h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

<> P-C

Well, that's not how the Greeks did it...

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So what is it then? Maths is the study of patterns, and this is one which is all around us...


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IIRC, pi would be a transcendental number whatever the units of reckoning, nothing to do with being an imported numbering system.


PS, one thing about pi which baffles me: if you look at the straight-line distance between the source of a river, and its mouth, and multiply it by pi, you get the actual length of the river. This is just an aside, but I find it fascinating.

Another fun fact about pi, turning up in the darndest places:

If you take all the perfect squares - 1, 4, 9, 16, 25, etc., and look at all their reciprocals - 1, 1/4, 1/9, 1/16, 1/25, etc., and add up all infinity of them :

1 + 1/4 + 1/9 + 1/16 + 1/25 + . . .

And then multiply the sum by 6, you get pi squared!

Traveller in Time fractalised
"It happens the fractal dimension of a river has pi in it.


Something I missed in previous pages:

'Fractals'

Any real life object fails to be accurate described by mathemathics if you look in close detail, a flat and smooth surface is not a plane, it has bumps and ridges. a fractal dimension of the plane as a way to say it. < A425972 > and < A2811502 >

How can something so near to us have such infinite dimensions ? "

PC:

P7:

Didn't they construct circles, for the purpose of measuring them? I was just trying to make the point that 'circularity' is an attribute we can detect and derive from the natural world, without the need for man-made props.

PC:

P7:

It's a ratio; no more or less than that. It's a relationship that we prefer to frame in terms of simple arithmetic. I think you're over-stating your case to describe a ratio as a pattern, don't you? And it's only "all round us" if we choose to derive and 'see' it. The pi-ness, the circularity, are our (map-based) perceptions laid over a natural world that just is.

Pattern-chaser

"Who cares, wins"

<<'Fractals'
Any real life object fails to be accurate described by mathemathics if you look in close detail, a flat and smooth surface is not a plane, it has bumps and ridges. a fractal dimension of the plane as a way to say it.>>

I think Pc asked earlier why we need to distinguish map from territory. This is one reason. That the territory is more intricate than the map.

He also asked if my contention that the territory consisted of rules was faith based. Yes it is, in the sense that it can't be proved. But if the map is actully to be map of the territory, information has to get from t to m without being randomised.

Noggin

<[PC] also asked if my contention that the territory consisted of rules was faith based.>

Actually that was GTB, so I don't mind, but he'll be insulted!



Interesting point: does it? In our example - where the M is someone's world model, and the T is the (allegedly ) real world - I start my reasoning with the axiom that the 'true' nature of T is unknown and unknowable, but our perceptions give us a usable approximation.

This being the case, one way of creating good Ms might be to generate (and then mutate) them randomly, then use the resulting Ms to navigate the real world. By discarding the under-performing Ms, after only a few centuries, our Ms would start to show signs of being distinctly useful! All without a direct information-connection between T and M.

How about it, Noggin?

Pattern-chaser

"Who cares, wins"

If there is no information exchange between T and M, no impingement, then in what sense does T exist?

On the other hand the "programs" that translate that information into maps (or one might say transform patterns of cause and effect into information) do mutate, the unsuccessful mutations are weeded out, and we get better (more useful) maps.

Noggin

As a probability on the basis of many long-term perceptions (known not to be objective)?

Pattern-chaser

"Who cares, wins"

Y'know all that druid wisdom's going to get dislodged, and drop out of your ears, if you carry on like that, Math.

Pattern-chaser

"Who cares, wins"

Why the second bang, drood? Did the bullet miss your head the first time?

What wisdom?

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But what is a perception if no informtion goes from t to m, and what is navigation if no information goes from m to t?

Noggin

Anyone fancy a pint....?

Got a already, thanks. You can probably tell....

Noggin

<> P-C

Why so? Is there some particular reason why this should be the case, or is that just a preference?

Our perceptions, the only means we have to receive information from the outside world, if there is such a thing, have been shown over and over again to be imperfect. Thus it is correct to observe that the 'true' nature of the real world is unknown and unknowable. I think it is reasonable to assume, based on our own experience of life, that our perceptions, despite the imperfections, give us an approximate and usable impression of what's out there. But this cannot be proven. So, in the name of honesty, I declared all this as axiomatic to my philosophy.

Do you see a flaw in my reasoning, P7?

Pattern-chaser

"Who cares, wins"

There is no means of transmitting information between the two without corruption (that I know of). But this does not mean there is no information transfer. It means that communication is limited by this corruption.

A perception is an observation that is probably, but not certainly, accurate. Navigation is finding your way around the real world. If you fail, at least you know you've failed!

Pattern-chaser

"Who cares, wins"

<>

You seem to have shifted the discussion slightly Pc. I was responding to a suggestion of yours that the map w*could* be updated by internal mutations, which if you got lucky would come to correspond better to the territory, without information transfer. My point was essentially that you couldn't test for better congruence without information transfer (in both directions).

An absence of such transfers altogether would result in a situation where t did not in fact exist, and the world consisted only of m.

Noggin

There is a good test of whether a discussion is going anywhere. You can examine whether opposite outcomes differ in their implications.

'If A then B....But if C then D'

So...what's this map/territory malarkey about again?