Imaginary Power

This blog has included many articles on imperial economic and political power, a reality that must be understood in order to make sense of the world. As something to consider as a contrast over the holiday period, following is a note on imaginary power taken from the work of Swiss genius, Leonhard Euler.

Firstly, start with Euler's famous formula:

e^ix = cosx + i sinx

For x = π, this produces the even more striking result

e^iπ + 1 = 0

(Nobody has constructed a simpler or more concise - some would say beautiful - equation, one that includes so many of the fundamental operations and core elements of mathematics: unity, zero, e, π, i, equality, addition, exponentiation and multiplication)

But, for x = π/2, Euler's formula can be used to answer the question: what is i, the so-called imaginary unit (the square root of -1), to the power of i?

In other words, what is iⁱ? This is a particularly weird question if translated as 'an imaginary number to the power of an imaginary number', stranger perhaps than asking: what colour is 5.6 and is it different from the flavour of 6.5?

Using x = π/2, Euler's formula becomes

e^iπ/2    = cos π/2 + i sin π/2

          = 0 + i

so

e ^iπ/2 = i

in which case, raising both sides of the equation to the power i gives

iⁱ        = (e^iπ/2)ⁱ

          = e^{i.i. π/2}

          = e^-π/2

So, it turns out that

          iⁱ = 0.2079 (to 4 decimal places)

and it is a real (and a positive) number.

But that is not the end of the process, because i = e^iπ/2 is just one of an infinite number of values for the equation

e^ix = cosx + i sinx

since sin π/2 , sin 5π/2 , sin 9π/2 , etc, are also equal to 1, while the respective cosx values are all equal to 0 (note these are measured in terms of radians, and that π/2 radians is 90 degrees).

So the general equation for i is:

i = e^i(4n+1)π/2

For example, when

          n= 0,             iⁱ = 0.2079…

          n = -1           iⁱ = 111.3178…

          n = 1            iⁱ = 3.3882… x 10^-4

etc, for positive and negative integer values of n

This odd result follows from the nature of i. I think that it is best to think of i as a mathematical operator that, when applied to itself squared, as  (i x i) or i², results in minus 1, rather than in the unnecessarily mysterious form of an 'imaginary' unit or number.

Perhaps surprisingly, Euler has not been considered to be one of the founders of Rastafarianism, despite his understanding of i to the power of i.

Tony Norfield, 14 December 2013


Note added on 4 July 2014: there are several ways of deriving the above results, some of which can be found on Wikipedia and in other Internet sources. However, the method used above was taken from a book by Y E O Adrian, The Pleasures of Pi, e and Other Interesting Numbers, World Scientific Publishing, 2006, pp. 205-207.

Sitting on the Dock of the Bay

(This is a guest article)

That millions of workers in Asia on minimal wages produce a huge amount of consumer goods for the West is such a well-established and undisputed fact that it does not require much further comment. These goods are often so cheap that their price astonishes us. Of course, once we consider the economics of the lives of the people who produce these goods, there is no mystery in this. Yet we rarely ponder such issues for long, because the inevitable conclusion can only be that living standards in the West are supported by the toil and sweat of millions of others.

But the systematic exploitation of what used to be called the ‘Third World’ - and is now fast becoming the First World in terms of industrial organisation and manufacturing competence - is not restricted to production. Every aspect of this production and trade is parasitical and hugely exploitative. Consider, for example, maritime shipping - the main way these goods get from the hands of distant toiling masses into the hands of consumers in the rich countries.

Almost all goods produced in Asia for the West are transported in large container ships. Airfreight accounts for less than 7% of the total. Despite the West’s clear technical superiority, not a single developed western nation builds container ships. They are all built in Asia, mainly in South Korea. So, it is not only the goods, but also the ships they travel in that are produced in Asia. What little shipbuilding of any kind remains in the West survives only because of the most stringent protective barriers or due to social policy protecting employment (the disparity in wages is so great that a global free market in shipbuilding would wipe out what is left of this protected industry).

