-400" style="border-width:0px;border-style:solid;border-color:rgb(217,217,227);font-family:inherit;font-size:16px;font-weight:inherit;line-height:inherit;margin:0px;padding:0.25rem;background-image:none;border-radius:0.375rem"></button><button class="gmail-p-1 gmail-rounded-md gmail-hover:bg-gray-100 gmail-hover:text-gray-700 gmail-dark:text-gray-400 gmail-dark:hover:bg-gray-700 gmail-dark:hover:text-gray-200 gmail-disabled:dark:hover:text-gray-400" style="border-width:0px;border-style:solid;border-color:rgb(217,217,227);font-family:inherit;font-size:16px;font-weight:inherit;line-height:inherit;margin:0px;padding:0.25rem;background-image:none;border-radius:0.375rem"></button></div></div></div></div></div><div class="gmail-group gmail-w-full gmail-text-gray-800 gmail-dark:text-gray-100 gmail-border-b gmail-border-black/10 gmail-dark:border-gray-900/50 gmail-dark:bg-gray-800" style="border-width:0px 0px 1px;border-style:solid;border-color:rgba(0,0,0,0.1);box-sizing:border-box;width:1344.47px;font-family:Söhne,ui-sans-serif,system-ui,-apple-system,"Segoe UI",Roboto,Ubuntu,Cantarell,"Noto Sans",sans-serif,"Helvetica Neue",Arial,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-size:14px"><div class="gmail-text-base gmail-gap-4 gmail-md:gap-6 gmail-md:max-w-2xl gmail-lg:max-w-2xl gmail-xl:max-w-3xl gmail-p-4 gmail-md:py-6 gmail-flex gmail-lg:px-0 gmail-m-auto" style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin:auto;display:flex;padding:1.5rem 0px;font-size:1rem;line-height:1.5rem;max-width:48rem"><div class="gmail-w-[30px] gmail-flex gmail-flex-col gmail-relative gmail-items-end" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex;width:30px"><div class="gmail-relative gmail-flex" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex"><span style="border:0px;box-sizing:border-box;display:inline-block;overflow:hidden;width:initial;height:initial;background:none;opacity:1;margin:0px;padding:0px;max-width:100%"><span style="border:0px;box-sizing:border-box;display:block;width:initial;height:initial;background:none;opacity:1;margin:0px;padding:0px;max-width:100%"><img alt="" aria-hidden="true" style="border: 0px; box-sizing: border-box; display: block; vertical-align: middle; height: initial; max-width: 100%; width: initial; background: none; opacity: 1; margin: 0px; padding: 0px;"></span><img alt="Giovanni Santostasi" src="https://chat.openai.com/_next/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxb_fMn05lxQvUqKvLioXvZtJTW9RIhl3ANKU0ilOg%3Ds96-c&w=64&q=75" class="gmail-rounded-sm" style="border: none; box-sizing: border-box; display: block; vertical-align: middle; height: 0px; max-width: 100%; border-radius: 0.125rem; inset: 0px; padding: 0px; margin: auto; width: 0px; min-width: 100%; min-height: 100%; max-height: 100%;"></span></div></div><div class="gmail-relative gmail-flex gmail-w-[calc(100%-50px)] gmail-flex-col gmail-gap-1 gmail-md:gap-3 gmail-lg:w-[calc(100%-115px)]" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex"><div class="gmail-flex gmail-flex-grow gmail-flex-col gmail-gap-3" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex"><div class="gmail-min-h-[20px] gmail-flex gmail-flex-col gmail-items-start gmail-gap-4 gmail-whitespace-pre-wrap" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex;min-height:20px;white-space:pre-wrap">But then a NLM doesn't need to have a direct experience of 2 of something, that concept can be totally abstract, right?</div></div><div class="gmail-text-gray-400 gmail-flex gmail-self-end gmail-lg:self-center gmail-justify-center gmail-mt-2 gmail-gap-3 gmail-md:gap-4 gmail-lg:gap-1 gmail-lg:absolute gmail-lg:top-0 gmail-lg:translate-x-full gmail-lg:right-0 gmail-lg:mt-0 gmail-lg:pl-2 gmail-visible" style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin-top:0px;display:flex;padding-left:0.5rem"><button class="gmail-p-1 gmail-rounded-md gmail-hover:bg-gray-100 gmail-hover:text-gray-700 gmail-dark:text-gray-400 gmail-dark:hover:bg-gray-700 gmail-dark:hover:text-gray-200 gmail-disabled:dark:hover:text-gray-400 gmail-md:invisible gmail-md:group-hover:visible" style="border-width:0px;border-style:solid;border-color:rgb(217,217,227);font-family:inherit;font-size:16px;font-weight:inherit;line-height:inherit;margin:0px;padding:0.25rem;background-image:none;border-radius:0.375rem"></button></div><div class="gmail-flex