<div dir="auto"><div><br><br><div class="gmail_quote gmail_quote_container"><div dir="ltr" class="gmail_attr">On Fri, Jul 31, 2026, 9:01 AM Ben Zaiboc 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:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="font-family:Arial,sans-serif;font-size:14px">Trying again..<br><br></div><div style="font-family:Arial,sans-serif;font-size:14px">------- Forwarded Message -------<br></div><div style="font-family:Arial,sans-serif;font-size:14px"><div>
From: Ben Zaiboc <<a href="mailto:benzaiboc@proton.me" target="_blank" rel="noreferrer">benzaiboc@proton.me</a>><br>
Date: On Thursday, 30 July 2026 at 21:40<br>
Subject: Re: [ExI] Wrong frequency? Astronomers rethink where to hunt for alien signals<br>
To: ExI chat list <<a href="mailto:extropy-chat@lists.extropy.org" target="_blank" rel="noreferrer">extropy-chat@lists.extropy.org</a>><br>
<br>
<blockquote type="cite">
<span>On 29/07/2026 16:55, Lloyd Miller wrote:</span><div><br></div><div><span> > Aren't numbers derived from counting objects?</span></div><div><br></div><div><br></div><div><span>My understanding is that we (humans) derive numbers from set theory.</span></div></blockquote></div></div></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Both are true. Numbers derive from counting objects, and this is also how set theory defines numbers (by counting distinct objects).</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto">In a universe of nothing *zero* would reflect the number of material things to count. But how many abstract things are there to count? There is at least one. The one number that exists to define the number of material things is zero.</div><div dir="auto"><br></div><div dir="auto">But if we have one number and it is one thing to count, now another number exists: one. We then have zero and one together as the only numbers. But now we have two numbers. Now two exists…</div><div dir="auto"><br></div><div dir="auto">This is how numbers are defined in set theory. Within set theory, each number is formed as the set of all previous sets. The process starts with the empty set (represented by { } or ∅) which contains zero things.</div><div dir="auto"><br></div><div dir="auto">0 = { } = ∅</div><div dir="auto">1 = { 0 } = {∅}</div><div dir="auto">2 = { 0, 1 } = { ∅, {∅} }</div><div dir="auto">3 = { 0, 1, 2 } = { ∅, {∅} , {∅, {∅}} }</div><div dir="auto">4 = { 0, 1, 2, 3 } = { ∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}} }</div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto">So set theory simply counts what sets can be uniquely formed out of sets, starting with the empty set and constructively building new distinct sets from there.</div><div dir="auto"><br></div><div dir="auto">But this is a relatively modern way of defining numbers, which only started in the 1900s. And we had numbers long before that.</div><div dir="auto"><br></div><div dir="auto">Jason </div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="font-family:Arial,sans-serif;font-size:14px"><div><blockquote type="cite"><div><span> </span></div><div><br></div><div><span>Don't ask me to explain that, I don't understand it, but it's what I've read. </span></div><div><br></div><div><span>Maybe aliens derive their numbers some other way. </span></div><div><br></div><div><span>Maybe it's inevitable that all sufficiently intelligent beings derive numbers the same way. Who knows. </span></div><div><br></div><div><span>Counting objects seems a nice, intuitive way of deriving numbers, and it makes sense to me, but talk to a mathematician. I suspect they'll soon confuse, er, I mean, disabuse you of that idea. You can't derive negative numbers that way, for example, or a lot of the other weird types of numbers that we have defined (I'm not going to get into the whole discovered/invented argument), or in fact, most of mathematics, it seems to me. </span></div><div><br></div><div><span>Counting things is probably an obscure, tiny and trivial corner of maths.</span></div><div><br></div><div><span>--</span></div><span>Ben</span>
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