Is the Board too wide?

[azrael86]

Historical battles were generally fought on infinitely large tables.

The number of infinitely large tables in the universe is of course zero.

[philqw78]

Surely if a machine started to build an infinately large table the number of infinately large tables in the universe would become infinite. Though it would be a small infinity. The universe having a larger infinity this must have already happened.

[timmy1]

Could one machine do it? Do you need an infinite number of machines to do it? Obviously a smaller infinity.

And before Nik says it, I know 'Tim is wrong'.

[philqw78]

Well if one machine did it for an infinite amount of time you would get the same sort of infinity as an infinite number doing it for a finite time. Then it depends when they started how big your infinity is.

But we only need a single infinitely large table. But it would take an infinite amount of time to build unless we had an infinite amount of builders. But then we would end up with an infinite number of infinitely large tables.

A bit of a quandry really. Perhaps we should just build one from shore to shore. Then let the naval gamers worry about infinity.

[dave_r]

Well if one machine did it for an infinite amount of time you would get the same sort of infinity as an infinite number doing it for a finite time. Then it depends when they started how big your infinity is.

But we only need a single infinitely large table. But it would take an infinite amount of time to build unless we had an infinite amount of builders. But then we would end up with an infinite number of infinitely large tables.

A bit of a quandry really. Perhaps we should just build one from shore to shore. Then let the naval gamers worry about infinity.

Infinity is infinitely big. Even a small infinity is infinitely big. If you take infinity and divide it by infinity, you still get infinity.

Therefore it would take an infinite amount of machines an infinite amount of time to make even one infinitely large table.

You lot has best be careful or Lawrence will get involved....

[philqw78]

Therefore it would take an infinite amount of machines an infinite amount of time to make even one infinitely large table.

You lot has best be careful or Lawrence will get involved....

No, an infinite amount of machines have made an infinitely large table already. Provided they have already started.
Also if the two infinities were the same, infinity divided by infinity would be 1. If they were not it would just be a smaller infinity.
So since the universe is infinite with infinite probabilities there are already an infinite number of infinitely large tables. Just, as I said, a small infinity, as it cannot be as big as they space they are put in. Which is infinitely larger. But if the size of that infinitely large space was divided by itself the answer would be one.

Dave is incorrect an infinite number of times.

[dave_r]

No, an infinite amount of machines have made an infinitely large table already. Provided they have already started.

Only if they started an infinitely long time ago.

Also if the two infinities were the same, infinity divided by infinity would be 1. If they were not it would just be a smaller infinity.

Nope, not in the world of mathematics. Infinity divided by Infinity is Infinity. Just like Infinity multiplied by Infinity is...... Infinity.

So since the universe is infinite

Nope, the universe is finite. If it wasn't, then it couldn't be getting bigger.

with infinite probabilities there are already an infinite number of infinitely large tables.

As mentioned, there aren't infinite probabilities. If there were then Heisenberg's uncertainty principle would declare that all bet's were off.

Just, as I said, a small infinity, as it cannot be as big as they space they are put in. Which is infinitely larger. But if the size of that infinitely large space was divided by itself the answer would be one.

But because infinity is infinitely large then something which occupies a space equivalent to infinity squared, could still fit in an infinitely large room. By definition there is no definition of the size of infinity.

Dave is incorrect an infinite number of times.

As is everybody in an infinite amount of time.

[philqw78]

Only if they started an infinitely long time ago.

No. An infinite amount of machines hold 1 plank each. When they fit them together they are an infinite number of planks. Therefore the table is infinitely large. This takes a finite time. They then get another plank and make another table. They have infinity and there are infinity of them so there are already an infinite number.

Nope, not in the world of mathematics. Infinity divided by Infinity is Infinity. Just like Infinity multiplied by Infinity is...... Infinity.

Wrong. You get larger and smaller infinities. They are not all the same size. So if you find one and divide it by itself the answer cannot be infinity.

Nope, the universe is finite. If it wasn't, then it couldn't be getting bigger.

Yes it could. Just like you can multiply infinity by infinity to get a larger infinity.

As mentioned, there aren't infinite probabilities

So if I rolled an infinite number of dice the probabilities would be finite then Dave?

[dave_r]

Only if they started an infinitely long time ago.

No. An infinite amount of machines hold 1 plank each. When they fit them together they are an infinite number of planks. Therefore the table is infinitely large. This takes a finite time. They then get another plank and make another table. They have infinity and there are infinity of them so there are already an infinite number.

But it would take an infinite amount of time to get an infinite number of machines to hold one plank each.

Nope, not in the world of mathematics. Infinity divided by Infinity is Infinity. Just like Infinity multiplied by Infinity is...... Infinity.

