Discussion:
Omniscience is finite
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Pete Olcott
2018-01-04 06:49:56 UTC
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<div class="moz-cite-prefix">On 1/3/2018 11:08 PM, Rupert wrote:<br>
</div>
<blockquote type="cite"
cite="mid:d2efedc4-d409-4f34-8532-***@googlegroups.com">
<pre wrap="">There is absolutely no way the observable universe can contain a book with 2^33660000 pages, or even 2^1000 pages.
</pre>
</blockquote>
<p><font face="Segoe UI Symbol">It could still be empirically
verified in that the monochrome bitmap image of any page of any
book would also specifies its own unique page number in this book
as a </font> 33,660,000 bit binary integer. <br>
</p>
<p>It does this by simply reading the bits in its bitmap in the same
order that one would read a book top left to bottom right. <br>
</p>
<p>The book would be produced (in theory) by simply incrementing the
33660000 bit binary integer, starting with 33660000 zero bits (for
white space) and ending with 33660000 one bits (for black dots). <br>
</p>
<div class="moz-signature">-- <br>
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        <b>Γ ⊢<sub><font style="font-size: 8pt" size="1">FS</font></sub>
A ≡ ∃Γ ⊆ FS Provable(Γ, A)</b> // MTT notational conventions<br>
<b>∀X True(X) ≡ ∃Γ ⊆ MTT ∧ Axioms(Γ) Provable(Γ, X) </b> // MTT
Truth Predicate </div>
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Pete Olcott
2018-01-04 16:37:11 UTC
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<div class="moz-cite-prefix">On 1/4/2018 1:57 AM, Rupert wrote:<br>
</div>
<blockquote type="cite"
cite="mid:4ec87067-cc65-4aec-a84a-***@googlegroups.com">
<pre wrap="">On Thursday, January 4, 2018 at 7:50:05 AM UTC+1, Pete Olcott wrote:
</pre>
<blockquote type="cite">
<pre wrap="">On 1/3/2018 11:08 PM, Rupert wrote:



There is absolutely no way the observable universe can contain a book with 2^33660000 pages, or even 2^1000 pages.



It could still be empirically
verified in that the monochrome bitmap image of any page of any
book would also specifies its own unique page number in this book
as a 33,660,000 bit binary integer.



It does this by simply reading the bits in its bitmap in the same
order that one would read a book top left to bottom right.



The book would be produced (in theory) by simply incrementing the
33660000 bit binary integer, starting with 33660000 zero bits (for
white space) and ending with 33660000 one bits (for black dots).
</pre>
</blockquote>
<pre wrap="">
I'm agreeing with you that, abstractly speaking, such a book with a finite number of pages could exist, I do not find it especially physically plausible that the book would be only 76 miles tall, or even of such a size that it could fit into the observable universe. I believe the number of elementary particles in the observable universe is only approximately 10^87.
</pre>
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<br>
Yes it was very late at night I got the number wrong. I was thinking
that it was 33660000 pages instead of 2 ^ 33660000 pages. I am still
trying to figure out how many bytes would be in its PDF file. <br>
<br>
In any case the concept can still be validated on the basis of my
last example. Encyclopedia Britannica pages take less than 8.5 * 11.<br>
<p style="margin-bottom: 0in"><span style="background: #ffff00"><b>Every
600 DPI (8.5 * 11.0) monochrome raster image of a page from a
book specifies its
exact page number in the book of all knowledge as a single
33,660,000
bit binary integer of the bits in this raster image. </b></span><br>
<span style="background: #ffff00"></span></p>
<br>
<br>
<div class="moz-signature">-- <br>
<meta charset="UTF-8">
        <b>Γ ⊢<sub><font style="font-size: 8pt" size="1">FS</font></sub>
A ≡ ∃Γ ⊆ FS Provable(Γ, A)</b> // MTT notational conventions<br>
<b>∀X True(X) ≡ ∃Γ ⊆ MTT ∧ Axioms(Γ) Provable(Γ, X) </b> // MTT
Truth Predicate </div>
</body>
</html>
Pete Olcott
2018-01-04 20:30:49 UTC
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<div class="moz-cite-prefix">On 1/4/2018 1:33 PM, WM wrote:<br>
</div>
<blockquote type="cite"
cite="mid:4771793c-e373-42af-86fb-***@googlegroups.com">
<pre wrap="">Am Donnerstag, 4. Januar 2018 18:03:05 UTC+1 schrieb Doc O'Leary:
</pre>
<blockquote type="cite">
<pre wrap="">For your reference, records indicate that
Pete Olcott <a class="moz-txt-link-rfc2396E" href="mailto:***@NoEmail.address">&lt;***@NoEmail.address&gt;</a> wrote:

</pre>
<blockquote type="cite">
<pre wrap="">A single printed book 76 miles tall would include every page of every book that could ever possibly be written in any language that currently exists or any language that could ever possibly exist.
</pre>
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<pre wrap="">
This is obviously wrong on the face of it. Since a language is just an
encoding of information, there could “possibly exist” an infinite
number of encodings for any base set of data you’re working with.
</pre>
</blockquote>
<pre wrap="">
That would require an infinity of language creators or an infinite time that has already elapsed (even if the creation of a language lasted only one second). Both can be excluded.

Regards, WM
</pre>
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<br>
<b>The actual number of pages is </b><b>the 33,660,000 bit binary
integer of all ones. <br>
<br>
</b>This the book is actually more than ten million decimal digits
of light years tall. ===<br>
<br>
<b>Since w</b><b><span style="background: transparent">e can
effectively determine the exact page number of every page of any
book ever written <br>
we have proved the validity of the assertion that conceptual
knowledge is finite ===</span></b><br>
<b><span style="background: transparent"></span></b><span
style="font-weight: normal"><span style="background: transparent"></span></span><br>
<span style="font-weight: normal"><span style="background:
transparent"></span></span><b><span style="background: #ffff00">Every
600 DPI (8.5 * 11.0) monochrome raster image of a page from any
book specifies its exact page number in the book of all
knowledge as a single 33,660,000 bit binary integer of the bits
in this raster image. ===</span></b><br>
<br>
<div class="moz-signature">-- <br>
<meta charset="UTF-8">
        <b>Γ ⊢<sub><font style="font-size: 8pt" size="1">FS</font></sub>
A ≡ ∃Γ ⊆ FS Provable(Γ, A)</b> // MTT notational conventions<br>
<b>∀X True(X) ≡ ∃Γ ⊆ MTT ∧ Axioms(Γ) Provable(Γ, X) </b> // MTT
Truth Predicate </div>
</body>
</html>

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