gmail-justify-between" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex"></div></div></div></div><div class="gmail-group gmail-w-full gmail-text-gray-800 gmail-dark:text-gray-100 gmail-border-b gmail-border-black/10 gmail-dark:border-gray-900/50 gmail-bg-gray-50 gmail-dark:bg-[#444654]" style="border-width:0px 0px 1px;border-style:solid;border-color:rgba(0,0,0,0.1);box-sizing:border-box;width:1344.47px;font-family:Söhne,ui-sans-serif,system-ui,-apple-system,"Segoe UI",Roboto,Ubuntu,Cantarell,"Noto Sans",sans-serif,"Helvetica Neue",Arial,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-size:14px"><div class="gmail-text-base gmail-gap-4 gmail-md:gap-6 gmail-md:max-w-2xl gmail-lg:max-w-2xl gmail-xl:max-w-3xl gmail-p-4 gmail-md:py-6 gmail-flex gmail-lg:px-0 gmail-m-auto" style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin:auto;display:flex;padding:1.5rem 0px;font-size:1rem;line-height:1.5rem;max-width:48rem"><div class="gmail-w-[30px] gmail-flex gmail-flex-col gmail-relative gmail-items-end" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex;width:30px"><div class="gmail-relative gmail-h-[30px] gmail-w-[30px] gmail-p-1 gmail-rounded-sm gmail-text-white gmail-flex gmail-items-center gmail-justify-center" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex;height:30px;width:30px;border-radius:0.125rem;padding:0.25rem;background-color:black"></div></div><div class="gmail-relative gmail-flex gmail-w-[calc(100%-50px)] gmail-flex-col gmail-gap-1 gmail-md:gap-3 gmail-lg:w-[calc(100%-115px)]" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex"><div class="gmail-flex gmail-flex-grow gmail-flex-col gmail-gap-3" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex"><div class="gmail-min-h-[20px] gmail-flex gmail-flex-col gmail-items-start gmail-gap-4 gmail-whitespace-pre-wrap" style="border:0px solid rgb(217,217,227);box-sizing:border-box;display:flex;min-height:20px;white-space:pre-wrap"><div class="gmail-markdown gmail-prose gmail-w-full gmail-break-words gmail-dark:prose-invert gmail-light" style="border:0px solid rgb(217,217,227);box-sizing:border-box;max-width:none;font-size:1rem;line-height:1.75;width:652.997px"><p style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin:0px 0px 1.25em">Yes, you are correct. A neural language model (NLM), like ChatGPT, does not need direct experience of "two of something" to understand or use the concept. NLMs learn from vast amounts of text data, and through this process, they develop an understanding of the abstract concept of numbers, including "2," based on the patterns and relationships observed in the data.</p><p style="border:0px solid rgb(217,217,227);box-sizing:border-box;margin:1.25em 0px">NLMs can learn about the properties and usage of numbers in language without having any real-world experience or direct interaction with objects. They can generate appropriate responses involving numbers or mathematical concepts because they have been exposed to numerous examples of how these concepts are used in various contexts during their training.</p></div></div></div></div></div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Mar 23, 2023 at 6:35 PM Adrian Tymes via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org">extropy-chat@lists.extropy.org</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"><div dir="ltr"><div dir="ltr">On Thu, Mar 23, 2023 at 6:18 PM Gordon Swobe via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org" target="_blank">extropy-chat@lists.extropy.org</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">I think it was Adrian who asked you that question. A referent as I use the term is something that exists outside of language to which a word refers. You have an apple in your hand and you say "this is an apple." The apple in your hand is the referent that corresponds to your word "apple."  <br></div><div class="gmail_quote"><div><br>As for whether referents are data, it is unclear to me how referents could be data. I am inclined to say no but I am not sure what Adrain is getting at here.<br></div></div></div></blockquote><div><br></div><div>Ah, I thought you meant that the referent was the *fact that* that was an apple, rather than the referent being the apple itself.  Facts are data; objects (such as apples) are not. </div></div></div>
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