Hey Alexis
I like thought experiments like that. :-) Shame I won't be around to
see it beat 3^^^3. The distance from the earth to the sun is
approximately 150,000,000 Km = 1.5*10^11 metres, so 10^10 metres is
less than 10% of the distance but your point about the rapid increase
is still valid - 1, 10, 10^10 (=10,000,000,000),
10^10,000,000,000,... ?!
You'll find that not only does the acceleration increase, but the
rate at which it increases also increases. And the rate of increase
(of the rate of increase) also increases, and so on recursively.
I don't think we have a term for the step beyond acceleration. (I
think you know all this but for the possible benefit of anyone
else...) It's a bit like with maths - we have addition (eg 2+2) which
allows us to change the value of a number, then we have iterated
addition (eg 2+2+2+2) which we call multiplication (=2*4), and then
we have iterated multiplication (eg 2*2*2*2) which we call raising to
a power (=2^4). Beyond that there are terms for iterated powers and
so on that have been coined based on the fact that they are the 4th,
5th, etc in the series; thus: "tetration", "pentation", etc.
In a somewhat related manner, with motion we have distance which
allows us to measure a change in position (value), velocity = rate of
change of distance, and acceleration = rate of change of velocity. We
need a term for the rate of change of acceleration. How
about "tetrocity" which allows us to continue that thinking
through "pentocity", "hexocity", etc?
How about "skwiirol nut" which is skwiirol raised to the power of the
corresponding (K)nut(h) number?
Thus, with each recursion: 1^1, 10^(2^^2),
10,000,000,000^(3^^^3),...
My brain hurts...
Mark
--- In [email protected], "prokofiev2006"
<alexis.monnerotdumaine@...> wrote:
I like thought experiments like that. :-) Shame I won't be around to
see it beat 3^^^3. The distance from the earth to the sun is
approximately 150,000,000 Km = 1.5*10^11 metres, so 10^10 metres is
less than 10% of the distance but your point about the rapid increase
is still valid - 1, 10, 10^10 (=10,000,000,000),
10^10,000,000,000,... ?!
You'll find that not only does the acceleration increase, but the
rate at which it increases also increases. And the rate of increase
(of the rate of increase) also increases, and so on recursively.
I don't think we have a term for the step beyond acceleration. (I
think you know all this but for the possible benefit of anyone
else...) It's a bit like with maths - we have addition (eg 2+2) which
allows us to change the value of a number, then we have iterated
addition (eg 2+2+2+2) which we call multiplication (=2*4), and then
we have iterated multiplication (eg 2*2*2*2) which we call raising to
a power (=2^4). Beyond that there are terms for iterated powers and
so on that have been coined based on the fact that they are the 4th,
5th, etc in the series; thus: "tetration", "pentation", etc.
In a somewhat related manner, with motion we have distance which
allows us to measure a change in position (value), velocity = rate of
change of distance, and acceleration = rate of change of velocity. We
need a term for the rate of change of acceleration. How
about "tetrocity" which allows us to continue that thinking
through "pentocity", "hexocity", etc?
How about "skwiirol nut" which is skwiirol raised to the power of the
corresponding (K)nut(h) number?
Thus, with each recursion: 1^1, 10^(2^^2),
10,000,000,000^(3^^^3),...
My brain hurts...
Mark
--- In [email protected], "prokofiev2006"
<alexis.monnerotdumaine@...> wrote:
>nearly
> Mark, your sqwiirol gives me an idea. It's certainly not a number
> since it doesn't have a precise and constant value but it can be a
> good unit of measure. (I keep on thinking about how big 3^^^3 is).
> Imagine the sqwiirol as a spaceship that accelerates according to
> his iterated definition:
> Every second the sqwiirol travels 1 with a sqwiirol zeros meters.
> - At second 1 the sqwiirol has travelled 1 meter
> - At second 2 the sqwiirol has travelled 10 meters
> - At second 3 the sqwiirol has travelled 10^10 meters, that's
> the distance to the sun. In between, the sqwiirol has surpassed thewhich
> speed of light.
> - At 3.0000001 seconds or so the squiirol has already reached the
> other side of the universe ! Beyond that point, talking about
> distance is useless. It surpasses also the number of particules in
> the universe then the googol (10^100) in a blink of an eye. This
> gives small idea about how big the acceleration of the sqwiirol is.
> It's not just constant acceleration but a gigantic exponential
> acceleration.
> - Just after 4 seconds, the sqwiirol surpasses the googolplex,
> is 10^googol.(3^
>
> So, with that fantastically growing acceleration, how long will it
> take for the sqwiirol to surpass 3^^^3 ?
> Just consider the sqwiirol reaching 3^^^3 and let's play the film
> backwards:
> - 1 second before, the sqwiirol equaled log10(3^^^3) = 0,477 * (3^
> (3^�&3))), where 3 is repeated 7,625,597,484,987-1 times
> - 2 seconds before, the sqwiirol equalled :
> log10(0,477 * (3^(3^(3^�&3))), where 3 is repeated
> 7,625,597,484,987-1 times)
> = log10(0,477) + log10((3^(3^(3^�&3))), where 3 is repeated
> 7,625,597,484,987-1 times)
> the first term, log10(0,477), is so small, considering the second
> one, it can be neglected.
> So, 2 seconds before, the sqwiirol equalled 0,477 * (3^(3^(3^�&3))),
> where 3 is repeated 7,625,597,484,987-2 times.
> The iteration then becomes simple, 7,625,597,484,987 seconds are
> needed.
>
> => The sqwiirol surpasses 3^^^3 after 241,640 years !
>
>
> Alexis (spending his precious time in frivolous calculations).
>
>
> --- In [email protected], "Mark" <secret.squirrel@> wrote:
> >
> > There you are. Thought you were dead!
> >
> > In the spirit of "googol" I've made up my own number. I've called
> it
> > a "skwiirol" which is a really good name.
> >
> > It's defined as "1 followed by a skwiirol of zeroes". The best
> thing
> > about it is that it is recursive - the more you try to work out
> how
> > many zeroes it actually has, the bigger it gets!
> >
> > So its reality (or state) is defined by the observer and the kind
> of
> > observation they do - very much like as it is with quantum
> physics.
> > It also obeys Scheissenberg's Uncertainty Principle: "Um, I'm not
> > really sure how big it is". However, it is known to be large
> enough
> > to have a black hole in the middle of the central "0".
> >
> > Mark
>