Super discussion about negative numbers on the BBC
 

OK....

Now, this _*IS*_ a trick question:

You come across another entity. All you know is that this entity is
intelligent and capable of self-replication. The means are unnecessary
to this discussion. You are genetically identical to a garden spider as
compared to this entity.

How would you communicate? What concept is absolute across the entire
known universe?

Once you think about it, it becomes pretty obvious. Once you get over
that obvious concept, getting to numbers is even more obvious.

Hint: The concept is really-and-truly obvious.
Hint: It would be descriptive of a shared class of things.
Hint: Yes, any entity within the known universe would share this class
of things.

I am trying to be nice. And I am trying to make it your idea rather
than beating it into you. It is not hard to grasp once you get past a
couple of pretty tough concepts... the point of the above exercise.

Peter Wieck
Wyncote, PA

Super discussion about negative numbers on the BBC
 

wrote in message
oups.com...
OK....

Now, this _*IS*_ a trick question:

You come across another entity. All you know is that this entity is
intelligent and capable of self-replication. The means are unnecessary
to this discussion. You are genetically identical to a garden spider as
compared to this entity.

How would you communicate? What concept is absolute across the entire
known universe?

OK, so we can't assume it has any sense of sight, touch, taste, smell or
hearing. It may have no sense of self. It may have no spatial awareness.
Existing without an appreciation of time would be difficult for us to
understand but could be possible.

No, I'm stumped. I guess you might be thinking of the concept of an "object"
but that's tied up with spatial awareness, which our entity might not have.

Super discussion about negative numbers on the BBC
 

Rich Wilson wrote:
mega-snip

I give up.

This is good, Rich. Giving up the struggle, going with the flow, is a
good way to grasp mathematics once you arrive at the anti-intuitive.
I'm sure there is a little bottle of snake oil labelled Zen or Bushido
or something to account for it but it works in plain English too.

By the way, I'm Andre Jute. I started this thread a week or so ago.

Here's a thought experiment first devised by John Rawls, the Harvard
philosopher:

On a table behind a veil is a cake. How do you know the cake is there?
You don't. How do you know how many cakes? You don't. Your name is
Rich. You're standing outside the veil with Poor. He tells you there is
a cake behind the veil. You may choose to believe him or not. The fact
that he has a knife in his hand is irrelevant to your decision. If you
believe him, there is one cake, even if unseen. If you don't believe,
there is one imaginary cake, in his mind and maybe behind the veil as
well.

You raise the veil. There is a cake. How do you know there is only one
cake? Because there aren't two.

Poor suggests that one person cuts the cake into two parts behind the
veil and that the other person then chooses his part first. One person
cuts, the other person chooses.

What is the logic of this prisoner's dilemma game? It is in the
interest of the cutter to cut the cake into two equal pieces. (Unless
he's Hopi, but I throw that in just to show how well-read I am.)

All right. Poor cuts the cake behind the veil. The veil is lifted. The
cake is cut into two. You each take a piece. How many pieces are there
now? Two, of course, because you each have a piece and you are each an
individual person. Or two, because there is more than one. Or two,
because I tell you that the next number after one is two.

(Or just a single piece of cake because you are Borg without a concept
of more than one. But in that case you aren't there either, because
without numbers you won't build a pogo-stick, never mind a spaceship to
carry you here.)

Another possibility. Poor cuts the cake unequally. You choose the
bigger piece. The difference between your pieces is a negative number
by which his piece is smaller than yours. If you were to cut off half
that amount to equalize your pieces, it would be a negative number off
your cake and an equal positive number onto his cake, and both numbers
would be a real piece of cake.

Another possibility: Poor cut the cake equally but after you choose he
believes your piece is bigger. He even thinks he knows how much bigger
your piece is. The difference by which he imagines his cake to be
smaller is an imaginary negative number.

Cake size can be measured as weight or area on the cake plate. You can
take it from there. All this writing has made me hungry. I'm off to eat
my cake.

HTH.

BTW: Those numbers are in your hand. They're made of cake.

Andre Jute

Super discussion about negative numbers on the BBC
 

No, I'm stumped.

No, you are not. You are well down one of several paths to the correct
answer.

Peter Wieck
Wyncote, PA

Super discussion about negative numbers on the BBC
 

wrote in message
oups.com...
No, I'm stumped.

No, you are not. You are well down one of several paths to the correct
answer.

OK, are you thinking of "nothing"?

Super discussion about negative numbers on the BBC
 

"flipper" wrote in message
...
On Fri, 17 Mar 2006 00:38:56 GMT, "Rich Wilson"
wrote:


wrote in message
roups.com...
* "idea" isn't necessarily the right word there but I'm sure you see
what
I mean...

Amongst the almost uncounted thousands of English words, Idea is just
fine. And it is 'necessarily' the right word.