The exploitative and parasitical nature of Western consumption even determines the design of container ships because of the unequal loading on the forward and return journeys. Ships stacked up with containers on the outward East-West journey can be the equivalent of a 10-storey building above the water line. A ship is stable when a proportion of it is below the water line, but a ship built to handle such huge capacities would be unstable in rough seas when unladen. Because we give Asia practically no goods in return, container ships have to return empty. So, to maintain stability the ships have to be built with huge ballast tanks to take on seawater. The ships are designed on the assumption that the West takes but does not give and that this will continue to be the case throughout the working life of the vessel!

A large container ship has a crew of around 30. The captain is almost always a very-well-paid European. The crew is invariably staffed by ratings from extremely poor countries that command extremely poor wages (mostly from the Philippines, Bangladesh and Malaysia). Were merchant seamen paid decent wages these would be reflected in a higher price for the goods transported.

Considering that 80% of world trade is from ‘East to West’, and that all container ships are built in the Far East, it would not be unreasonable to expect Far Eastern operators to dominate world maritime business. Not a bit of it. For 120 years very powerful Western companies, backed by monopoly practices of linked banks and insurance companies, and supported by port authority regulations, ensure that a whopping 90% of world shipping is controlled by a dozen Western cartels. Only 8% of shipping is in the hands of Far Eastern operators, the people who build the ships, who sail them, who make the goods transported in them, and who dispose of the ships at the end of their working life. Cartel shipping fees represent another transfer of income from Asia to the West.

A container ship has a working life of around 20 years. The cost of disposal is also a cost that must be reflected in the price of goods transported. Ship breaking is a very labour intensive and extremely dangerous activity. There are no breaker’s yards catering for large ships in the West. They are all located in countries where wages are extremely low (Bangladesh, Pakistan), where health and safety legislation is non-existent or not enforced, and where the compensation for death and injury at work is a pittance. Another sign of how cheap goods are bought on the exploitation of others.

O Redding, 13 December 2013

Destroying the Evidence

Britain's colonial empire was remarkable in two respects. Not only in the extent of territory controlled around the world, but also in the degree to which the British colonial governments documented their activities. Millions of files were kept on everything from petty administrative details to lists of spies and informers, to methods of exploitation and oppression, to the latest communications with the Foreign and Colonial Office.

This caused a problem when the Brits retreated from different countries, starting with India. What to do with the files? The political sensitivity of each file was indicated by a code that determined which officials could read it, for example, to exclude those of 'non-European descent'. However, this sometimes meant that there were not enough white Brits available to sift through the documents. What could be left behind for the post-colonial administration? What should be put on the bonfire, and what should be sent back to London? The key thing was to destroy anything that could embarrass Her Majesty's Government if it fell into the wrong hands.

While this story of getting rid of the evidence is not new - see, for example, Britain's Gulag, on the end of British colonial rule in Kenya, by Caroline Elkins,  - an article in the Guardian gives fascinating details of the extent of the cover up. The Foreign Office retains a huge cache of undisclosed files from the colonial period.


Tony Norfield, 29 November 2013

Cameron's Sharia Bond and British Parasitism

To be the political leader of an imperialist power that has attacked a number of Muslim countries in the past decade, it takes a certain, how can one put it, chutzpah, to say:

"I don't just want London to be a great capital of Islamic finance in the Western world, I want London to stand alongside Dubai as one of the great capitals of Islamic finance anywhere in the world."

Yet that was British Prime Minister Cameron, talking to the World Islamic Economic Forum in London on Tuesday. Part of the plan is for the UK Treasury to launch an 'Islamic bond' worth £200m next year, presented as the first Islamic bond issued outside the Muslim world.

One UK financial lobby group report suggests that 'global Islamic finance assets' - namely those which are 'Sharia compliant' - already amount to some $1.5 trillion and are growing fast. Hence the UK wants some of the action. There are 22 Islamic banks in the UK, more than in all other western countries combined. The UK government has even established an Islamic Finance Task Force, but this one is not weaponised.

The contradiction between Britain's foreign policy and its financial policy is only apparent. Despite the invasions of Afghanistan and Iraq, and the bombing of Libya, not to mention other covert interventions, Britain is not anti-Islam or anti-Muslim. It just wants to see its interests protected. It has no problem backing jihadist rebels if they will serve that policy, as in Syria, just as it supported the Moslem Brotherhood against the nationalist threat from Nasser in Egypt from the late 1950s. Today British imperialism steadfastly supports Sunni elites throughout the Middle East, and most of the families were put in place by British policy. Further afield, in Brunei, 1000 British army Gurkhas are also paid for by the Sultan to back his 'security' - and the interests of Royal Dutch Shell plc. Brunei is not a big place, so if you had some doubts about the wisdom of the autocracy you would think twice about expressing it with these guys coming at you.

