Everyone wants to see his geek to geek answer?? Okay but it's your funeral.
Here's what my husband wrote:
>This was posted in another forum (it's unedited).... I am trying to
>compile it, I didn't do a good job communicating it in the other
>thread so here is the beginning of it. Note it's hypothetical at this
>point but I'm working on
It's hard to say much about the following, because it appears to be
"untrained" in the sense that he does not know (has not yet been
trained well) in the language of mathematics. So it's like me having
to try and learn a new language, reading the following, and I've no
idea what underlying assumptions to apply when reading it. Not
necessarily the fault of anyone, just a lack of a common basis for
communication.
>what I call "boolean field probability",
Now, this makes me feel as though the terms are taken from "book
learning without understanding." I certainly recognize each of the
three words. But put together it carries no meaning unless the author
can carefully define it.
>the numbers boolean numbers
>are "made of (note this is a very poor metaphor, it's still not clear
>in my head)" +1, -1 ... I haven't got it all worked out yet....
Boolean numbers? My only context for understanding this phrase comes
from it's usual use -- that there exists only "one binary bit" so to
speak and can either be 0 or 1 (instead of false and true.) There is
no subtraction, for example, defined.
This all gets into the idea of fields, rings, and algebras and group
theory. But I've no idea why the author chooses terms +1 and -1,
here.
>I was thinking (more) today that if binary (numbers)
Change of subject noted. Introduction of "binary" when talking just a
moment ago about "boolean numbers."
>can convert any
>recognizable data, into anything else (i.e. a number can represent a
>picture, or a sound, or a letter, etc,etc).
Actually, it's all just representation. Nothing much deeper there.
>Then, what represents binary? If there are only two numbrs 1, and "0"
>(in binary)
What happened to "boolean numbers?" Is the subject dropped? No, I
think not. Actually, since the author says "there are only two
numbers" when talking about binary, I think we may be back to talking
about boolean numbers, conflating the term with binary. Not a good
sign of crafted, quality thinking.
>Then binary must have some self-recursive property.
Premises not accepted, so I don't find this conclusion logically sound
or meaningful, yet.
>I thought about it like this...
>
>If 1(boolean-object-number) = yes, and 0 is not a binary number
But zero is both a semantic concept within rings, fields, and algebras
(the additive identity, no matter how the author defines members of a
symbol set and addition) as well as a syntactic element of
representation in binary and other notational methods for specifying
numbers (such as decimal.) 0 is a number, at least in the sense that
it is a member of the set of integers, real numbers, etc. That is, at
least if the author has addition and an additive identity, at all.
Just claiming, simply by fiat, that 0 is not a binary number isn't
very convincing to me. And the logic leading up to this point is in
no way helpful, by way of convincing me.
>(because zero is really "null" = nothing in everyday usage... then 0 =
>not a number, then it really looks like....
Perhaps the author means to define another term, here, that means
"nothing." I think that the author is sadly moving way too fast
across ideas and comflating terms in the process into an unclear and
muddy mush. The purpose of 0 (zero) is "additive identity" as part of
an algebra, for example. This is a very strict, very precise purpose.
The concept of "nothing" has _nothing_ to do with this additive
identity purpose in mathematics. Conflating the two ideas will not
help, in any way at all.
>1(boolean-object-number) = (positive)+ yes =*+ on*
>-1(boolean-object-number) = (negative)- yes =*- on*
New term, boolean-object-number, noted. I don't know what it is or is
about. But I can see it introduced.
>So it would look like
>
>+1 is equal to +ON
>-1 is equal to -ON
>
>+1 = "+1"(1)
>-1 = "-1"(-1)
Looks like restatements, to me. But no additional meaning developed.
>Therefore, the operators themselves (+ and minus) can also be
>represented as binary....
New term, again, 'operator' introduced here. It does have precise
meaning in some contexts, such as in "operator calculus," for example.
Or, as in "unary operator," "binary operator," and "trinary operator"
in compiler parsing, for example.
If the author is instead talking about algebras that define addition,
an additive identity, that additive inverses exist (which, when added,
result in the additive identity -- in other words, the set S includes
additional elements that when added to their inverse elements in set S
result in the additive identity symbol), then this concept of
'operator' is merely a "binary operator" in a group.
I'd recommend reading:
http://mathworld.wolfram.com/Group.html
http://mathworld.wolfram.com/Ring.html
http://mathworld.wolfram.com/Field.html
http://mathworld.wolfram.com/AbstractAlgebra.html
At a minimum. Plus some follow-up with general group and field theory
books.
>Therefore and because binary is a NUMBER, then it can have "fractional
>binary numbers"
Um.... Yes. There exist "fractional binary numbers" in the sense
that rational fractions of binary numbers can be defined. But not
because of the logic used above. Merely saying, by fiat, that "binary
is a number" doesn't cut it. One could say that "decimal is a number"
too. In fact, that could be said of any representation. But saying
so doesn't lead inevitably to the idea of "fractional ... numbers."
That occurs by careful definitions in mathematics defining certain
sets. The above "therefore" clause is NOT used by mathematicians to
get there, either.
>Because a binary number is self-referencing in logic,
No. It is not. The concept of various sets of numbers themselves are
founded upon simple axioms in mathematics and logic. A binary number
is a representation! It is NOT a number, per se. At least, I can't
get there from the author's above logic, anyway.
Not accepted!
>so you'd have...
>(0.9+on) is equal to
>+1 on.
I've thoroughly confused at this point.
>+0.9 = +1 (and/or?) +0.9 (not sure hence the "?")
>-0.9 = -1 (and/or?) -0.9 (at same time?)
I'm still confused.
>Which is strange but it works...
If the author is confused <<hence the "?">>, I'm not sure why the
author now concludes "strange but it works." I remain confused and
don't find that it works. 'Strange,' yes. 'Works,' I've no idea.
>so "binary operators"? are a 'superset-operator'?
By "superset operator" does the author mean an operator on some
superset, hitherto undisclosed?
>that is close or
>near energy equivalent to energy in some way?
Hmm????? How did energy get into the discussion?
I think the author is sorely conflating a lot of ill-understood words
into a conceptual mush -- a Gordian knot that cannot be easily undone.
>it makes my brain
>hurt... anyone who can clear this up would be appreciated.
There is irony here!
>It seems a boolean number contains a NUMBER and a VECTOR inside the
>number, and then also a "frequency" (i.e. part-on, part-off.... +0.6 =
>+1, (and/or) +0.6 (because it's a fraction of binary can be
>represented by binary, since it is a fraction of itself!)
>
>so +0.6 is actually a binary number it would be like... a voume for
>"yes" (I am sort of yes, very yes, extremely yes(on/in-direction),
>etc).
I wouldn't know where to begin. One could define a particular
representation of a number as a vector of boolean numbers, I suppose,
and call that a 'binary representation of numbers.' But that is just
me struggling to help extricate the author's use of various terms I
think are actually ill-understood and I have little hope that at this
stage this poor attempt on my part is of any real use.
Jon
_________________
Time flies like an arrow. Fruit flies like a banana.
11 Nov 2007, 6:52 am
