Stephen Gloor

Brendan Nelson Deviates From the Script on Iraq

For the first time one of the players in Iraq has accidentally (I hope) deviated from the script that was made up when no weapons of mass destruction were found in Iraq.

Brendan Nelson, the Australian Minister for Defence, has actually said that Australia's deployment in Iraq is about securing oil supplies:

Mr Rudd says the statement is a clear backflip on what the Howard Government said when the Iraq war started.

"Mr Howard makes it up as he goes along on Iraq," he said.

"Mr Howard was asked back in 2003 whether this war had anything to do with oil. Mr Howard said in no way did this have anything to do with oil. This government simply makes it up as it goes along."

But Dr Nelson says that when it comes to Iraq, Australia needs to support its allies, stop Al Qaeda securing a foothold, and secure oil supplies.

"There are many countries, including developing countries which rely substantially on energy supplies from the Middle East," he said.

Yes Mr Nelson, there are a lot of countries dependent on ME Oil its just that whenever anybody asked previously whether this war was about oil it they were treated with contempt for even contemplating such a thing even though anyone with half a brain could see that it was.  I even got a spat from Bolty for having the temerity to suggest that maybe the invasion of Iraq had something to do with oil.

Perhaps Mr Nelson needs another visit to the USA to have his chip adjusted - it obviously needs a service for allowing this slip through.

The Many Problems of the Canadian Oil Sands

Our addiction to oil is causing havoc as we desperately find 'alternatives' to oil rather that bite the bullet and accept that maybe our cars are unsustainable as maybe we cannot zoom as fast as we can, anywhere we want, anytime we want.  The operative word here is WANT.

Anyway this is a report on the environmental destruction of the Canadian Oil Sands.

The development of Canada's oil sands is laying waste to its great northern forest and western plains, say critics who point to skyrocketing greenhouse gas emissions, diverted rivers and razed backwoods. And the devastation can only get worse, they say, as energy companies pump billions of dollars into new projects to triple local oil production to some 3.0 million barrels per day within the next decade.

As the report says this is pretty crazy stuff for a barrel of oil.  Not to be outdone we are now running down our foodstocks to make fuel for our beloved SUVs.

So far in Britain we have been insulated from the early effects of these price rises by the competitive nature of our retail system. But the supermarkets cannot shield us for long. The European Commission no longer has reserves to help cushion its citizens. Its mountains of unsold butter and meat and its lake of powdered milk have disappeared after reforms to the Common Agricultural Policy.

Then there is corn. While relatively little corn is eaten directly it is of pivotal importance to the food economy as so much of it is consumed indirectly. The milk, eggs, cheese, butter, chicken, beef, ice cream and yoghurt in the average fridge is all produced using corn and the price of every one of these is influenced by the price of corn. In effect, our fridges are full of corn.

In the past 12 months the global corn price has doubled. The constant aim of agriculture is to produce enough food to carry us over to the next harvest. In six of the past seven years, we have used more grain worldwide than we have produced. As a result world grain reserves - or carryover stocks - have dwindled to 57 days. This is the lowest level of grain reserves in 34 years.

The reason for the price surge is the wholesale diversion of grain crops into the production of ethanol. Thirty per cent of next year's grain harvest in the US will go straight to an ethanol distillery. As the US supplies more than two-thirds of the world's grain imports this unprecedented move will affect food prices everywhere. In Europe farmers are switching en masse to fuel crops to meet the EU requirement that bio-fuels account for 20 per cent of the energy mix.

Ethanol is almost universally popular with politicians as it allows them to tell voters to keep on motoring, while bio-fuels will fix the problem of harmful greenhouse gas emissions. But bio-fuels are not a green panacea, as the influential economist Lester Brown from the Earth Policy Institute explained in a briefing to the US Senate last week. He said: "The stage is now set for direct competition for grain between the 800 million people who own automobiles, and the world's 2 billion poorest people."

Already there are signs that the food economy is merging with the fuel economy. The ethanol boom has seen sugar prices track oil prices and now the same is set to happen with grain, Mr Brown argues. "As the price of oil climbs so will the price of food," he says. "If oil jumps from $60 a barrel to $80, you can bet that your supermarket bills will also go up."