However, to return to the financial issues. Cameron's Sharia bond is planned as a sign that the City is 'open for business', to use Bank of England governor Carney's phrase (see below). The size of the planned bond issue is minuscule in terms of state finance, but it will show that the City is willing to do whatever is necessary to attract business from this previously untapped area. It will encourage other financial activity and it will give enterprising specialists in Islam a profitable role as arbiters of what is Sharia-compliant. From the City's perspective, dealing spreads can be important, not just interest rate returns. In any case, it will not be difficult to transform interest remuneration into something that does not look like interest and so be Sharia-compliant. Best of all, Britain's lack of capital controls will make it easy for rich foreign investors to put money in, and take it out, while there will be little fear of political moves against them. Well, perhaps less confidence these days, since Assad's wife no longer shops at Harrods and the Gaddafi family no longer have a residence in Hampstead.

Details of Cameron's bond are to be finalised, but early reports suggest that coupon payments will be based on rentals from government property. Will the rentals come from chemical weapons plants, MoD buildings, GCHQ, MI5/6, US bases in Britain or the leased bases around the world? That can be sorted out later, and the result will no doubt be deemed 'ethical' and compliant.

Two other issues are worthy of note related to imperial finance, but not to Islamic finance. The connection is that these two and the previous discussion all relate to a desperate attempt by the British state to boost the scale of financial dealing, with all the opportunities this offers for skimming off more surplus value from the rest of the world. My previous note (see this blog, 22 October 2013), showed that the balance of payments flows are worsening for the UK so, as one might expect, the focus of British policy now is on how to leverage what the Brits are best at in order to get more revenues in the future. No, not by marketing self-deprecating humour in BBC video exports, but by increasing financial deals to make money from other people's money.

The first is Britain's attempt to build on its already prominent role in the offshore trading of China's currency, the renminbi. It took a while before the People's Bank of China gave the Bank of England the currency swap line it wanted. It was delayed until June this year and was CNY 200bn, embarrassingly less than the CNY 350bn agreed with the European Central Bank in October. This may have been aimed to cast a deliberate shadow over the status of the City of London, although the swap is for sterling versus CNY not for the much larger euro currency. As if to ward off any further problems, the UK Treasury went out of its way to make it easier for Chinese banks to set up in London in October, lifting regulatory hurdles and risking annoyance from the Americans, together with embracing a pan-European visa deal - for Chinese tourists only.

Outside China and Hong Kong, the City already manages some 60% of offshore trading in China's currency, with the US at just 15% and France at 10%. In October, the UK Treasury announced the opening up of direct trading of China's currency with sterling and that it had gained a (small) quota for accessing Chinese equities and bonds. These factors will increase the potential for City dealing, at least until China changes its mind.

The second is the latest policy change from the new Bank of England governor, Mark Carney. The theme of a keynote speech to a Financial Times anniversary event last Friday was that London was 'open for business'. So he introduced policies to boost the volume of financial dealing. He envisaged bank assets in the UK growing from some 4 times GDP at present to more like 9 (!) times by 2050. Then, in a squaring of the circle that was a wonder to behold, he argued this could be done with lower costs for private banks getting central bank aid while at the same time making the overall system more secure.

I am not one to make ad hominem comments, for example noting that he, like Mario Draghi of the European Central Bank, is an alumnus of Goldman Sachs. This is because, despite him being Canadian, and despite him being in the job only since July, last week he showed that he had the best interests of British imperialism at heart. This, together with the Sharia bond and China policies already discussed, is the clearest sign that the British ruling class knows how to adopt and to bring on board whomever and whatever policies look like having some upside in these difficult times.

Tony Norfield, 30 October 2013

Bad News for British Finance

The UK government lauds the fact that recent measures of changes in economic output have a plus sign in front of them, rather than a minus. Yes, UK GDP is +1.3% y/y in the second quarter of 2013, though do not mention the fact that the level of GDP is still lower than it was five years earlier in 2008. However, something else is going on that is far more significant.

