[118989] in Cypherpunks
[jestaff2@unity.ncsu.edu: CDR: Re: Square roots of nonsingular binary matrices (fwd)]
daemon@ATHENA.MIT.EDU (Jim Choate)
Tue Oct 12 08:34:23 1999
Message-ID: <19991012072804.A21034@einstein.ssz.com>
Date: Tue, 12 Oct 1999 07:28:04 -0500
From: Jim Choate <ravage@einstein.ssz.com>
To: cypherpunks@einstein.ssz.com
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Reply-To: Jim Choate <ravage@einstein.ssz.com>
----- 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.
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