Hi Roger Clough,

### ROGER:  Quanta are different from particles. They don't move
from A to B along particular paths through space (or even through space), they move through all possible mathematical paths - which is to say that they are everywhere at once- until one particular path is selected by a measurement (or selected by passing through slits).

Do you agree with Everett that all path exists, and that the selection might equivalent with a first person indeterminacy?

Note that intelligence requires the ability to select.

OK. But the ability to selct does not require intelligence, just interaction and some memory.

Selection of a quantum path
(collapse or reduction of the jungle of  brain wave paths) produces
consciousness, according to Penrose et al. They call it orchestrated
reduction. .

Penrose is hardly convincing on this. Its basic argument based on Gödel is invalid, and its theory is quite speculative, like the wave collapse, which has never make any sense to me.

Why would the physical not be infinitely divisible and extensible,
especially if "not real"?

#### ROGER:  Objects  can be physical and also infinitely divisible,
but L considered this infinite divisibility to disqualify an object to be real because
there's no end to the process, one wouldn't end up with something
to refer  to.

In comp we end up with what is similar above the substitution level. What we call "macro", but which is really only what we can "isolate".
The picture is of course quite counter-intuitive.

> Personally. I substitute Heisenberg's uncertainty principle
> as the basis for this view because the fundamental particles
> are supposedly divisible.

By definition an atom is not divisible, and the "atoms" today are the
elementary particles. Not sure you can divide an electron or a Higgs
With comp particles might get the sme explanation as the physicist, as
fixed points for some transformation in a universal group or universal
symmetrical system.
The simple groups, the exceptional groups, the Monster group can play
some role there (I speculate).
#### ROGER: You can split an atom because it has parts, reactors do that all of the time. of this particular point, Electrons and other fundamental particles do not have parts.
You lost me with the rest of this comment, but that's OK.

Yes. Atoms are no "atoms" (in greek άτομο means not divisible).
But if string theory is correct even electron are still divisible (conceptually).

I still don't know with comp. Normally some observable have a real continuum spectrum. Physical reality cannot be entirely discrete.

> I'm still trying to figure out how numbers and ideas fit
> into Leibniz's metaphysics. Little is written about this issue,
> so I have to rely on what Leibniz says otherwise about monads.

OK. I will interpret your monad by "intensional number".

let me be explicit on this. I fixe once and for all a universal
system: I chose the programming language LISP. Actually, a subset of
it: the programs LISP computing only (partial) functions from N to N,
with some list representation of the numbers like (0), (S 0), (S S
0), ...

I enumerate in lexicographic way all the programs LISP. P_1, P_2,
P_3, ...

The ith partial computable functions phi_i is the one computed by P_i.

I can place on N a new operation, written #, with a # b = phi_a(b),
that is the result of the application of the ath program LISP, P_a, in
the enumeration of all the program LISP above, on b.

Then I define a number as being intensional when it occurs at the left
of an expression like a # b.

The choice of a universal system transforms each number into a
(partial) function from N to N.

A number u is universal if phi_u(a, b) = phi_a(b). u interprets or
understands the program a and apply it to on b to give the result
phi_a(b). a is the program, b is the data, and u is the computer. (a,
b) here abbreviates some number coding the couple (a, b), to stay
withe function having one argument (so u is a P_i, there is a
universal program P_u).

Universal is an intensional notion, it concerns the number playing the
role of a name for the function. The left number in the (partial)
operation #.

#### ROGER:  Despisers of religion would do well to understand
this point,  as follows:

Numbers, like all beings in Platonia  are intensional and necessary,
so are not contingent, as monads are. Thus, arithmetical theorems and proofs do not change with time, are always true or always false. Perfect, heavenly,
eternal truths, as they say. Angelic. Life itself.  Free spirits.
Monads are intensional but are contingent, so they change (very rapidly) with time (like other inhabitants of Contingia). Monads are a bit corrupt like the rest of us. Although not perfect, they tend to strive to be so, at least those motivated by intellect (the principles of Platonia, so not entropic. Otherwise, those dominated by the lesser quality, passion, weaken. Entropic. As they say, the wages of sin is death. Those less dominant monads are eaten or taken over by the stronger ones.
It's a Darwinian jungle down here.  Crap happens.

Crap happens also in arithmetic when viewed from inside. Contingency is given by selection on the many computational consistent continuation. There are different form of contingencies in arithmetic: one for each modal box having an arithmetical interpretations.
In modal logic you can read
[]p by p is necessary, or true in all (accessible) worlds
<>p by p is possible  or true in one (accessible) world
~[]p or <>~p    by p is contingent (not necessary)
What will change from one modal logic to another is the accessibility or the neighborhood relations on the (abstract) worlds.

