Re: What is more primary than numbers?

```

On 12/8/2018 2:46 PM, Jason Resch wrote:

On Sat, Dec 8, 2018 at 4:13 PM Brent Meeker > wrote:

On 12/8/2018 11:02 AM, Jason Resch wrote:

On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift
mailto:cloudver...@gmail.com>> wrote:

What is more primary than numbers?

1. Numbers come from counting.

Numbers come from relationships upon which objective statements
can be made (with or without objects to count).
For example, I can make and prove a statement about a number with
a million digits.  Despite that there are not that many things
(in my vicinity) to count.

But only by abstracting from and generalizing some rules based
counting and then postulating that they apply to arbitrarily large
numbers of things.  For example, arithmetic assumes that you can
add 1 to 10^1000 and get a different number.  But that is purely
an assumption. Counting could never confirm it.

So then we agree that numbers don't inherit their existence or
properties from from counting.

No, I agree that numbers do get their properties from counting by
generalization, but not that they exist.

Brent

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Re: What is more primary than numbers?

```On Sat, Dec 8, 2018 at 4:13 PM Brent Meeker  wrote:

>
>
> On 12/8/2018 11:02 AM, Jason Resch wrote:
>
>
>
> On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift
> wrote:
>
>>
>> What is more primary than numbers?
>>
>> 1. Numbers come from counting.
>>
>
> Numbers come from relationships upon which objective statements can be
> made (with or without objects to count).
> For example, I can make and prove a statement about a number with a
> million digits.  Despite that there are not that many things (in my
> vicinity) to count.
>
>
> But only by abstracting from and generalizing some rules based counting
> and then postulating that they apply to arbitrarily large numbers of
> things.  For example, arithmetic assumes that you can add 1 to 10^1000 and
> get a different number.  But that is purely an assumption.  Counting could
> never confirm it.
>

So then we agree that numbers don't inherit their existence or properties
from from counting.

Jason

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Re: What is more primary than numbers?

```

On 12/8/2018 12:27 PM, Jason Resch wrote:

On Sat, Dec 8, 2018 at 2:06 PM Philip Thrift > wrote:

On Saturday, December 8, 2018 at 1:02:25 PM UTC-6, Jason wrote:

On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift
wrote:

What is more primary than numbers?

1. Numbers come from counting.

Numbers come from relationships upon which objective
statements can be made (with or without objects to count).
For example, I can make and prove a statement about a number
with a million digits.  Despite that there are not that many
things (in my vicinity) to count.

But one counts things (things that are not numbers
themselves, in the primitive case). So the things one
counts + the one that counts must be more primary than
numbers.

2. Numbers come from lambda calculus (LC). But LC - a
programming language - needs a machine LCM to interpret LC
programs. So LC + LCM is more primary than numbers.

You can build computers and programs out of equations
concerning the arithmetical relationships that exist between
numbers.  See my post "Do we live in a Diophantine equation":

Jason

But what are /relations/? Are /relations/, or /functions/, then
primitive?

I think truth is primitive.

"True" means quite different things in different contexts.

Brent

cf. *Relations Versus Functions at the Foundations of Logic:
Type-Theoretic Considerations*
https://mally.stanford.edu/Papers/rtt.pdf

What language are /equations/ written in?

Things only need to be written for purposes of communication. Writing
a description has no bearing on the ontological status of the thing
described.

Jason
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Re: What is more primary than numbers?

```

On 12/8/2018 11:02 AM, Jason Resch wrote:

On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift > wrote:

What is more primary than numbers?

1. Numbers come from counting.

Numbers come from relationships upon which objective statements can be
made (with or without objects to count).
For example, I can make and prove a statement about a number with a
million digits.  Despite that there are not that many things (in my
vicinity) to count.

But only by abstracting from and generalizing some rules based counting
and then postulating that they apply to arbitrarily large numbers of
things.  For example, arithmetic assumes that you can add 1 to 10^1000
and get a different number.  But that is purely an assumption.  Counting
could never confirm it.