No, not the fact that to keep the lights on the government has given a huge subsidy to a French-Chinese nuclear power plant that the Brits could neither construct nor finance. It is a development clear only to those who delve deep into the pages of international finance statistics, thus evident to almost nobody. For the first time in more than a decade, Britain is making less on its international assets than foreign capitalists earn on assets in Britain - and the deficit is getting worse.

Personally, I find this annoying because it complicates a point I could otherwise easily make before. My previous point was that one of British imperialism's privileges was shown by the fact that, despite having a net deficit in its international investment position, it managed to earn more from its foreign assets than it paid on its foreign liabilities. The difference in returns is still true, but it does not generate the same results. Previously, high earnings on foreign direct investment, especially investments in low wage countries and in rent-rich investments in oil, gas and minerals overseas managed to offset the other net payments on the portfolio accounts (bonds and equities) and on bank borrowing. No longer. Although I thought that at some point this privilege would be undermined by the trend of a growing net deficit, on the data for 2012-13 it seems that this has happened already.

The latest annual data show that in 2012 the UK had a net deficit on its income payments on foreign investment of £2bn. Not much in the context of a big GDP, but much less than the +£22.7bn in 2011 and the first deficit since 1999. Data so far for the first half of 2013 show a worsening trend: an income deficit of £9.4bn in six months! The significance of this goes beyond me losing an easy sound bite. The main reason behind the drop is a decline in net earnings on foreign direct investment, but there is also a bigger net deficit on portfolio investment income. At the same time, the net surplus earnings of the financial services sector are flattening out and the UK current account deficit has widened to over 4% of GDP at present - the highest since 1989 - from just 1.5% in 2011. To cap a list of alarm signals, the visible trade deficit reached an all-time record of 7.0% of GDP in 2012.

British imperialism cannot pay its way in the world and the former means of relying on revenues from foreign investment and financial services, very effective in the 2000s boom period, is no longer working. A huge volume of short-term borrowing in 2012 funded these record deficits - and other outflows on the direct investment and portfolio accounts. This is all fine … until you have to pay the money back. Do not expect an end to austerity, despite any pick up in the UK GDP figures.

Tony Norfield, 22 October 2013

Historical Materialism Conference in London

The journal Historical Materialism is holding its tenth annual conference, entitled 'Making the World Working Class', in central London on Thursday 7 to Sunday 10 November 2013.

The venue is SOAS, near Russell Square, London WC1. Further details regarding the conference, accommodation, etc, are to be found here.

It is a big conference, covering a wide range of topics! There are 14 sessions over the 4 days, each with up to 11 different panel discussions including 3 or 4 speakers.

For those interested, I will be presenting a paper: 'Is British imperialism’s financial strategy turning toxic?'. It will discuss how the crisis has changed the balance of forces between the world's major powers and developments in British policy.

The schedule for this will no doubt change, but is set at present for Thursday 7 November, from 15.45 - 17.30.

Tony Norfield, 17 October 2013

Information Flows

Fibre optic submarine cables carry the vast bulk of Internet and other communications traffic between continents. If you - by which I mean your government - wanted to access the information flowing through these, then the location of the cables is important - relative to where your government has (military) bases or national jurisdiction.

It is striking that the bulk of the transatlantic cables go through the UK. As for the other continent-connecting ones that do not, these tend to go through places like Cyprus, the home of a British military base. Isn't it nice to know we are all 'connected' - probably at most just one or two junctions away, at least from GCHQ?

Take a look at the submarine cable map, of which a portion is shown below. The full world map is available from here - scroll in/out from this site (not from the image below) to get a smaller/bigger geographical picture, or from a different central location.

This is the physical infrastructure for Edward Snowden's story.