> Previously I noted that numbers could not be monads because
> monads constantly change.

They "change" relatively to universal numbers.

The universal numbers in arithmetic constitutes a sort of INDRA NET,
as all universal numbers reflects (can emulate, and does emulate, in
the UD) all other universal numbers.

Universal numbers introduce many relative dynamics in arithmetic.

Given that "time is not real", this should not annoy you in any way.

> Another argument against numbers
> being monads is that all monads must be attached to corporeal
> bodies.


#### ROGER: By atttached I mean associated with. The association is permanent. Each monad is an individiaul with individual identity given by the corporeal body it is associated with. Its soul. All corporeal bodies are different and unique.

I am OK, in some of the first person perspective. But that is "not real". The body is an epistemological construct, yet a every stable one, locally, apparently. The mind is not attached or associated to a body, but to an infinity of number relations (and the felt body is a construct of the mind).

> So monads refer to objects in the (already) created world,
> whose identities persist, while ideas and numbers are not
> created objects.

Hmm... They "emanate" from arithmetical truth, so OK.

The problem is in the "(already)" created world.
##### ROGER: To some extent there is continuous creation,
such as the unfolding of subsequent generations of seed--> plant.
seed----> plant,  etc. woman----> baby--> next generation, etc.
within a particular plant. or woman.
Yet, according to L, monads cannot be created or destroyed.
Not to worry as there are  an infinite number of them.

OK in comp, if you accept that the monad are the number coding machine relatively to universal numbers.

BRUNO: The existence of a "real physical world" is a badly express problem.
All we can ask is that vast category of sharable dreams admits some
(unique?) maximal consistent extension satisfying ... who? All
universal numbers?

### ROGER: This is too complex an issue to answer here in great detail..
The ideas and numbers etc of Platonia can also inhabit the
minds of men, and there is some limited sharing of ideas
mentally, as well as some dim knowledge of the past
and future.

Men are in Platonia. But their bodies and consciousness are in the limiting internal view of Platonia from inside.

With comp Platonia is very simple. It is basically the structure (N, 0, s, +, *), arithmetic. But after Gödel, we know that such a structure is not simple at all. Indeed, unlike physics, there is just no hope to get a complete theory about N, + *.

BRUNO: I don't know. I mean, I cannot make sense of an "already created
world", nor of objects in there.

So my attempt to intepret monads by universal number fails, but in
your definition here you are using concept which I attempt to explain,
and so I cannot use them.
####ROGER:  Right. Monads and numbers are two different animals,
although the inhabitants of Platonia can be "thought" or "proved"
in the minds of men-monads..

It looks like you have objects separated from Platonia. In Plato- Plotinus and comp, Platonia contains the whole of being. That is why Plotinus says that the ONE, and the MATTERs are not being, as they are not *in* Platonia, and with comp they don't belong properly to Platonia, but are an effect of perspective from inside Platonia.

BRUNO: But I refute your argument that numbers cannot change, as they do
change all the time through their arithmetical relations with the
universal numbers.
##### ROGER: IMHO By not changing I meant that 1 can never change to 2, it must always be 1.

But I, in some context (added to 3, for example) can be said to be changed or to produces 4.

that  numbers as numbers cannot change. However....
IMHO Different numbers can be generated by different calculations, using different inputs, or at some different time, but the resulting numbers are particulars to that particular calculation. And to my mind at least, members of, or belonging to,
Contingia in some fashion.

Yes, exactly. In two very different ways: as being an input, and as being a machine, with respect to some universal numbers.

> While numbers and ideas cannot be monads, they have to
> be are entities in the mind, feelings, and bodily aspects
> of monads.

Numbers get the two role, at least from the pov of the universal
numbers. That's the beauty of it.

##### ROGER:  ?

Let phi_i an enumeration of all computable functions. In phi_i(j), the number i has a role of dynamical machine, and j of passive input.

> For Leibniz refers to the "intellect" of human
> monads.

BRUNO: I refer to the "intellect" (terrestrial and divine) of the universal
numbers, among mainly the L bian one (as the other are a bit too much
mute on the interesting question).

ROGER: IMHO  Again let me refer to
a) Numbers themselves. numbers as numbers themselves, and these do not change.
3 is always 3.

OK.   (Let us hope!)

b) Calculated numbers. But numbers resulting from calculations obviously can differ and change, depending on the type of calculation and varying inputs.

OK. As input. But they can also be machine---he one who get the input, like i in phi_i.


> And similarly, numbers and ideas must be used
> in the "fictional" construction of matter-- in the bodily
> aspect of material monads, as well as the construction
> of our bodies and brains.

OK. But even truer at another level made possible by comp. As I try to
illustrate. Arithmetic is full of life and dreams.



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