Brent

But one counts things (things that are not numbers themselves, in
the primitive case). So the things one counts + the one that
counts must be more primary than numbers.

2. Numbers come from lambda calculus (LC). But LC - a programming
language - needs a machine LCM to interpret LC programs. So LC +
LCM is more primary than numbers.

You can build computers and programs out of equations concerning the
arithmetical relationships that exist between numbers.  See my post
"Do we live in a Diophantine equation":

Jason

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Re: What is more primary than numbers?

```On Sat, Dec 8, 2018 at 2:06 PM Philip Thrift  wrote:

>
>
> On Saturday, December 8, 2018 at 1:02:25 PM UTC-6, Jason wrote:
>>
>>
>>
>> On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift  wrote:
>>
>>>
>>> What is more primary than numbers?
>>>
>>> 1. Numbers come from counting.
>>>
>>
>> Numbers come from relationships upon which objective statements can be
>> made (with or without objects to count).
>> For example, I can make and prove a statement about a number with a
>> million digits.  Despite that there are not that many things (in my
>> vicinity) to count.
>>
>>
>>> But one counts things (things that are not numbers themselves, in the
>>> primitive case). So the things one counts + the one that counts must be
>>> more primary than numbers.
>>>
>>> 2. Numbers come from lambda calculus (LC). But LC - a programming
>>> language - needs a machine LCM to interpret LC programs. So LC + LCM is
>>> more primary than numbers.
>>>
>>>
>> You can build computers and programs out of equations concerning the
>> arithmetical relationships that exist between numbers.  See my post "Do we
>> live in a Diophantine equation":
>>
>> Jason
>>
>
>
>
> But what are *relations*? Are *relations*, or *functions*, then
> primitive?
>
>
I think truth is primitive.

> cf. *Relations Versus Functions at the Foundations of Logic:
> Type-Theoretic Considerations*
>  https://mally.stanford.edu/Papers/rtt.pdf
>
> What language are *equations* written in?
>
>
Things only need to be written for purposes of communication. Writing a
description has no bearing on the ontological status of the thing described.

Jason

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Re: What is more primary than numbers?

```

On Saturday, December 8, 2018 at 1:02:25 PM UTC-6, Jason wrote:
>
>
>
> On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift  > wrote:
>
>>
>> What is more primary than numbers?
>>
>> 1. Numbers come from counting.
>>
>
> Numbers come from relationships upon which objective statements can be
> made (with or without objects to count).
> For example, I can make and prove a statement about a number with a
> million digits.  Despite that there are not that many things (in my
> vicinity) to count.
>
>
>> But one counts things (things that are not numbers themselves, in the
>> primitive case). So the things one counts + the one that counts must be
>> more primary than numbers.
>>
>> 2. Numbers come from lambda calculus (LC). But LC - a programming
>> language - needs a machine LCM to interpret LC programs. So LC + LCM is
>> more primary than numbers.
>>
>>
> You can build computers and programs out of equations concerning the
> arithmetical relationships that exist between numbers.  See my post "Do we
> live in a Diophantine equation":
>
> Jason
>

But what are *relations*? Are *relations*, or *functions*, then primitive?

cf. *Relations Versus Functions at the Foundations of Logic: Type-Theoretic
Considerations*
https://mally.stanford.edu/Papers/rtt.pdf

What language are *equations* written in?

- pt

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Re: What is more primary than numbers?

```On Sat, Dec 8, 2018 at 4:04 AM Philip Thrift  wrote:

>
> What is more primary than numbers?
>
> 1. Numbers come from counting.
>

Numbers come from relationships upon which objective statements can be made
(with or without objects to count).
For example, I can make and prove a statement about a number with a million
digits.  Despite that there are not that many things (in my vicinity) to
count.

> But one counts things (things that are not numbers themselves, in the
> primitive case). So the things one counts + the one that counts must be
> more primary than numbers.
>
> 2. Numbers come from lambda calculus (LC). But LC - a programming language
> - needs a machine LCM to interpret LC programs. So LC + LCM is more primary
> than numbers.
>
>
You can build computers and programs out of equations concerning the
arithmetical relationships that exist between numbers.  See my post "Do we
live in a Diophantine equation":

Jason

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Re: Extended Wigner’s Friend

