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Archive for June, 2010

We have just had a rather interesting budget from the LibCons, so I thought I would indulge myself with a little lucubration on economics.

Not long ago, the fiasco at Copenhagen highlighted a few cracks in the global community. All is not accord and conviviality amongst nations. The main problems appear to be distrust and vested interests, which have lead to a ‘them and us’ attitude for both individual nations and blocks of nations. No nation wants to give away too much without reaping at least as much benefit from it as everyone else, because otherwise their people might slip down the global wealth rankings and not be best pleased with their leaders.

This is sadly resonant of the Tragedy of the Commons, as are the recent attitudes of Canada et al regarding the arctic. Without a system of rewards and punishments, there is very little incentive for nations to conserve resources for the future. Indeed, the only incentives are to exploit now or hoard for later, depending on which will give the greatest economic advantage for the particular circumstances of the nation. Conservation and fair distribution are just not politically sensible in a world dominated by consumer-capitalist economic systems.

The budget today nodded towards a green economy, but no more than that. I think it is safe to say that the ensuing period of austerity and deficit reduction will banish any attempts at wholesale economic overhaul. So consumer-capitalists we will stay for the forseeable future.

Stuck with the current global economic system, we need rewards and punishments to tip the balance towards acting responsibly for the world as a whole, which means we need global environmental treaties. Such treaties appear to be focusing on emissions at the moment – caps of CO2 per country and technology transfer to allow this to happen – but this is treating the symptom rather than the cause. Emissions treaties are highly desirable in controlling climate change, with the fairest system possibly being a per capita global cap with sliding-scale reductions for wealth, but they will not be successful in addressing the tragedy of the commons. For this we need wider controls on consumption of resources.

It is very difficult to control consumption without changing the consumer-capitalist system we operate, or becoming unacceptably draconian. However, what can be done is to make rampant consumption unattractive. The easiest way to do this is to make it desirable to use renewable energy, to recycle waste and conserve natural habitats. There are many mechanisms for achieving this, but they ultimately boil down to economic necessity: keep your forests to make money, use fossil fuel to lose money.  

This will work very well if all the nations sign up to the necessary treaties, which is unlikely to happen without a lot more trust and cooperation. This leaves the option of unilateral action, such as border taxation. Is the EU strong enough to impose its vision of necessary action on the rest of the world? Can we tax carbon-intensive goods as they enter the EU? Probably not, but it is probably immaterial as the resulting conflict could be more damaging to the world than inaction. The climate is becoming less stable and resources dwindling, so any action that heightens international tension is probably a bad idea.

Is it possible to overcome the political impasse by private means? Can corporations lead where politicians fear to tread? Well, there is already the technical capability to convert the world to use 100% renewable energy, which is a start. This capability is also improving all the time due to scientific advances, but is it practicably possible or economically viable?

Some recent rough calculations suggest that wind energy is cheaper than nuclear power for the UK and that 2500km2 of solar panels could supply the UK with all its energy needs. The latter would be rather ridiculous as there are much more efficient ways to generate transport fuels and electricity in the UK, which brings us to the idea of a supergrid. This could distribute renewable energy across Europe and beyond, making the most of local power sources and evening out local gaps in production.  This makes renewable energy very attractive with incentives such as FIT or ROC, but without subsidies renewables cannot currently compete with fossil energy. Partially this is due to various subsidies (largely indirect) that fossil energy enjoys and partially due to the infrastructure, but as with all finite resources this will change.

The supply of oil and many important minerals is rapidly diminishing. The simple economics of supply and demand mean that these commodities will become more expensive. There will therefore become a time when it is cheaper to use renewable energy and recyclate than virgin minerals. The only problem with this is that resource consumption will probably increase as a proportion of reserves, so that volumes of sales remain high and revenue streams are maintained. This will keep sustainable practices on the fringes or requiring subsidies until the mineral resources become extremely scarce, at which point there will be insufficient time to build the necessary infrastructure to avoid production loss. This is turn will probably lead to civil dissatisfaction and international tension.

The nations or trading blocks that have promoted renewable energy, recycling and conservation will at that time be better able to continue production as they will have the infrastructure and social practice already in place. They will have far greater energy security and civil stability than those nations that build economic growth on mineral exploitation and do not invest in a sustainable society.

The greatest aim currently should be for international treaties to reduce resource exploitation, minimise climate changes and ready the world community for a sustainable future. However, this is currently unlikely to happen sufficiently robustly or soon enough to avoid damaging resource depletion. The private sector within the EU will not be able to change the block into a sustainable community without economic advantage or subsidies implemented by government. It may not be possible for the EU to impose tax burdens or other trade tariffs on resource-intensive imports, but this should not deter us from pursuing a sustainable European community within 50 years or so. This may reduce our competitive advantage in the short term, but it will lead to safe, equitable and comparatively comfortable future for all within our community. It can be done, but only with political will from our national and EU parliaments.

Unfortunately, that puts the burden back onto you and I. Only if we push our politicians to act, show them that we are brave enough to take some pain now so we can build a viable future, will they be able to lead us through such difficult changes.