In the developed world this could mean a change of lifestyle. Elsewhere it could cost lives. Soaring food prices have already sparked riots in poor countries that depend on grain imports. More will follow. After decades of decline in the number of starving people worldwide the numbers are starting to rise. The UN lists 34 countries as needing food aid. Since feeding programmes tend to have fixed budgets, a doubling in the price of grain halves food aid.

Obviously it is far more important to satisfy our wants than to satisfy starving people's need.

All this so we do not have to put up with boring electric cars that only go 200 km on a charge.  Fancy that not being able to drive 600km on a whim without recharging on the way.  Gee that's bad isn't it.

Very Interesting Article on Iraq

With Peak Oil approaching perhaps invasions of countries for oil will become commonplace.  The invasion of Iraq had nothing to do with any of the stated aims and we were a big enough sucker to go along with it. 

                                                Shame Howard Shame.

The Labor Party's policy to withdraw troops from Iraq is not 'cut and run' or cowardly.  It is a realisation that we killed thousands of innocent Iraqis, thousand of troops from both sides and spent trillions of dollars to secure the profits of large oil companies.

Try reading this article from Alternet and see if you feel the same way about the invasion of Iraq.  Some quotes:

raq is sitting on a mother lode of some of the lightest, sweetest, most profitable crude oil on earth, and the rules that will determine who will control it and on what terms are about to be set.

The Iraqi government faces a December deadline, imposed by the world's wealthiest countries, to complete its final oil law. Industry analysts expect that the result will be a radical departure from the laws governing the country's oil-rich neighbors, giving foreign multinationals a much higher rate of return than with other major oil producers and locking in their control over what George Bush called Iraq's "patrimony" for decades, regardless of what kind of policies future elected governments might want to pursue.

and

Of course, the plans for Iraq's legal framework for oil have to be viewed in the context of the overall transformation of the Iraqi economy. Clearly, the idea was to pursue a radical corporatist agenda during the period of the Coalition Provisional Authority when the U.S. occupation forces were a de facto dictatorship. And that's just what happened; under L. Paul Bremer, the CPA head, corporate taxes were slashed, a flat-tax on income was established, rules allowing multinationals to pull all of their profits from the country and a series of other provisions were enacted. These were then integrated into the Iraqi Constitution and remain in effect today.

Among the provisions in the Constitution, unlike those of most oil producers, is a requirement that the government "develop oil and gas wealth … relying on the most modern techniques of market principles and encouraging investment." The provision mandates that foreign companies would receive a major stake in Iraq's oil for the first time in the 30 years since the sector was nationalized in 1975.

Herbert Docena, a researcher with the NGO Focus on the Global South, wrote that an early draft of the constitution negotiated by Iraqis envisioned a "Scandinavian-style welfare system in the Arabian desert, with Iraq's vast oil wealth to be spent upholding every Iraqi's right to education, health care, housing, and other social services." "Social justice," the draft declared, "is the basis of building society."

What happened between that earlier draft and the constitution that Iraqis would eventually ratify? According to Docena:

While [U.S. Ambassador to Iraq Zalmay] Khalilzad and his team of U.S. and British diplomats were all over the scene, some members of Iraq's constitutional committee were reduced to bystanders. One Shiite member grumbled, "We haven't played much of a role in drafting the constitution. We feel that we have been neglected." A Sunni negotiator concluded: "This constitution was cooked up in an American kitchen not an Iraqi one."

With a constitution cooked up in D.C., the stage was set for foreign multinationals to assume effective control of as much as 87 percent of Iraq's oil, according to projections by the Oil Ministry. If PSAs become the law of the land -- and there are other contractual arrangements that would allow private companies to invest in the sector without giving them the same degree of control or such usurious profits -- the war-torn country stands to lose up to 194 billion vitally important dollars in revenue on just the first 12 fields developed, according to a conservative estimate by Platform (the estimate assumes oil at $40 per barrel; at this writing it stands at more than $59). That's more than six times the country's annual budget.

All done in the name of democracy - it leaves a bitter taste in the mouth doesn't it?

Peak Oil in a Nutshell

I read this article on the ABC news site.  It is about the NRMA forseeing $1.80/litre petrol.  The thing that caught my eye was this:

However, metropolitan motorists who are baulking at the prospect of paying a possible $1.80 a litre for petrol should consider those living in the Torres Strait, where residents on the outer islands are already paying $2.65 a litre.