```On Wed, Dec 5, 2018 at 10:57 PM Mason Green  wrote:

*> Ah, yes, multiple histories. Given only what we know now about the
> universe (and not what we “remember from before”, since our memories are
> actually just patterns encoded in our brain at the present moment),*

I've never understood the distinction some people make between many worlds
and many histories, if many worlds is correct then I have a unique history
the one I remember, but I have many different futures. Memories are part of
the universe and so is our subjective sense of the passage of time and that
needs an explanation. Yes the entire universe could have popped into
existence 2 seconds ago complete with memories of me in the second grade
and dinosaur bones in the ground but the simplest explanation is the past
existed.

*> what’s to stop us from thinking that entropy was higher in the past and
> things just spontaneously arranged themselves into the present low-entropy
> state? *

Because there are VASTLY more high-entropy states than low entropy states
(because there are more ways something can be disordered than ordered) so
the probability is overwhelming that the next state will have a higher
entropy than the one you're in now.  But entropy isn't always bad. Maximum
information
, or at least maximum
information that intelligence finds
interesting
,

midway between maximum and minimum

entropy. Put some cream in a glass coffee cup and then very carefully put
some coffee on top of it. For a short time the 2 fluids will remain
segregated and the

entropy will be low and the information needed to describe it would be low
too, but then tendrils of cream will start to move into the coffee and all
sorts of spirals and other complex
and pretty
patterns will form, the entropy is higher now and the information needed to
describe it is higher
too
, but after that the fluid in the cup will reach a dull uniform color that
is darker than coffee but lighter than cream, the entropy has reached a
maximum but it would take less
interesting
information to describe it.

Another example is smoke from a cigarette in a room with no air currents,
it starts out as a simple smooth laminar flow but then turbulence kicks in
and very complex patterns form, and after that it diffuses into a uniform
featureless
very dull
fog.

*> To go into further detail, creatures who perceived time that way would
> not be able to maintain a sense of personal continuity or selfhood for very
> long,*

When we look at the arrow of time we see it pointing in one direction so we
remember the past but not the future and (if Many Worlds is correct) we
have  one unique past but many different futures; a being that looked at
the arrow of time and saw it pointing in the opposite direction would
remember the future but not the past and have one unique future but many
different pasts, and I don't see why that wouldn't generate a continuity of
selfhood just because it's going in the opposite direction.

*> I’m thinking I might write a story about beings who perceive time as
> parabolic, with their present selves at an entropy minimum: their language
> is structured so that they can only talk about possible pasts and not “the”
> past, and also they have words for all the Second Law-violating reverse
> processes that had to have occurred in the high-entropy majority of their
> possible pasts.To go into further detail, creatures who perceived time that
> way would not be able to maintain a sense of personal continuity or
> selfhood for very long, *

If the arrow of time were reversed you would discover different laws of
thermodynamics. For example you would remember that in the distant future,
that is to say a long way from your "now", perfume molecules "were" (the
most difficult part of time travel or reverse time thought experiments is
the grammar)  evenly distributed throughout the room, and you would
remember that in the more recent future the molecules were only in the
lower right part of the room, and you would remember that in the very
recent future (very close to your "now") all the molecules were confined
inside one small perfume bottle. You would then conclude that entropy
always decreases or remains the same. But as to how the bottle got into
that room in the first place well, you can make educated guesses but
essentially the past is unknowable, only the future is certain.