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The paradoxes currently associated with infinity are only products of applying finite logic to describe infinity. Trying to understand infinity by analogies within the finite word are a bit like asking ‘what flavour is Buckingham Palace’? It’s absurd. To think about infinity one has to think within an infinite term of reference, as only this can lead to a sensible understanding of what infinity means. Once the true nature of infinity is understood, the paradoxes disappear but the very existence of infinity becomes questionable. Infinity and zero begin to look remarkably similar, although so far I have in no way managed to demonstrate the impossibility of infinity; it just seems a bit shaky from what I have so far thought. Further exploration by greater mind would be most appreciated – Prof Doron Zeilberger very kindly suggested I was on the right track, but had no time to comment further. Hey ho.
 
Here are some examples of infinitely erroneous logic.
 
1) ∞ + 1 = ∞
 
This is an absurd notion using finite logic to describe infinity.
 
Imagine the Grand Hotel, with an infinite number of rooms, each of which is occupied. This means that there must be an infinite number of people in the hotel. What happens when an additional person checks into the hotel? Does everyone just move up one room to accommodate them? After all, with infinite rooms there must always be more space to accomodate people, no?
 
The answer is don’t be stupid: nobody else can check in. Any infinite set of objects necessarily contains every single one of those objects that could possibly exist. Now, the hotel contains an infinite number of people, which means that every single person who can possibly exist MUST already be in the hotel. There can be nobody left outside the hotel to check in.

This is not just fatuous nit-picking and semantics, it is fundamental to the possible nature of infinity. It demonstrates that the only way to add to an infinite set of objects is to add an entirely different type of object. This would lead to the type of mathematical question ‘what do you get if you divide Buckingham Palace by a tomato?’ It’s meaningless.
 
∞ + 1 = a ridiculous idea
 
2) ∞ and ‘endless’ are the same thing
 
The Grand Hotel concept confuses ideas of ‘endless’ with infinity. Imagine that a person in Room 10 of the hotel is a notorious gangster and is tipped-off that the police are coming to get him. He has been told that the hotel is infinite, so runs out of his room and sprints down the corridor. He knows that in an infinite hotel he can keep running & running and never get caught until the end of time (assuming the police are not faster at running, of course). However, in his panic to get a head-start on the police, he turns the wrong way and quickly runs into the foyer, out the front door and into the arms of the police. What a nasty surprise!
 
The hotel is not infinite: as our gangster demonstrates the hotel comes to an end. It might go on for ever in one direction – ascending room numbers – but it ends at Room 1. The hotel would only be infinite if the rooms carried on under the numbers 0, -1, -2, -3…
 
It is possible that the corridor of rooms would loop back to the other side of the foyer, so that our gangster would run past Room 1 and straight to Room ∞, but the latter would have to be at the position of Room 0. ∞ & 0 are looking rather similar if ∞ is to make any kind of practical sense.
 
3) Different ∞s are different sizes
 
Cantor’s Diagonals apparently show that an infinite list of integers will be smaller than an infinite list of decimals. However, this is not possible and actually refers to large or endless sets of numbers, not infinite. The diagonal logic is fine apart from the beginning and end points. If the integers start at 1 and carry on for ever, they are not infinite as they also finish at 1. To be truly infinite, the list of integers MUST contain every conceivable integer including 0, -1, -2, -3…These numbers exist (I’ve just used them, after all) so they have to be in the list.
 
It is therefore impossible to pick a diagonal that has no integers (and corresponding endless decimal number) above it, so it is impossible to be sure that the new number made from such a diagonal is not represented above it. In fact, in an infinite list it MUST be represented.
 
The idea is:
      
  -forever
  .
  .
-100  0.8979878565657…
-99     0.9768543456788…
-98     0.3456789987654…
-97     0.089764390005…
.
.
1      0.4647448847464…
2      0.5775858493933…
3      0.4647438387464…
4      0.3758594837636…
.
.
+forever
 
0.4748…. can be changed to 0.5657….. and this number is unique for all decimals from 1+. However, there must be this decimal somewhere between 0 and –forever. There is no way to create a new diagonal that does not exist above the point at which the original diagonal starts, in this case ‘1’.
 
Therefore ∞=∞. All ∞s are equal.
 
It is interesting to note that the standard Cantor Diagonal concept has a non-infinite but endless number of integers, each one of which is paired with a decimal number, the expression of which can is infinite. They are simply numbers so have no dimension associated with them – no start or finish, just value. If the expression of this value involves an endless list of numbers, the lack of dimension makes this endlessness be the same as infinite (the expression of the number, not its value).
 
4) ∞ universe.
 
The idea of there being an infinite number of infinite universes comes from finite logic being used for infinity. The universe has direction, not just value, so to be infinite it has to be endless in all directions. This does not appear to be the case, as the universe appears to have started at the big bang. Or possible was just very finite at that point.
 
If the big bang was the start, a real singularity, then the universe cannot be infinite: it started at the big bang, which means it has limits in at least one of its directions and so is finite. Big I’ll grant you, but not infinite. I’m not sure it the finite nature of the big bang means that the universe is now finite, or if the universe could have changed from finite to infinite in the last few billion years – one to work on!

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