Fuel prices affect everything in the Torres Strait.

Diesel powers electrical generators, desalination plants and the barges that bring fresh food to the remote islands.

Dennis Wong is selling diesel for $2.49 per litre on Murray Island and unleaded for $2.27.

He says many local fisherman cannot afford to leave shore and if prices continue to rise he predicts people will not be able to afford fresh fruit and vegetables.

"Our freight prices for groceries have probably gone up about 20 per cent in the last three or four months," he said.

"There's nothing anybody can do about it except their way of life will just have to be curtailed and live in a third world sort of lifestyle.

"I think everybody's going to have to starve, I suppose."

Of course that is not what will happen however it really neatly summerises the Peak Oil problem in a very real way.  An isolated island completely dependant on imported fossil fuels could suffer if petrol and diesel become really expensive.

The problems the Torres Strait faces are exactly the same as we all face in the future.  Why do we think that we will be immune?

Problems With Getting Fossil Fuels

Let us hope that this does not happen ever again in our never ending quest for fossil fuels. This is from a news report on the ABC

Poisonous mud and gas is erupting from kilometres below the earth and 8,000 people are displaced and hundreds hospitalised on the Indonesian island of Java.

The calamity has been caused by a gas exploration project near Surabaya in East Java that has gone horribly wrong, and for the past six weeks, has unleashed hundreds of tonnes of hot toxic mud.

Indonesia's police are threatening to charge some of the drill operators with criminal negligence, with two Australian companies caught up in the row.

Oil and gas giant Santos is a minority shareholder in the venture, while the expertise of another Australian company - Century Resources - has been called in to try and halt the blow out.

Six weeks ago, a drilling rig on this site reached three kilometres underground and encountered a problem.

Attempts were made to shut the well, but then the earth opened up.

First, a major crack appeared and now they have appeared all around, spewing at least 500 cubic metres of toxic mud every day.

An area of 12 square kilometres has now been covered and four entire villages have been affected, displacing almost 8,000 people.

With more and more drilling going on in more and more marginal places this sort of thing might become more commonplace.  Let us hope that it doesn't.

Review of Peak Oil Program on 4 Corners

I watched the show and it was excellent.  Jonothan Holmes covered all the major players and produced a comprehensive view of the problems with Oil supply in the future.  The forum after was interesting as well.  A lot of my comments were moderated but anyway I got some posts in.

Probably the thing that most stood out was the blank looks on the panel from ABARE when Rachal Seiwart asked about Peak Oil.  Talk about the 3 wise monkeys.  When pressed the 'leader' said something like "If the price of eggs is high enough even the roosters will be laying them".  Just to refresh your memory ABARE is:

about abare                          

The Australian Bureau of Agricultural and Resource Economics (ABARE), located in Canberra, is an Australian government economic research agency noted for its professionally independent research and analysis.

Our objective is to contribute to the competitiveness of Australia’s agricultural, fishing, forestry, energy and minerals industries and the quality of the Australian environment by providing rigorous and independent economic research analysis and forecasting.

The bureau’s executive director is responsible for the research methods employed, the conclusions reached and the dissemination of results. ABARE disseminates the results of its research through the media, our web site, the national Outlook conference, regional Outlook conferences around Australia and many other speaking engagements. All information on our web site is available free.

So this government research agency, that has repeatedly said that oil will return to $30.00 per barrel soon, thinks that if the price is high enough market forces will magically create oil for us to use - such is the power of market forces.  This is so far from reality it makes me wonder what sort of bullshit is this agency feeding the Government.  Oh wait it is feeding it what it wants to hear - Oil is plentiful, global warming is a myth and coal and nuclear is good.

Now to another subject this is probably why Peak Oil is such a problem.  Read this article about electric cars.  Here are a couple of examples of the misinformed rubbish that automotive writers think.

To refresh your memory, the auto industry created many electric vehicles in its early days but abandoned them as soon as a superior propulsion system (the internal combustion, or IC, engine) came along. Primarily it was a question of cost and range, since batteries were expensive 80 or 100 years ago and couldn't hold enough of a charge to carry vehicles as far as their owners wanted them to go.

NO what happened is that a man called Kettering worked out a way to hook up an electric motor so that it could start the IC engine.  IC cars use the incredible and short lived energy density of petrol to get range despite being only about 15% efficient.