John K Clark

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Re: Coherent states of a superposition

```

On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com
> wrote:
>>
>>
>>
>> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>>>
>>> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>>>
On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com
wrote:
>
> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>
>> On Wed, Dec 5, 2018 at 2:36 AM  wrote:
>>
>>>
>>> *Thanks, but I'm looking for a solution within the context of
>>> interference and coherence, without introducing your theory of
>>> consciousness. Mainstream thinking today is that decoherence does
>>> occur,
>>> but this seems to imply preexisting coherence, and therefore
>>> interference
>>> among the component states of a superposition. If the superposition is
>>> expressed using eigenfunctions, which are mutually orthogonal --
>>> implying
>>> no mutual interference -- how is decoherence possible, insofar as
>>> coherence, IIUC, doesn't exist using this basis? AG*
>>>
>>
>> I think you misunderstand the meaning of "coherence" when it is used
>> off an expansion in terms of a set of mutually orthogonal eigenvectors.
>> The
>> expansion in some eigenvector basis is written as
>>
>>|psi> = Sum_i (a_i |v_i>)
>>
>> where |v_i> are the eigenvectors, and i ranges over the dimension of
>> the Hilbert space. The expansion coefficients are the complex numbers
>> a_i.
>> Since these are complex coefficients, they contain inherent phases. It
>> is
>> the preservation of these phases of the expansion coefficients that is
>> meant by "maintaining coherence". So it is the coherence of the
>> particular
>> expansion that is implied, and this has noting to do with the mutual
>> orthogonality or otherwise of the basis vectors themselves. In
>> decoherence,
>> the phase relationships between the terms in the original expansion are
>> lost.
>>
>> Bruce
>>
>
> I appreciate your reply. I was sure you could ascertain my error --
> confusing orthogonality with interference and coherence. Let me have your
> indulgence on a related issue. AG
>

Suppose the original wf is expressed in terms of p, and its
superposition expansion is also expressed in eigenfunctions with variable
p. Does the phase of the original wf carry over into the eigenfunctions as
identical for each, or can each component in the superposition have
different phases? I ask this because the probability determined by any
complex amplitude is independent of its phase. TIA, AG

>>>
>>> The phases of the coefficients are independent of each other.
>>>
>>
>> When I formally studied QM, no mention was made of calculating the phases
>> since, presumably, they don't effect probability calculations. Do you have
>> a link which explains how they're calculated? TIA, AG
>>
>
> I found some links on physics.stackexchange.com which show that relative
> phases can effect probabilities, but none so far about how to calculate any
> phase angle. AG
>

Here's the answer if anyone's interested. But what's the question? How are
wf phase angles calculated? Clearly, if you solve for the eigenfunctions of
some QM operator such as the p operator, any phase angle is possible; its
value is completely arbitrary and doesn't effect a probability calculation.
In fact, IIUC, there is not sufficient information to solve for a unique
phase. So, I conclude,that the additional information required to uniquely
determine a phase angle for a wf, lies in boundary conditions. If the
problem of specifying a wf is defined as a boundary value problem, then, I
believe, a unique phase angle can be calculated. CMIIAW. AG

>
>>> Bruce
>>>
>>>
>>>
>>

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What is more primary than numbers?

```
What is more primary than numbers?

1. Numbers come from counting. But one counts things (things that are not
numbers themselves, in the primitive case). So the things one counts + the
one that counts must be more primary than numbers.

2. Numbers come from lambda calculus (LC). But LC - a programming language
- needs a machine LCM to interpret LC programs. So LC + LCM is more primary
than numbers.

...

- pt

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Re: Towards Conscious AI Systems

```

On Friday, December 7, 2018 at 5:52:31 PM UTC-6, John Clark wrote:
>
> On Fri, Dec 7, 2018 at 6:40 AM Bruno Marchal  > wrote:
>
>
>>> >>No program can be executed without a computer that is made of matter
>>> and uses energy.
>>
>>
>> >*That contradicts the definition of execution in computer science.*
>>
>
> The graduates of any school of computer science that used a definition of
> "execution" that have nothing to do with time or space or matter or
> energy would NEVER be able to get a job, so it's fortunate no such school
> of computer science exists; or if it does the school is invisible and does
> not change in time or space.
>
>>
>>

There is indeed a type of semantics (along with denotational, operational,
etc.) in computing and programming language theory where the physical
nature (matter, energy) of the computer is taken into account: *physical
semantics.*

e.g. Building connections between theories of computing and physical systems
https://dl.acm.org/citation.cfm?doid=2509578.2509587

- pt

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