[118991] in Cypherpunks
Re: [jestaff2@unity.ncsu.edu: Re: Square roots of nonsingular binary
daemon@ATHENA.MIT.EDU (Jonathan Stafford)
Tue Oct 12 11:21:37 1999
Date: Tue, 12 Oct 1999 11:01:13 -0400 (EDT)
From: Jonathan Stafford <jestaff2@unity.ncsu.edu>
To: cypherpunks@einstein.ssz.com
In-Reply-To: <19991012072804.A21034@einstein.ssz.com>
Message-ID: <Pine.SOL.4.05.9910121051000.7448-100000@eos00du.eos.ncsu.edu>
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Reply-To: Jonathan Stafford <jestaff2@unity.ncsu.edu>
On Tue, 12 Oct 1999, Jim Choate wrote:
>
>
> ----- Forwarded message from Jonathan Stafford <jestaff2@unity.ncsu.edu> -----
>
> Date: Tue, 12 Oct 1999 01:09:13 -0400 (EDT)
> >From: Jonathan Stafford <jestaff2@unity.ncsu.edu>
> Subject: CDR: Re: Square roots of nonsingular binary matrices (fwd)
>
> On Mon, 11 Oct 1999, Jim Choate, confused by odd binary math, wrote:
>
> > ----- Forwarded message from bill payne -----
> >
> > Date: Mon, 11 Oct 1999 20:42:55 -0600
> > >From: bill payne <billp@nmol.com>
> > Subject: CDR: Square roots of nonsingular binary matrices
> >
> > ...
> >
> > Let’s try it.
> >
> > 011 011 0 1 0
> > 111 111 = 0 0 1
> > 101 101 1 1 0
> >
> > Mission accomplished.
> >
> > ...
> >
> > ----- End of forwarded message from bill payne -----
> >
> > There's something wrong with your math...
> >
> > 0 1 1 0 1 1 2 1 2
> > 1 1 1 1 1 1 = 2 2 3
> > 1 0 1 1 0 1 1 1 2
>
> You missed the subject line...
> > Subject: CDR: Square roots of nonsingular binary matrices
> ^^^^^^
> This is binary, not normal math. And not even normal binary matrices.
> Usually, at least in the class I took, you use OR and not XOR:
>
> 011 011 abc
> 111 111 = def =
> 101 101 ghi
>
> a = (0 & 0) ^ (1 & 1) ^ (1 & 1) = 0 ^ 1 ^ 1 = 0
> b = (0 & 1) ^ (1 & 1) ^ (1 & 0) = 0 ^ 1 ^ 0 = 1
> ...
>
> The remainder is left as practice for the reader.
>
> ----- End forwarded message -----
>
> Thank you for falling into the dumbest trap I've seen in quite a while.
>
> God help us if this is how they teach Boolean Algebra now...
>
> Take your first line for example, the result is 1 not 0 as you and Bill
> Payne put it...
>
> 0 OR 0 OR 1 = 1
>
> This particular matrix becomes,
>
> 1 1 1
> 1 1 1
> 1 1 1
>
> When you replace multiplication by AND, and addition by OR as one does with
> binary matrices. If there is EVER a AND of two 1's on the OR'ing then the
> result is ALWAYS a 1.
Excuse me, but what the hell are you talking about? In your first post
you multiply the matrices as if they contain normal numbers. In your next
post you (supposedly) treat them like binary matrices, but I'm unsure
where you get 0 | 0 | 1 = 1 from (except perhaps the (3,1) element, but
why the hell would you be using that anyway).
If you use XOR (which I never thought was correct as you would have been
able to tell if you'd read my post) the (1,1) element is:
m[1,1] = (0 & 0) ^ (1 & 1) ^ (1 & 1) = 0 ^ 1 ^ 1 = 0
If you used normal binary math (probably should be written not as normal,
but as correct):
m[1,1] = (0 & 0) | (1 & 1) | (1 & 1) = 0 | 1 | 1 = 1
I do agree that under OR binary matrix multiplication the result is:
111
111
111
I never said that what Bill was doing was correct, I just explained it.
Jonathan
--
carry on underling