Wrong. You get larger and smaller infinities. They are not all the same size. So if you find one and divide it by itself the answer cannot be infinity.

They are all infinity. Infinity cannot be larger or smaller than infinity - they are all infinitely large. There are simply different types of infinity. If one infinity was bigger or smaller than another infinity, then by definition, one of them couldn't be an infinitely large number could it?

Nope, the universe is finite. If it wasn't, then it couldn't be getting bigger.

Yes it could. Just like you can multiply infinity by infinity to get a larger infinity.

As mentioned above - it isn't a larger infinity, it is merely a different infinity.

As mentioned, there aren't infinite probabilities

So if I rolled an infinite number of dice the probabilities would be finite then Dave?

No, there are an infinite amount of results.

The mistake you are making is that you are treating infinity like another number, which it isn't. Infinity is always an infinitely large number. Even when divided by infinity.

[gozerius]

Finis!

[peter777]

I agree that varying the board size would make for more interest, and smallewr boards might make foot armies viable.

Most 15mm competitions I play in have 6 feet by 4 tables. Largely, they do this because they were once DBM tables and that was the most common size (hence organisers have tables and cloths in 6 foot multiples). In DBM many troop types fought fine in a single rank plus the odd reserve. Hence filling th4 46 base widths of a 6 foot table was possible for many armies.

Most FoG troop types fight in two ranks to be effective hand to hand. So it's rare to be able to fill 6 feet of table width, hence there is frequently a fairly open flank. Of course, opinions will differ as to whether this is a good thing.

Since there will always be divided opinions on what the ideal table width would be, it might be interesting to see a competition where there were tables of different width (say 5, 6 and 7 feet), allocated randomly. That would test the skills of foot generals finding themselves in the open and mounted finding themselve in close terrain.

[mellis1644]

Isn't the point not what table is too big but what table size is too small.

If a table does not offer space for movement or allow for the possibility of open flanks or forces players into a line up and charge style game then it's too small. Movement as well as deployment and dice rolls should be key to playing a game. In the real world the table edge does not exist.

If trying to change the board size get a result between mismatched heavy foot and light horse armies, then to me that's trying to fix one problem with another. That does not work in the general case and likely just adds issues to the rules set. In these cases of total mismatched armies, other factors such as control of camps and/or of the board should likely decide winners of games if the armies/players can't do it themselves. However, in some non historical match ups the games just won't be good no matter what rules say...

[grahambriggs]

Isn't the point not what table is too big but what table size is too small.

If a table does not offer space for movement or allow for the possibility of open flanks or forces players into a line up and charge style game then it's too small. Movement as well as deployment and dice rolls should be key to playing a game. In the real world the table edge does not exist.

The issue here is that the 'standard' of 15mm on a 6 foot by 4 foot table evolved in previous rule sets. In FoG armies are somewhat narrower than other sets as many troops are better in multiple ranks. Of course very narrow tables would make it a game of head on clashes between power troops. I think the concern that has been raised is that 6 foot is too much the other way. You don't, after all, see much of a clamour for playing on wider tables.

The real world might not have table edges but most ancient and medieval battles were head on affairs nonetheless. Frequently this was due to terrain effects which effectively produce a table edge

[peter777]

A few comments.

I would be keen to try variable table sizes the next comp I run, it could be fun change. A mix of 6x4 and 5x4 to start with, the finals would be on 6x4 tables. I am happy to add some variability into the games, real world generals did not have the luxury of even fights on fixed battle sizes.

Even a narrow frontage battle or in a standup fight a general still needs to decide where to place his troops to get the best match ups.

And sometimes even LH armies had to make a stand to save a village or something else when the LH army could have ran away.

The other options of Themed comps are worth considering as well but mot comps in Australia are open book. Higher APs is another option but not all player can field armies above 800pts.

I think a 1 foot reduction in table width is a small change that would hardly be noticed in most games.

Peter

[gozerius]

Be aware that reducing the table size will affect how much terrain can be placed. You may need to alter the terrain laying rules accordingly.

[expendablecinc]

Be aware that reducing the table size will affect how much terrain can be placed. You may need to alter the terrain laying rules accordingly.

The net effect doesnt seem that great. We are playing a league with 5* 4 tables and 600 point armies (starter armies).

The proportion of table space to terrain size is reduced (ie a double sized villiage has a greater impact on available table space. However there is also a greater chance of pieces not fitting so people tend to select smaller pieces if they want terrain so they are more likely to remain on table.

It all seems to balance out. The exception is steppe armies with initiative but there are none in our league and generally not a lot of light horse around.
- Early Scots Isles and Highlanders
- Classical Greek
- Han
- Late Heian to Muromachi Japanese
- Mid Republic Roman
- Dominate Roman
- Later Seleucid
- War of the Roses

[azrael86]

Leaving aside the point that you can't have started infinitely long ago , as yo can only have started c.14billion years ago (before which time didn't exist)....