Accordingly, you trap yourself into necessarily-human concepts (no, I
am not going 'intelligent design').

That's EXACTLY what I was trying to get you to avoid... never mind.

Tree capillaries are nearly perfect
circles. Something dropped into still water causes near-perfectly
circular ripples which propagate based on pi-based relationships.
Molecules make up these circumferences and fit as perfectly as our
pen-or-ink efforts, or more-so. So, if nothing else, Nature understands
pi perfectly... and uses it. All the time. What humans did is merely
_describe_ it.

What you're saying there is that our current way of understanding the
universe, involving numbers, circles, ratios like pi and so on - is the
ONLY
way to understand it.

Not so. The 'real world' is the real world and our understanding of it
changes, hopefully in the direction of improvement, all the time.
That's how you have man not realizing pi exists and then discovering
it does. The nature of circles didn't change, man's understanding of
them did and pi existed whether man understood it or not.

I'll rephrase. You're saying there is exactly 1 way of thinking about the
universe that works and it's not possible that someone, somewhere could have
a totally different but equally accurate set of ideas. Because if they did,
how would you pick the one that was "real" and the one that was merely an
accurate theoretical model?


You would, presumably, deny that some other race or
species could start from scratch and come up with a totally different but
equally valid way of thinking about the world.

It doesn't matter how an alien would 'think' of it, the properties of
a circle are the properties of a circle. Whether we'd understand the
'language' they use to say the same thing is a different matter. And
we'd have just as much problem with their version of "apple."

I don't think you've quite got the gist of what I'm suggesting - it's not
different names for the same things, it's a different set of concepts that
you couldn't "pair up" with our own.


pi does not 'look the same' in binary, base 8 or base 16, as it does
in base 10 but it is still pi whether one says it in French or
Chinese.

OK, pi=pi however you write it. OK...

That's one reason why it's 'real', it is not 'just a concept'
and not an invention of the mind.

I could make up a number and argue exactly the same, and it would still be
made up.


That seems very unlikely to me.


By the way, I thought of a good analogy...

Your insistence that numbers exist is, to me, like insisting that numbers
are green. Or female. Or Welsh. The human brain lets us take a concept
like
colour from one type of object and stick it on to something else, whether
or
not it has any meaning in that situation.

And that is precisely what one can *not* do with mathematics because
it would contradict reality.

Alternatively you might invent something useful that way. For example, by
taking the idea of a square root and applying it to something that you
wouldn't normally apply it to, like -1.

Super discussion about negative numbers on the BBC
 

"Andre Jute" wrote in message
oups.com...

Rich Wilson wrote:
mega-snip

I give up.

This is good, Rich. Giving up the struggle, going with the flow,

I'm not giving up my belief, I just thought the argument wasn't worth
wasting any more of my life on!

is a
good way to grasp mathematics once you arrive at the anti-intuitive.
I'm sure there is a little bottle of snake oil labelled Zen or Bushido
or something to account for it but it works in plain English too.

By the way, I'm Andre Jute. I started this thread a week or so ago.

Hi, nice to meet you. Hope you don't mind us hijacking your thread!


Here's a thought experiment first devised by John Rawls, the Harvard
philosopher:

On a table behind a veil is a cake. How do you know the cake is there?
You don't. How do you know how many cakes? You don't. Your name is
Rich. You're standing outside the veil with Poor. He tells you there is
a cake behind the veil. You may choose to believe him or not. The fact
that he has a knife in his hand is irrelevant to your decision. If you
believe him, there is one cake, even if unseen. If you don't believe,
there is one imaginary cake, in his mind and maybe behind the veil as
well.

You raise the veil. There is a cake. How do you know there is only one
cake? Because there aren't two.

Poor suggests that one person cuts the cake into two parts behind the
veil and that the other person then chooses his part first. One person
cuts, the other person chooses.

What is the logic of this prisoner's dilemma game? It is in the
interest of the cutter to cut the cake into two equal pieces. (Unless
he's Hopi, but I throw that in just to show how well-read I am.)

All right. Poor cuts the cake behind the veil. The veil is lifted. The
cake is cut into two. You each take a piece. How many pieces are there
now? Two, of course, because you each have a piece and you are each an
individual person. Or two, because there is more than one. Or two,
because I tell you that the next number after one is two.

(Or just a single piece of cake because you are Borg without a concept
of more than one. But in that case you aren't there either, because
without numbers you won't build a pogo-stick, never mind a spaceship to
carry you here.)

Another possibility. Poor cuts the cake unequally. You choose the
bigger piece. The difference between your pieces is a negative number
by which his piece is smaller than yours. If you were to cut off half
that amount to equalize your pieces, it would be a negative number off
your cake and an equal positive number onto his cake, and both numbers
would be a real piece of cake.

