My prediction is this: If we could calculate Pi to tens of trillions of digits further we would see the far end digits shifting ever upwards away from 3.

My belief is that in the early universe before too much expantion (and therefore entropy) had occurred, Pi would have started at much closer to the number 3. But entropy slowly creeps the number further upwards as the universe expands and warps.

The universe is roughly 14 billion years old - Pi is 14 points off 3.0

Coincidence...? Perhaps not

Assuming that there are no ripples/waves (glassy conditions) on the river and it is flowing smoothly to the sea (key point is that it must be flowing), is the surface of the river completely level/flat, or does it actually have a slope towards the sea? If it does have a slope, how could you measure what gradient it is at any one point?

I am trying to take out the obvious by measuring the height above sea level the river surface is at one point and subtracting that from the sea level when it enters the ocean over a direct distance between those points....you can only absolutely confirm that there is indeed a gradient (best fit), but how would you go to a river at any point and measure what the gradient is, if it actually exists at that point at all?

I just finished reading New Scientist's article entitled "the hardest problem" (June 4, 2011). To me all of these NP problems (knapsack, traveling salesman, etc...) seem to have roots in evolutionary science-- in that they represent an optimal foraging strategy. So where better to look for a solution than in the computer simulation that's been running for the last 4 billion years (i.e. the natural world)? It seems like a fitness landscape of all possible combinations would be a worthwhile vein of research. Granted, computing every single combination would defeat the purpose of developing a formal solution. Therefore, like Dawkins if we imagine a fitness landscape and skirt the valleys (at least those that run too deep) and save our computing power for the higher ground it seems like a workable solution (though maybe no formal proof would present itself). In this sense maybe evolutionary algorithms (discussed in an earlier article on double pendulums and the fundamental laws of thermodynamics) would be the best approach. 

When I put large bed sheets in the tumble dryer they sometimes roll up into a ball and are still wet when the drying cycle has finished.Since smaller items do not seem to do this is there a threshold at which the area of the fabric gets too big for the dryer and rolls up? Would folding it a few times to make it smaller help and what effect would this have on drying time as if you fold it too many times this would have the same effect as it being rolled into a tight ball and it not drying properly? Has anyone devised a cunning method of putting their large sheets into the dryer that stops them from rolling up?Paul GaultNewcastle-under-Lyme, UK.

Having recently overheard my son and niece playing dare recently, i sat and listened to them 'one up' each other in the usual logical way: dare, double dare, triple dare etc...

eventually it came to 'i dare you times infinity', which was naturally followed by 'i dare you times infinity, plus one!'...

this got me thinking, i was always taught that infinity represented the ultimate highest number that could never be reached.. but, infinity plus one seems like a perfectly natural and logical mathematical equation.

If this IS a perfectly acceptable equation, then surely infinity must be finite? otherwise it would be equal to 'infinity plus one' which, is obviously one larger.

or is this a case of George Orwell popping his head into maths and science with 'All infinities are equal, but some infinities are more equal than others'?

Garderners question time :)

I am just about to lay a new lawn, it is 15 sq metres and i need to  level the ground by 8cm all the way round. I have ordered 1.2 cube of compost will this be enough, how do i work out the volume required???

Dictionary.com says a billion is "a cardinal number represented in the U.S. by 1 followed by 9 zeros, and in Great Britain by 1 followed by 12 zeros." It also seems it indicate that British definition is no longer used, although it's unclear on that.

Does a billion still represent two different numbers among scientists? If not, when did this change? Wouldn't older papers still use the old definition? Has this discrepency caused any practical problems in scientific projects--particularly in relation to astronomy and physics?

Cheers,

John

How many lottery tickets would have to be bought for there to be a >=50% probablility that every single possible combination has been chosen?  Or for smaller numbers how many people would you need in a room for there to be a >=50% probability that every day of the year is one or more of these people's birthdays?  

If these numbers are too large then how many people/tickets would be needed that there is a >=50% probability that >=50% of the lottery tickets/birthdays have been chosen?

Assume that birthdays and lottery tickets are chosen at random and not bunched, and forget about leap years to keep things slightly simpler.