Tony Norfield, 19 September 2013

Saudi vs Syria: Imperial Policy Crisis

US president Obama has today assured the word of his intention to launch missiles at Syria for its alleged use of chemical weapons, but he has also decided to make the action dependent on the decision of the US Congress to vote for blood. Such is the nature of imperialist democracy. This could delay the attack for a week or so, something that the warmongering news media are mightily frustrated with. It may also not be a foregone conclusion that Congress votes for its additional war, even though Obama, like UK prime minister Cameron, promised to constrain its scope to a 'one off' punishment. Cameron's defeat by a parliament sceptical of what value lay in another war (ie an overt military action, rather than just supporting the so-called rebels) and worried about potential blowback could find an echo in the US.

That is problematic enough for Obama and for US policy. However, what if no evidence emerges that the Syrian regime was responsible? The danger of a debate (even in Congress) is that you have to present some evidence. Even worse, what if there is some evidence that the Saudi-supported opposition to Assad were responsible?!

One report explicitly claimed this yesterday, but has (so far) received no widespread coverage - partly because it embarrasses the stance of the western media, partly because it will cause a major crisis in imperialist policy. However, the report is co-authored by an AP journalist with good credentials, rather than being the ramblings of a dissident blogger. The story is entitled: 'Syrians in Ghouta Claim Saudi-Supplied Rebels behind Chemical Attack'. This is the link to it.

Let's see how this plays out.

Tony Norfield, 31 August 2013

The Australia-Hong Kong War of 1994

Life imitates art, as shown by the following link to an excellent satire on TV news, The Day Today, first shown on British TV in 1994.

The scene is all too appropriate for the Anglo-American news media's warmongering today.

The link to the YouTube video, roughly 4 minutes, is here.

Understanding the Syrian Situation

(Here is a guest article on a key issue for imperialism today)

Most radical thinking on Syrian is convinced that the West, and particularly the US, Britain and France, are keen to create a situation in Syria that will justify Western intervention so that the major powers can take over the country - as in Iraq and Afghanistan - isolate Iran, and help Israel’s ailing position in the Middle East.

This is a serious misreading of the situation. The dominant Western powers are forced to adopt a policy position on anything that happens in the world because they must constantly remind the international community who is in charge. That does not mean, drawing out the purely logical conclusion of these public policy positions, that they necessarily have any real intention of getting involved or of intervening in any particular conflict. It is important, when judging world events, to avoid the simplistic radical counter-propaganda model and to examine what is really going on.

The conflict in Syria is being driven by Saudi Arabia and the Gulf States. These countries all have either large Shia communities or majority Shia populations. In addition, the ruling elites in these countries are a tiny minority within the minority Sunni population. It is only a matter of time before democratic and demographic realities impose themselves. Iran has made it clear that it does not want to use its Shia influence in the region to destabilise these regimes. Indeed, Iran has made it clear that what it wants is a strategic but respectful relationship with these Sunni states - particularly as Western sanctions bite more and more. Iranian commercial elites need these Sunni states to prosper.

Nevertheless, these Sunni states, and particularly Saudi Arabia, are not comforted by such Iranian assurances. In a way, they are right. What they fear is not Iranian backed subversion, of which there is very little evidence, but that the struggles of their own Shia communities will inevitably drag Iran in, whether it wants to or not. This is sound reasoning. Iran cannot ultimately remain aloof from Shia struggles that flare up despite its conservative foreign policy.

So, the Saudis and the Gulf States are extremely anxious to deal Iran a knock out blow. Fostering regime change in Iran has shown itself to be a total failure. Iran is a relatively compact and orderly society and any attempts to undermine its internal cohesion do not prosper. A large part of the population hates the rule of the mullahs, but, if the country is attacked, all Iranians close ranks.

In any case, the policy of the Saudis and the Gulf States is too primitive to run the kind of sophisticated strategy needed to undermine Iran internally. The only international politics they know is to offer huge bribes, which is not enough in this case. That’s what happens when you have too much money and you do not have to work or think for a living. Your brain goes to mush. When the Saudis or the Gulf States need to play a more intelligent game, they always get the Israelis to do it for them.

The eruption of the Syrian civil war has created the illusion in the minds of the Saudi and Sunni elites that by financing regime change they can deal Iran a severe blow by isolating it in the region. This is more wishful thinking born of desperation than geopolitical understanding. It is what really fuels the fighting in Syria and why the West does not want to get involved. The Saudis and Qataris are pouring in billions of dollars – but all their money is able to buy is an undisciplined rabble of jihadist head-bangers who could never form an alternative political leadership and which the West does not want to touch with a barge pole.