For the most part these vehicles were leased at low rates as part of a testing program, and the results were predictable to anyone who knew the technology and the behavior patterns of California buyers. Despite an enormous amount of publicity and the best intentions in the world, they did not catch on. People were afraid that EVs wouldn't get them where they wanted to go and back, and they were right to worry, particularly in the LA area where nowhere that you need to go ever seems to be close.

To the surprise of almost no one, the EV1 and all of the other electric vehicles failed, and the whole idea of forcing them into the dealerships where they wouldn't be bought died on the vine.

In order to protect the public and reduce their legal liability, the car companies decided to get their EVs and their dangerous batteries off the road, which is what GM and the other companies did, before destroying them in the way that most concept and test vehicles are destroyed -- by crushing.

Absolute and complete bullshit.  The EV1 was leased to a few lucky individuals who to a person would have bought the car if GM had let them.  The batteries were not dangerous.  There was a huge waiting list for the cars and a desperate attempt was made to stop the cars being crushed from the people who supposedly had a 'bad' car they did not want.

Isn't funny how so many of the automotive writers rabbet on about range when time and time again studies have shown that 90% of car trips are well under 100km. These people are selling dreams rather than reality. I stopped even looking at car mags when they reviewed the latest Ferrari. Who can afford a Ferrari?

If you don't believe me about the average trip length have a look at this report

The Department of Infrastructure Planning and Natural Resources (DIPNR) (2003, p.2)
reports that the average daily VKT for residents of eastern Sydney was 21.8 km in 2003,
compared to 27.4 km for those in middle west areas and 54.6 km for those in the city’s outer west. The spatial trends in VKT growth are also uneven.

Why do we need cars that can go 500km when the average trip length is at the very worst 54km.  Why is a vehicles top speed important when it spends most of its life travelling at 20km/hr in traffic and is limited to 110km/hr on the freeways everywhere?

When are these people going to face reality?  This is why Peak Oil is a problem - cars have been sold as a dream and we do not want our dream shattered by hard facts.  We would much rather sleep-walk to disaster.

4 Corners Doing Show on Peak Oil

I just saw that 4 Corners is doing an hour show on Peak Oil.   Should be worth a watch.  I will add a critique at the end of this post after I have watched it.

Program Summary:

Peak Oil?

Reporter: Jonathan Holmes

Broadcast: 10/07/2006

"The price of petrol is disgusting, absolutely disgusting…"

"It’s just going up and up…"

"It’s outrageous…"

"I get so mad – you ever get so mad you can’t even talk about it no mo’?"

(Vox pops – motorists in Australia, UK and US)

If, like these motorists, your fury rises with the numbers ticking over on the petrol bowser, get a grip. You may soon look back fondly on the good old days when petrol was $1.40 a litre.

The world is at the beginning of the end of the age of oil, according to a growing body of analysts. It stands at a precipice of "peak oil" – the point at which oil producing countries can no longer keep up with growing demand, where production climaxes and then plunges into irrevocable decline.

This, say the doomsayers, may send national economies spinning into turmoil, up-ending comfortable urban lifestyles that rely on oil for the cheap transport of people and goods and for the manufacture of thousands of mundane household and office items – from mousepads, banknotes and drink bottles to carpets, clothes, cosmetics and deodorants.

The crunch will come some time in the next few years, without warning, they say. "The worst case is that it’s occurring now or very soon because the world is unprepared, it’s absolutely unprepared," says one of the most influential pessimists.

But this is just scaremongering, say many authoritative oil industry voices. While they agree that oil is unlikely to get cheaper any time soon, they insist that oil production will keep pace with demand for decades to come. There is simply no end in sight to the black gold bonanza, according to these optimists.

They check off their list: vast untapped oil reserves claimed by Middle Eastern nations; the prospect of further discoveries; and smarter technology that will extend the life of existing oil fields and make new ones easier to exploit.

Even the optimists concede that massive discoveries of easy-to-reach oil are a thing of the past. But, they say, higher prices will make other ways of producing oil and alternative fuels commercially viable.

Who is right? Four Corners investigates a truly global issue that reaches into every home and every car and touches every human life. This special report* explains why oil prices are high right now and asks how long the world has left to prepare for a day when there is not enough oil to go around.