Another possibility: Poor cut the cake equally but after you choose he
believes your piece is bigger. He even thinks he knows how much bigger
your piece is. The difference by which he imagines his cake to be
smaller is an imaginary negative number.

Cake size can be measured as weight or area on the cake plate. You can
take it from there. All this writing has made me hungry. I'm off to eat
my cake.

Yeah, good idea. And I'll have the other piece if there's any left.

What *was* the point of all that, by the way?


HTH.

BTW: Those numbers are in your hand. They're made of cake.

Super discussion about negative numbers on the BBC
 

OK, are you thinking of "nothing"?

Rich:

No, not hardly. Trick question... Trick Question.

Note the form of the question (trick). You know that the entity is
intelligent and capable of self-replication. From this, assume the
following:

a) The form you perceive (by whatever means) is organized in a way that
you see it as a definable entity. It may be a collective or a single
entity, but it is definable.
b) You see activity, material, evidence or results that show
self-replication. From replication one deducts self-awareness or
purpose. (Careful here, though. Don't mistake something like a crystal
growth process as self-replication.)
c) You also see activity, evidence or results that strongly suggest
intelligence. So, this entity will pass the Turing test. That making
the test mutually understandable may be difficult is beside the
point... right now.

Bottom line here. DON'T try too hard.

Having gone as far as the above three things (as they are assumed by
the form of the question): How would one communicate? Apart from magic?


You would start with numbers. 1.414..... starting in binary, and then
in any base as might fit. Any entity with mathematics would know this
number. Or, 3.1415.... and so forth. Numbers no good? Make patterns
that do not exist in nature. The pythagorean triangle with the squares
shown.

You are leaping in: Does this entity have eyes that (it) can see? Go to
c) above. Impinge onto that evidence. If you perceive it as
intelligent, that requires that you see what part of it shows such.
Affect that part with an obvious sign of intelligence (to you) and it
*might* be mutually discernable. Otherwise, try another impingement...
say there are a bunch of pins stuck in the ground in a line spaced at
some distance apart. Reverse or invert the pattern.

Obvious commonalities between any intelligent entities in the Known
Universe:

The periodic table. Oxygen on the Planet Widget in the Galaxy
Gezortenphlat is oxygen here.
Arithmatic. Two items here will remain two items there.
Spatial relationships. A Mobius Strip will be 100% the product of
intelligence wherever it might be found. As will be a Klein Bottle, or
a Tesseract.
Gas Laws.
And so forth.

Point being that if intelligence can be recognized, then communication
will be possible. The problem is in its recognition. Superficially,
ants and bees may be mistaken for intelligent. It is perhaps the case
that we will see either too much or too little when we view possible
intelligence outside ourselves. There was a time within the Catholic
Church when belief in possible 'other' intelligence was called the
"pathetic fallacy" and denied altogether within the natural world.

But, the properties of numbers exist independently of us. We describe
them and from that think we own them and that knowledge. But the
relationships of the sides of a right triangle as descibed by
Pythagorus existed before he described them, and will obtain any time
they are tested. The relationship between the circumference of a circle
and its diameter existed long before pi was described, and is also
immutable. One of the first obvious external indications of
'intelligence' is the use and understanding of these relationships.

What I meant by "being down the path" is that you have all the evidence
you need to initiate communications on any of several obvious plains
(another trick, when I 'suggested' in the original question only one
concept... I tried to give it away when I suggested 'several paths'.).
YOU KNOW THE ENTITY IS INTELLIGENT. So, work with that knowledge and
make changes in how you gained that knowledge. That is the means to
communicate.

Peter Wieck
Wyncote, PA

Super discussion about negative numbers on the BBC
 

Rich Wilson wrote:


That's one reason why it's 'real', it is not 'just a concept'
and not an invention of the mind.


I could make up a number and argue exactly the same, and it would still be
made up.


Going to regret this but...

Thats the point, pi isn't a "made up number", its a direct result of the
geometry of the universe we live in, it would have the same value at any
place in space, and any race that had the concept of the loci of a
moving point on a plain, and so the concept of a line and a circle,
would arrive at the ratio that is pi.

Just because you could make up numbers does not put them in the same set
as pi and a few others.



Alternatively you might invent something useful that way. For example, by
taking the idea of a square root and applying it to something that you
wouldn't normally apply it to, like -1.

Again, you are looking at it from the wrong side. All you are doing, is
taking the concept of a square root, and applying it to exactly what you
expect to apply it to, that is a number, no more, no less, the fact
that numnber is negative has no meaning to the mathematics, only to your
attempt to expect all matematical concepts to have a analog in what we
regard as reality. There is nothing different between 1+0i (square root
of 1) and 0+1i (square root of -1). They are both just different complex
numbers. It would make more sense if we called complex numbers just
numbers, and numbers with a zero imaginary part simple numbers.

--
Nick

Super discussion about negative numbers on the BBC