[ExI] Fw: Re: Wrong frequency? Astronomers rethink where to hunt for alien signals

[Jason Resch]

On Fri, Jul 31, 2026, 9:01 AM Ben Zaiboc via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> Trying again..
>
> ------- Forwarded Message -------
> From: Ben Zaiboc <benzaiboc at proton.me>
> Date: On Thursday, 30 July 2026 at 21:40
> Subject: Re: [ExI] Wrong frequency? Astronomers rethink where to hunt for
> alien signals
> To: ExI chat list <extropy-chat at lists.extropy.org>
>
> On 29/07/2026 16:55, Lloyd Miller wrote:
>
>  > Aren't numbers derived from counting objects?
>
>
> My understanding is that we (humans) derive numbers from set theory.
>
>
Both are true. Numbers derive from counting objects, and this is also how
set theory defines numbers (by counting distinct objects).


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.

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…

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.

0 = { } = ∅
1 = { 0 } = {∅}
2 = { 0, 1 } = { ∅, {∅} }
3 = { 0, 1, 2 } = { ∅, {∅} , {∅, {∅}} }
4 = { 0, 1, 2, 3 } = { ∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}} }

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.

But this is a relatively modern way of defining numbers, which only started
in the 1900s. And we had numbers long before that.

Jason


> Don't ask me to explain that, I don't understand it, but it's what I've
> read.
>
> Maybe aliens derive their numbers some other way.
>
> Maybe it's inevitable that all sufficiently intelligent beings derive
> numbers the same way. Who knows.
>
> 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.
>
> Counting things is probably an obscure, tiny and trivial corner of maths.
>
> --
> Ben
>
>
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