Reporter Jonathan Holmes goes in search of an answer in the Middle East, the US and Europe, interviewing the key protagonists. He asks if the world is being told the truth about the vast unexploited reserves that are claimed to lie beneath the desert sands of the Middle East. He looks at alternative oil sources and the obstacles to exploiting them. And he explains what peak oil means for Australians who depend so heavily on oil for transport and tourist income.

"Peak Oil?" … on Four Corners, 8.30 pm Monday 10 July, ABC TV.

This program will be repeated about 11 pm Wednesday 12 July; also on ABC2 digital channel at 7 pm and 9.30 pm Wednesday.

*Four Corners also presents a Broadband Edition on "Peak Oil?" … See the program in full; watch extended interviews with the experts; delve into interactive maps showing who produces the oil and who buys it; browse key reports about how much oil remains untapped; learn about the alternatives; and discover the impact of peak oil on Australia’s economy and way of life.

 

The Practical EROI of Ethanol

I have been researching ethanol production.  There is a lot to it and it is not just a case of boiling up a few plants and out comes ethanol.  For a sustainable farm producing your own fuel it is not easy to do if you remove all fossil fuels.

Starting with the growing.  It is very labor intensive to grow plants for ethanol.  I was considering Jeruselum Artichokes as they are fairly easy to grow.  However there is the labour of planting, watering, and harvesting the plants.  In my time budget that would be limited as it is on a farm there would be say 5 days a month devoted to growing fuel crops.

Second stage is that the plants have to be chopped ready to cook.  This can be done in a large blender however it takes energy to run it.  Assuming that there is sufficient wind or sun to generate power then there is no problem.  If I have to use a generator, running on alchohol then this reduces the energy return of the crop.

Third stage is cooking.  Very energy intensive.  I can use a methane digester to produce gas for cooking or do I use electricity.  Again if it electricity and I have to generate it with my diesel backup then this is further reducing the EROI of the alchohol I eventually produce.  If I use a methane digester then this is a further system to maintain and break down on a limited time budget.  A pressure cooker reduces the time taken and energy however they can be dangerous.  I do not want to set up my retirement only to be hurt from steam.

Fourth stage is fermenting - no energy required here only time as yeast does the work.  However it has to be closely monitored taking further time.

Fifth stage is distilling the beer from the fermenting tank.  I can use a vacuum system to reduce the energy requirement however they are more expensive.  If I use a atmospheric pressure distiller then this takes more energy and time to do the distilling.

Finally the alchohol has to be dried.  No energy required here as zeolite can do the job and be reused.
To make an acceptable diesel fuel however an additional step is required.  You need to mix it with a dry veggie oil to preserve the injectors.  I can grow soybeans as I am going to anyway however making vege oil is another multi step process taking yet more time.

All of this to produce fuel and you wonder why fossil fuels are so attractive.  The process to extract and refine oil is much less energy intensive than this process.   Really it makes much more sense for me to buy a couple of litres of diesel fuel and store it for power backup that go thorough this process.  It only makes sense if fossil fuels are not available which even if oil peaks this will not happen for many many years, far beyond my lifetime.  Again even if oil peaks and supplies become extremely expensive then I can probably just buy ethanol.  Or fuel production could be a community effort to avoid duplicating expensive equipment.

Signs of Peak Oil

Peak Oil is not about running out of oil.  The lower 48 states of the USA peaked in 1970 yet there is still oil pumped out today.  Peak Oil is about the easy oil running out making the harder oil, the less economic oil, a necessity.

Evidence that this is happening is the mad scramble that the major powers, China and India, the US, and Europe are engaged in for energy.  I was reading this article about recent happenings in the world that largely go unreported.  One of the significant things is the creation of the SCO.  You probably have not heard of it - here it is:

The latest developments surrounding the Shanghai Cooperation Organization (SCO) and Iran further underscore the dramatic change in the geopolitical position of the United States.

The SCO was created in Shanghai on June 15, 2001, by Russia and China along with four former Soviet Central Asian republics, Kazakhstan, Kyrgyzstan, Tajikistan and Uzbekistan. Prior to September 11, 2001, and the US declaration of an "axis of evil" in January 2002, the SCO was merely background geopolitical chatter as far as Washington was concerned.

Today the SCO, which has to date been blacked out almost entirely in US mainstream media, is defining a new political counterweight to US hegemony and its "unipolar" world. At the next SCO meeting on June 15, Iran will be invited to become a full SCO member.