It seems evident to me that the table is too wide, and that the authors agree, as in Fog/R they have reduced the differential movement, increasing that of foot in many cases, and decreasing that of LH in particular.

Combined with the increased power of shooting it clearly is aimed at restricting the sort of gamey LH/LF/drilled MF/CV tactics that have become prevalent in FOG/AM. The obvious solution is to change the deploymentzones in AM from 10/15 to 12/18 or suchlike.

Although banning people called dave might be a viable alternative.

[bertalucci]

An infinity ago in this thread someone mentioned HF deployed in a single line across the board to stymie the flank attacks of LH armies.
And I've seen this tactic advocated elsewhere, by Roman Table Top Generals

Now that kind of totally unhistoric deployment really has to be stopped.

After all you picked which army and the troops you wanted to use!
PS I use Mongols and Alexandrians and Saxons and Romans and Cartheginians and ......

Board size is fine - but the victory conditions need looked at.

All sorted in FoGR

[dave_r]

Incidentally, the infinity thing went on and on and on and on, ad infinitum in fact. Here is how it went....

you will need to wait till tonight for the Bosphorans. But you do need to open your eyes about infinity. You have a very 1970's view. The below contains a cricket analogy so may be more acceptable to you. If you get bored see the comment I put in at the bottom before you delete.

"German mathematician Georg Cantor demonstrated in the late 19th century that there exists a variety of infinities—and some are simply larger than others.

Take, for instance, the so-called natural numbers: 1, 2, 3 and so on. These numbers are unbounded, and so the collection, or set, of all the natural numbers is infinite in size. But just how infinite is it? Cantor used an elegant argument to show that the naturals, although infinitely numerous, are actually less numerous than another common family of numbers, the "reals." (This set comprises all numbers that can be represented as a decimal, even if that decimal representation is infinite in length. Hence, 27 is a real number, as is π, or 3.14159….)

In fact, Cantor showed, there are more real numbers packed in between zero and one than there are numbers in the entire range of naturals. He did this by contradiction, logically: He assumes that these infinite sets are the same size, then follows a series of logical steps to find a flaw that undermines that assumption. He reasons that the naturals and this zero-to-one subset of the reals having equally many members implies that the two sets can be put into a one-to-one correspondence. That is, the two sets can be paired so that every element in each set has one—and only one—"partner" in the other set.

Think of it this way: even in the absence of numerical counting, one-to-one correspondences can be used to measure relative sizes. Imagine two crates of unknown sizes, one of apples and one of oranges. Withdrawing one apple and one orange at a time thus partners the two sets into apple-orange pairs. If the contents of the two crates are emptied simultaneously, they are equally numerous; if one crate is exhausted before the other, the one with remaining fruit is more plentiful.

Cantor thus assumes that the naturals and the reals from zero to one have been put into such a correspondence. Every natural number n thus has a real partner rn. The reals can then be listed in order of their corresponding naturals: r1, r2, r3, and so on.

Then Cantor's wily side begins to show. He creates a real number, called p, by the following rule: make the digit n places after the decimal point in p something other than the digit in that same decimal place in rn. A simple method would be: choose 3 when the digit in question is 4; otherwise, choose 4.

For demonstration's sake, say the real number pair for the natural number 1 (r1) is Ted Williams's famed .400 batting average from 1941 (0.40570…), the pair for 2 (r2) is George W. Bush's share of the popular vote in 2000 (0.47868…) and that of 3 (r3) is the decimal component of π (0.14159…).

Now create p following Cantor's construction: the digit in the first decimal place should not be equal to that in the first decimal place of r1, which is 4. Therefore, choose 3, and p begins 0.3…. Then choose the digit in the second decimal place of p so that it does not equal that of the second decimal place of r2, which is 7 (choose 4; p = 0.34…). Finally, choose the digit in the third decimal place of p so that it does not equal that of the corresponding decimal place of r3, which is 1 (choose 4 again; p = 0.344…).

Continuing down the list, this mathematical method (called "diagonalization") generates a real number p between zero and one that, by its construction, differs from every real number on the list in at least one decimal place. Ergo, it cannot be on the list.

In other words, p is a real number without a natural number partner—an apple without an orange. Thus, the one-to-one correspondence between the reals and the naturals fails, as there are simply too many reals—they are "uncountably" numerous—making real infinity somehow larger than natural infinity."

So there are some infinities bigger than others and this has practical use. Only the known universe is finite, since we 'know', it but the known universe contains infinite distances and probably other infinities, so is also infinite.

