Where would one be on the number line when you reached Skewes Number?

Have you heard of Graham's number? It is the biggest number ever obtained as part of a mathematical proof (see Guiness Book of World Records).

It is the upper bound solution of a exotic problem in Ramsey Theory. Ramsey Thoery asks questions such as , 'Can order be found in what apepars to be disordered?' If so, how much order would be found and how much disorder is needed for local order to be found ? To get a notion of this question, toss a dice several times (ie., 50). Look at the list of numbers you obtained. Within that list you see localised structures (ie., three sixes in a row) but no overall structure. However, a six-sided dice is a very constrained environment for random behaviour. Ramsey theory is concerned with much bigger systems. (Ramsey died aged 26 after a bout of jaundice; his brother was Archbishop of Cantebury from 1961-74).

The problem explored what was the smallest dimension n of a hypercube such that if the lines joining all pairs of corners are two-colored, a planar complete graph of one colour will be forced. This can be put in a plain language as 'Take any number of people. list every possible committee that canc be formed from them, and consider every possible pair of committees. How many people must be in the original group so that no matter how many assignments are made, there will be four committees in which all the pairs fall in the same group, and all the people belong to an even number of committees?'

The upper bound of the solution is Graham's Number, which is so large it can only be written in Knuths' up-arrow notation. If Graham's number was written in conventional digits then there would not be enough ink even if the materials in the whole universe was turned into ink !

I got the above information from,

Darling, D. (2004). The Universal Book Of Mathematics. Wiley & Sons.
Wells, D. (1997). The Penguin DIctionary of Curious and Interesting
Numbers. Penguin.

GRAHAMS

In the hypercube problem referred to in my previous comment the upper bound of the solution was Graham's Number. However, Gardner (Martin?) quotes experts as saying that the most likely solution was 6.

SKEWES

Returning to Skewes Number, Wells talks about the number arose (in 1933) because of theoretical predictions of how the frequency of prime numbers changes as n increases. G.H. Hardy a famous mathematician of the time said that Skewes number was the largest number that was useful in mathematics. Hardy suggested that if all the particles in the universe were used as chess pieces in a game that finished when the same position occurred for the 3rd time, then the number of possible games would be about Skewes number

The above is taken from the book by David Wells.

A SUPER-LONG NUMBER LINE - I had to print it off.
It's a great number line - it raises some fascinating issues, scientifically and philosophically.

LEAVING THE EDGE OF THE GLOBE

What is the edge of the globe ? - obviously not like a cliff (assuming you're not a member of the flat earth society). So it must be a tangent leaving the earth's surface and going through the atmosphere slowly ascending through it.

But by this description what is meant by straight? If straight is relative to the earth's surface (ie., a plane flies in a straight line round the world) then you would never leave the globe (by angling it right & assuming a nanometre width the place on the number line when it reached the beginning again would be a monstrous number - & what if then the number line on the surface of the earth was wound like a ball of wool - at what number would it leave the atmosphere ? At what number would the line reach the moon - edge of the solar system etc.?

So straight here is not relative to the earth. But straight must be relative to something. Obviously not the solar system (because it would assume equal distance from the sun as a straight line on the earth is equal distance from the centre of the earth. Similarly at larger units of the universe. My solution is that straightness here is relative to the first nonmetres of your line. Hence straightness here is relative to the switch.

So the line leaves the earth tangentially.

THE SOLAR SYSTEM

Your numbers for the moon and planets amused me. I thought how kind God is to align the planets for the number line and ensure that each one was a million km from each other. I know the numbers are rounded and that the essential idea behind the numbers is to reflect the relative distances between the planets. (And of course, the distances between the planets varies given their orbits).

THE EDGE OF THE SOLAR SYSTEM

I guess the edge of the solar system is like the edge of the atmosphere .
There probably isn't one like there's the edge of the road. Or the edge of your house (but at macroscopic levels is there a clear border between the road & whatever is next to it / your house and the outside).

Presumerly, the gravitional pull just slowly peters out as you go further out into space. So imagine a spaceship going away from the sun at an angle where there are no planets. At different distances, the engine of the spaceship is turned off. Assumerly till some specific distance from the sun is reached the unpowered spaceship would fall back into towards the sun. And beyond that point the spaceship would simply float off into space. If I'm right then the edge of the solar system is going to relative to the weight / size of the spaceship.

So the edge of X , like the straightness of Y is determined by how we chose to define and measure it.

THE EDGE OF THE UNIVERSE

Can you have an edge of the universe. Surely an edge can only be defined if there is something outside it, or something touching it? Perhaps a safer notion is the edge of the visual / measurable universe. In that way, the edge is like the place on early maps where the mapping stopped (because the mappers had not gone any further).

I assume now the universe is considered to be rather like a plate (in contrast to ball-like). If it is like a plate then you are assuming your line is going out to the edge of the universe at a right angle to the edge (when it actually reaches it). If in contrast the angle is much shallower (ie., 0.000001 degrees) then the line might be considerably longer.

A further measuring issue is the direction that your line moves through space. Imagine your line starting somewhere between the centre and the edge of a plate. If you take the line straight to the edge then the distance to the edge will be much shorter than if you go through the centre of the universe.

Of course, the universe might not be like a plate. My book UNIVERSE - the definitive visual guide (DK 2005) says that the Universe might have no centre or edges and might curve in on itself. If so, the Universe would be something like a mobius strip - where a straight line following the curve of the strip would simply go round for ever (& be on both sides of the surface !). If the Universe is infinite in the sense it curves back on itself then assumerly your number line would never reach the end of the universe. The usual estimates of the size of the Universe is based on the minimal size should it be finite .

Now imagine a galaxy several million / billion light years from earth. Imagine you are travelling along the number line starting now (& the distant galaxy is observable from earth. It would have taken the light from the galaxy billions of years to get to earth and you (travelling at the speed of light) the same number of the years to get to the point in space where the galaxy is/ was.
But of course, the galaxy (1) may no longer exist and (2) would have moved if the universe is expanding. Imagining another scenario - the number line is coming out of a very powerful spaceship (& very tiny) as it travels through space. INtermittently a light shines back towards earth so we can estimate how far the number line has got by the time it takes the light to reach earth (assumerly, the length of time between paris of flashes will increase over time). So when the spaceship reaches the point where the galaxy is/was then it has travelled billions of light years. It then flashed it's light in the direction of earth (which of course may have moved or no longer exist) and so the light takes another few million/ billion light years to travel. UNders uch circumstances it would take the light 3x N light years for the information to get back to earth that the number line has reached the point since when the light we originally detected left earth.
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I gone on far too long so I better go and do some planning for next week at school. I teach severely intellectually disabled teenagers.

I guess that Kaisers don't have much else to do.

Assuming 11 zeroes counted a second then counting the lot would take approx. 28% of an hour (approx. 16-17 minutes). But this is assuming no loss of attention or lost of place. (& if Herr Kaiser had pre-grouped them (ie., in 3s; should this preparation be included in the count time ?)

Why Herr Kaiser would indulge himself in such an activity can not be ascertained with the present data.

Perhaps Herr Kaiser needs to find himself a Kaisership that is more demanding on his skills. And dare we ask about the preceding eleven C.Ws.

I must admit I have have a fascination with zeroes. When I can't sleep I count the zeroes on my bedroom walls, ceiling and on the inside of my eyelids (& I'm not telling you how they're lit or how they got there - it's my secret).

So relaxing with zero is not only for the Imperial Majesties of this Universe. And I'm not going to tell you where my country is. You'll just have to invade somewhere else.