Iran as a member of this would tie up a significant part of the remaining good oil from Iran and the rest of the difficult oil from the 'stans.  Just to make it worse these countries are being invited to join:

Iran is also moving on plans to deliver natural gas via a pipeline to Pakistan and India. Energy ministers from the three countries met in Doha recently and plan to meet again this month in Pakistan.

The pipeline progress is a direct rebuff to Washington's efforts to steer investors clear of Iran. Ironically, US opposition is driving these countries into one another's arms, Washington's "geopolitical nightmare".

At the same SCO meeting next month, India, which Bush is personally trying to woo as a geopolitical Asian "counterweight" to China, will also be invited to join the organization, as well as Mongolia and Pakistan. The SCO is gaining in geopolitical throw-weight quite substantially.

Nobody would be stitching up these deals if there was plenty of oil.  Why bother with this complex strategy if there is plenty of easy to get oil?  Surely it would just be easier to explore and find the huge new oilfields that debunkers of Peak Oil say remain to be discovered.   The article is a bit of an eye opener and is worth a read.

ExxonMobil's 2005 Energy Report - the Oil Resource

Thank you forester for posting this link in a comment in my last post.  This is the graph that Exxon-Mobil  think world oil resources are:

 

And here is the text of the slide:

While global demand for oil will continue to rise through 2030, what trends can we anticipate in oil supply?

This chart shows conventional crude and condensate resources around the globe. This resource estimate is a technical assessment developed by Exxon-Mobil’s geoscientists and engineers.

We estimate that global conventional oil resources total 3.2 trillion barrels (TBO), with non-conventional “frontier” resources such as heavy oil bringing that total to over 4 trillion barrels.

These numbers include discovered and undiscovered resource estimates. They also contain a “growth” component that reflects the well-established tendency of resource estimates to increase over time.

From the beginning of its history through 2004, the energy industry has produced about 1 trillion barrels, leaving more than 2 trillion barrels of conventional resources still to be produced. (Shown by the dark green section of the bars.)

Almost every region of the globe has more conventional crude and condensate remaining than what has been produced. The Middle East and the Russia/Caspian region have the largest remaining resources.

Only North America is beyond the 50 percent produced point.

It would seem that people who think Peak Oil is going to be a near term problem are wrong and there is plenty of oil.  The only major problem with this is that it is pure fantasy.

So lets start with absolutely known reserves.  Here are a couple of links.

This is the Physics Factsbook that compilates quite a few different sources gives the mean value of all these estimates to be about 950 billion barrels of oil.  All these estimates include the figures from the Middle East.  Around 1985 when oil quotas were set to be proportional to the countries known reserves then this happened from this article:

Previous OPEC estimates, inherited from private companies before governments took them over, had probably been conservative, P90 numbers. So some upward revision was warranted. But no major new discoveries or technological breakthroughs justified the addition of a staggering 287 Gbo. That increase is more than all the oil ever discovered in the U.S.—plus 40 percent.

So there is possible 280 billion barrels of this number that are imaginary as the true reserve figures of Saudi Arabia, Kuwait etc are not audited and even closed to Exxon-Mobil.

Now if Exxon-Mobil think that there are 3000 billion barrels of oil left then they must be estimating the yet to be discovered resources as 2000 billion barrels.  If the oil reserves of Middle Eastern countries are over estimated, as Kuwait's were recently was exposed to be, then that figure could be over 2200 billion barrels yet to find.

Now the largest oil field yet discovered is Ghawar in Saudi Arabia.  Ghawar had about 120 billion barrels and about 60 or 70 billion barrels remain.  The figure that Exxon-Mobil want you to believe is the the ultimate oil reserve represents discovering 16 Ghawar size fields between now and 2030.

So lets go back to the graph that I posted in a previous post.

This data was compiled from known oil data and you can clearly see that since the last field of 50 billion barrels was discovered in 1970 and none this size have been discovered since.  Also it it immediately apparent that the rate of discovery has dropped from the peak in about 1965 and has been dropping ever since.  So Exxon-Mobil is asking you to believe that they can turn around this 40 year trend and discover a Ghawar size field a year until 2030.

Peak Oil is not a greenie conspiracy theory.  It can be seen with simple mathematics and a bit of logic.