So, why is the West making ominous war-like noises that sometimes sound very much like the run up to the Iraq war? Actually, carefully analysis shows that, despite surface similarities, there is a marked difference between Iraq and Syria. Every statement that the US, the UK and France has made in the last two years has indeed been full of hype and hot air – but has also been self-limiting and vague on detail and timetable. There is no build up, no momentum, no traction to this phoney war effort. Now, General Martin Dempsey, chairman of the US Joint Chiefs of Staff and Barack Obama's chief military adviser, has made it clear the US is not going to get involved.[1]

If the West continues with this phoney war it is only because its close allies, the Saudis and the Gulf States, have got themselves into a huge jam and need to be shored up diplomatically. If the Syrian regime manages to hang on, and all indications are that it will, it will be a strategic disaster for the Saudis and their allies and, for them, a disastrous victory for the Iranians who will tell the world: 'You see, these dumb Saudis, they have all the money, they can buy anything they want, they have all the power of the United States and the West behind them, and yet they are useless. They are not fit to be leaders of the Islamic world.'

Western politicians must be hugely relieved to have the excuse of Putin ostensibly stopping them from intervening!

David Isbert, 22 August 2013

---

[1] 'US "will not intervene in Syria as rebels don't support interests", says top general', Daily Telegraph, 21 August 2013.

The Economics of Spying

The UK's Guardian newspaper has had a good run of scoops based on US-fugitive Edward Snowden's revelations about the scale of spying activity by the American government, and its connections with British and other government spy agencies. Until Monday evening, 20 August, however, it had denied itself another scoop - that UK government officials came to its London offices in July to demand the leaked US National Security Agency files. In the event, they agreed with these officials to destroy the copy the Guardian had in London, and yesterday published pictures of the relevant dismembered hard drive. It is not clear why there was such a delay in reporting the July visit, but one suspects that it might have been due to the 9-hour detention of David Miranda, partner of the main story reporter, Glenn Greenwald, by the Brits. The latter is likely to provoke Greenwald into more embarrassing revelations and this would make the Guardian's continued silence on its own treatment by the UK government also a little embarrassing.

Much of the coverage of official spying activity has been in terms of the potential loss of personal privacy on the Internet, in phone calls and emails. By contrast, the state response has been to stress the need for such actions in the fight against 'terrorism'. When officials sense that might not be enough to assuage liberal concerns, they sometimes also mention how it is needed to combat 'serious organised crime'. The much more plausible rationale for the huge extent and cost of this surveillance, however, is that it makes good business sense!

Far from trawling through zillions of gigabytes of data to uncover the latest plot, the intelligence agencies are much more likely to be monitoring a select subset of the communications, the ones that really interest them. As the Guardian itself reported two months ago, the UK's GCHQ has intercepted communications at G20 summits. Less politically charged, more mundane, but much more profitable surveillance of key corporate communications about business deals, strategy and innovations will also take place on a regular basis. Any problem they might have with continuing this activity is the main 'threat to national security'.

I'm just a little surprised that the UK government has not had the sense to explain this to the public. I am sure they would understand, given the consensus that exists on doing what is good for the country.

Tony Norfield, 21 August 2013

Monopoly #2

Why waste words when the numbers speak for themselves? However, a little explanation may be useful in this case. *

The numbers in the table below are taken from a study of some 43,000 international companies in 2007. That means some of the information is now a little dated, with the demise of Lehman Brothers being one example. However, the broad picture remains and it is one showing that the top 50 companies 'controlled' (ie had ownership of 50% or more of the equity in) some 40% of the network of 43,000. US monopolists account for nearly half of the entries in the table, but the UK is second in line.

Analysing these relationships is complicated since it must take into account the common fact that company A owns a share of company B; B also owns a share of company C, and C may also own a share of the equity in A and B. Such relationships are open to network analysis, however, and the results show the concentration of power in a core group of companies, of which these are the top 50.