After you have waded through that I can also prove to you that infinity is finite and measurable, psssibly due to being finite and infinite at the same time. And I thunk this one up myself. Though someone clever has probably done it as well.

The main problem with this theory is that it is from the late 1800's. Which is before 1970? Therefore since my view is later it must be more correct?

If you could send the Bosporan list to my civvy address. I think if I can minimise the lancers and get a wodge of Armoured Light Spear Sword that is going to be the way to go.

OK then. Inifinity is finite and can be measured.
phil

No, it hasn't been proven. I presume all this is from Wikipedia?

If infinity could be measured then it wouldn't be infinite would it?

Wikipedia my arse.

And what do you mean it hasn't been proven, the mathematical proof is there to see.

To measure infinity:

Start with fractals. The distance around the coast of Britain is measurable. However, if we measure the distance around every grain of sand the distance becomes larger. If we then measure down to a molecular scale larger still. Untill we get down to a sub atomic scale where it becomes immeasurable, and therefore infinite. We know the distance around the coast of the Americas is larger, since it can be observed, it is then a larger infinity. But we can predict where the sub atomic particles are so we can predict the distance involved. So its finite and infinite at the same time.

But for even more proof on measuring infinity it takes exactly zero seconds to travel an infitite distance. Consider:

To any observer it takes an infinite time to travel an infinite distance. But when travelling at the speed of light time, for the traveller, does not exist. It therefore takes 0 seconds to travel an infinite distance. Therefore infinity has been measured.

I thought that last bit up. Though as I said someone else has probably done it as well
phil

Start with fractals. The distance around the coast of Britain is measurable. However, if we measure the distance around every grain of sand the distance becomes larger. If we then measure down to a molecular scale larger still. Untill we get down to a sub atomic scale where it becomes immeasurable, and therefore infinite

Just because we don't know what the value is that doesn't mean to say it is infinite - the coast of Britain has a specific definitive value. Even if we don't know what it is at a sub-atomic level.

But we can predict where the sub atomic particles are so we can predict the distance involved. So its finite and infinite at the same time.

This is 100% untrue. Heisenberg's uncertainty principle states that if we know where something is, we don't know how fast it is travelling. Similarly, if we know how fast something is travelling we don't know where it is. Therefore the distances cannot be calculated.

To any observer it takes an infinite time to travel an infinite distance. But when travelling at the speed of light time, for the traveller, does not exist. It therefore takes 0 seconds to travel an infinite distance. Therefore infinity has been measured.

This also is not true. Time exists for the traveller, just that for the non-traveller it appears that because the traveller is moving at the speed of light then logically they can exist in two places at the same time. Because the speed of light is known (186 000 miles per hour or 300 000 000 Metres per second) then if you are travelling to somewhere that is 372 000 miles away it will take two hours. Just to the non-traveller it will appear instantaneous. This sort of argument underlines why it is impossible to travel at the speed of light.

Also Heisenberg's uncertainty is used for the prediction. So you seem to be destroying your own arguments dave.
phil

Heisenberg's uncertainty principle simply states that it isn't possible to predict two givens that will make a known fact. If you know one then by definition you can't know the other.

Most people use the example of the position and speed of an electron as an example - if you know the speed of an electron then you can't for certain state where it is - simply have a percentaile guess at the best place.

Also you are stating it incorrectly. It isn't possible to know the position and velocity at the same time. It is possible to predict them though. Being more accurate in one reduces the accuracy of the other.
phil

That's exactly what I said!!!

Accuracy is very different to precision. You can have a fairly good guess at the position, but you can never be certain.

OK. I miss-read it. But use of quantum physics like this does not disprove larger and smaller infinities. It just adds to them.
phil

No, but it does disprove your theory that you can know at a sub-atomic level the circumference of the British coast, which you were saying is both finite at a macro level and infinite at a micro level. I merely put forward the arugment that it was not infinite, but that it was un-measurable at an atomic level.

But going to a sub atomic level makes new, very small, infinities. Since the bits that make sub-atomic particles are infinitely small if they are not touching they are in effect an infinity apart. It would take infinite magnification to see them. And we can see things billions of light years away without infinite magnification. So within an atom we have tiny infinities.

When you say infinitely small, what you mean is microscopic. Infinitely small is a paradoxical term, which doesn't actually mean anything in real terms.

You are still defining infinity in relation to each other - just because something is incredibly small, that doesn't mean that something which is huge is then infinitesimal compared to the microscopic thing.

[philqw78]

You missed one of my replies Dave. The one about travelling at the speed of light. To travel infinity does take zero seconds for the traveller at light speed (tiem in effect does not exist), but an infinite amount of time for the observer. Your answer to this was wrong.