Loren Pechtel

I would call it cheating, also--you're assuming an integer address space.

Farren

Aah, but mathematical solutions and schema's are not merited or demerited on their ubiquitousness. Its logical equivalence or inequivalence that determines the merit of a mathematical solution

Farren

I'd advise anyone who finds this reasoning dubious to bone up a little on Turing Machines and/or Lambda calculus.

Here is a starting point.

Essentially every mathematical computation known to man can be reduced to a Turing Machine. Conversely, one cannot build every possible computation from, say, the common or garden arithmetic operators ( "+", "-","x","\"). The Universal Turing Machine is the underlying formal grammar of all modern computations.

The kinds of "problems" plaguing binary negatives can, once reduced to this common form, be shown to hold functionally true for conventional representations of negatives.

In other words, as soon as we formerly encode, say, "-2000" with the kind of rigour with which we encode a 2's complement, 8-bit binary number according to a common encoding scheme, we are forced to make the "-" an operator, which would be encoded as a number, so "-2000", once truly formly encoded, might end up "102000", with the "10" being the negative instruction.

Another way of seeing this is to realise that the negative itself is an operator. The base encoding scheme only allows for positive natural numbers, and operations must be performed to yield reals, negatives and imaginary numbers. All operations are themselves encoded as numbers, and the processing schema determines what acts (10) and what is acted on (2000).

The 8bit 2's compliment schema I used appeared to differ slightly in the sense that the sign was pegged on the 8th column, but I can easily adopt a schema that demonstrates the functional equivalence to +-Number style notation by simply stating "the leftmost bit is always the sign bit", so that the number, like conventional notation, can expand to the left infinitely and have sign:

0101 -> positive
1101 -> negative

01101 -> positive
11101 -> negative

010101 -> positive
110101 -> negative

... and so on

Anyway, I'm not just being argumentative I'm bored and over and above the fascinating riddle this is kicking off all kinds of ideas in my head.

starling

I thought of another solution. How about the factorial of 0000 in base 1?

Base 1 to Base 10 could go:
(0 is 1)
(00 is 2)
(000 is 3)
(0000 is 4)

I just thought of a solution with only 1 zero! Pick up your phone, dial '0' and ask the operator to tell you the exchange prefix for Burlington, Iowa.

Then take the square root.

Starling

Farren

:notworthy

Pure Genius

Jayjay

(Haven't read anything but the opening post, so I'm probably making a fool of myself...)

Draw the zeroes on two lines like this:

0 0
0 0

which looks something like two eights. Wipe out the left half of the second eight, and there's an 8 and a 3. Add multiplication operator in the middle and you get

8*3=24

...or it could be something less stupid. This is just all I can think of.

EDIT: Reading thread. Factorial. Of course. Bah. :banghead:

TiredJim

Why do I take more joy in finding out that the catholic message board COULDN'T get the answer, than I do in having gotten it myself?

stretch

They did eventually. And heck, I'm on that board and I knew the answer. The answer is pretty obvious if you work with permutations and combinations on a regular basis. And an atheist colleague of mine who I was sure would get it right away, didn't.

Loren Pechtel

I would have gotten it if I had remembered that 0! = 1. I was thinking it was undefined. It's been too long.

Farren

Loren, I've gotta say to be gracious that for all my arguments, the "~" solution seems somethow categorically different, and certainly less elegant than the others, but I've convinced myself cos everything in math comes down to state machines for me.

I don't think it fits with the way the framers of the problem were thinking, at least

p.s. I've also noticed something interesting since engaging you on this thread. You're a late, late nighter, aren't you? Or do I have my time zones wrong?