Most of the corporations listed are in the financial sector, a fact that illustrates both how equity markets enable the centralisation of ownership through cross-shareholdings, mergers and takeovers, and how financial companies are at the centre of this relationship nexus. I have some qualms with the view that this means actual control, however. There may be an accumulation of relatively small shareholdings by a wide range of subsidiaries and loosely linked companies, so that implementing control may prove to be difficult, even if it were attempted. Furthermore, if 20 separate financial institutions owned 60% of a particular company's equity, they will not necessarily act as a group. Nevertheless, this does not change the picture of monopolistic ownership of the world's companies.

A different issue that could upset the calculation either way, and I do not think this was (or could have been) allowed for in the study, is that owning 1% of the equity does not necessarily give 1% of the voting rights. It may give more, or even zero, voting power, depending on the type of equity. Take Facebook's Zuckerberg as an example: he is reported to own 18% of the company's shares but has more than 50% of the voting rights.

The original study giving the method behind the analysis and some more information on the work done is found here.

For those who may frustrated with the way that mathematics is often used to obscure economic relationships, let this stand as one of the rare examples where it elucidates them!

Rank	Company name	Country	Cumulative % network control
1	Barclays Plc	GB	4.1
2	Capital Group Companies, Inc	US	6.7
3	FMR Corp	US	8.9
4	Axa	FR	11.2
5	State Street Corp	US	13.0
6	JP Morgan Chase & Co	US	14.6
7	Legal & General Group Plc	GB	16.0
8	Vanguard Group Inc	US	17.3
9	UBS AG	CH	18.5
10	Merrill Lynch & Co	US	19.5
11	Wellington Management Co LLP	US	20.3
12	Deutsche Bank AG	DE	21.2
13	Franklin Resources Inc	US	22.0
14	Credit Suisse Group	CH	22.8
15	Walton Enterprises LLC	US	23.6
16	Bank Of New York Mellon  Corp	US	24.3
17	Natixis	FR	25.0
18	Goldman Sachs Group Inc	US	25.6
19	T Rowe Price Group Inc	US	26.3
20	Legg Mason Inc	US	26.9
21	Morgan Stanley	US	27.6
22	Mitsubishi UFJ Financial Group Inc	JP	28.2
23	Northern Trust Corp	US	28.7
24	Société Générale	FR	29.3
25	Bank Of America Corp	US	29.8
26	Lloyds TSB Group Plc	GB	30.3
27	Invesco Plc	GB	30.8
28	Allianz Se	DE	31.3
29	TIAA	US	32.2
30	Old Mutual Plc	GB	32.7
31	Aviva Plc	GB	33.1
32	Schroders Plc	GB	33.6
33	Dodge & Cox	US	34.0
34	Lehman Brothers Holdings Inc	US	34.4
35	Sun Life Financial Inc	CA	34.8
36	Standard Life Plc	GB	35.2
37	CNCE	FR	35.6
38	Nomura Holdings Inc	JP	35.9
39	The Depository Trust Company	US	36.3
40	Massachusetts Mutual Life Insurance	US	36.6
41	ING Groep NV	NL	37.0
42	Brandes Investment Partners LP	US	37.3

43	Unicredito Italiano Spa	IT	37.6
44	Deposit Insurance Corporation Of Japan	JP	37.9
45	Vereniging Aegon	NL	38.3
46	BNP Paribas	FR	38.6
47	Affiliated Managers Group Inc	US	38.9
48	Resona Holdings Inc	JP	39.2
49	Capital Group International Inc	US	39.5
50	China Petrochemical Group Co	CN	39.8

Source: Vitali S, Glattfelder J B, Battiston S 2011, ‘The Network of Global Corporate Control’, PLoS ONE 6(10): e25995. doi:10.1371/journal.pone.0025995

Notes: 'Home countries' of the corporations are shown by their 2-letter ISO code. Note that CA is Canada, CH is Switzerland and CN is China.


Tony Norfield, 19 August 2013

* Clarification note, 20 August 2013: Vitali et al's document makes a clear distinction between ownership and control. To clarify, the table above gives figures for control, not ownership. The control estimate is based on owning 50% or more of the equity and thus having control over a company's decisions. In an extreme case, owning 50.1% of equity would give 100% control. Hence, the measure of control will overstate the actual figure of ownership. So these top 50 companies do not own nearly 40% of the network of corporations, although, by their measure they control nearly 40% of them.