# Original Work

I have done original work in a number of fields including Economics and Mathematics. This work is original work by myself, Mark Laurence McIlroy, it has not been peer-reviewed.

• Black and White
• Pricing model for consumption assets
• 2-Dimensional Numbers
• Solution to the Travelling Salesman Problem
• Pictographic Numbers
• Money and Inflation
• Interest Rates and Inflation
• Foreign Exchange Rates
• Asset Prices
• Economic Growth and the Law of One Price
• Commercial activity rules
• The Wealth of Nations
• Full employment
• Suggestions for third-world countries
• Violence and economic development
• Poverty
• United Nations poverty elimination program
• Financial Regulation
• Basic Society
• Physics
• Computer Science
• Music

Black and White (2 pages)

This document contains observations on the spirit of life, and engineering.

Black & White

Economics

Pricing Model of Consumption Assets (2009)

I have developed an economic model for pricing consumption assets.

The model is:

Desirability

Price = ———————————–

Volume + 1

In this model the term ‘desirability’ is a numeric value that represents how desirable an individual finds the asset in question.

This is a personal value that is different for each individual, for each asset.

There are no units or physical range associated with the ‘Desirability’ value, a set of nominal numeric values should be assigned to it for each model that is built.

‘Volume’ is the volume of that asset that the individual currently holds.

The model will produce a different ‘price’ for the asset for each person, and trading between individuals occurs when the prices are different.

In the simulations I assumed that the trade transaction occurred at the mid-point of the prices set by the buyer and the seller.

This model is deceptively simple. In practice it is actually quite powerful.

‘consumption assets’ can include land and buildings (but would not generally include financial assets).

I have done a number of simulations using this model to predict resource allocation in model economies.

The model can also be applied to individual trades and transactions.

Simulation using this model of wealth and trading in a society produced the following results, some of which are common sense while others are counter-intuitive..

1. A person with high desire for something they don’t currently hold ends up with nothing because they give up huge amounts for very little.
2. Alternatively, the person who holds the items that OTHERS have desire for ends up with the most.
3. Having a high desire for what you already hold is good (helps you keep more) because you don’t give up much in possible trading.
4. In a steady-state condition, a sudden decrease in wealth for one party actually gets WORSE for that party, with even more distributed to other parties (desperation trading), before a new equilibrium is established.
5. If an additional volume of a product is injected into a system, the steady-state market price of that commodity falls, and vice versa.
6. An increase in desirability of a commodity increases the commodity’s market price.

Mathematics

2-dimensional Numbers (2009)

My work includes the definition of a new type of number, known as a ‘2-dimensional number’ or ‘n-dimensional number’.

Consider a square that is divided into four equal sections, labelled 0, 1, 2, and 3. Now chose a point within the main square. The sub-section that the point lies within forms the first digit of this number (in this case either 0, 1, 2 or 3).

Now take that quarter, and divide it in turn into four equal parts. The part that our chosen point lies in forms the next digit of the number.

Repeat this process to finer levels of accuracy until the desired accuracy of specifying the number is achieved.

Using this process, a single sequence of digits can specify a point in 2-dimensional space, a process that normally requires two independent parameters.

2-dimensional numbers have a very wide range of possible applications, from aircraft navigation to defining colours.

The example given above is for a flat plane. The same process can be applied to a cube to specify a point in 3-dimensional space, or also in higher-dimensional spaces.

In the cube example, divide the outer cube into eight sections labelled 0, 1, 2, 3, 4, 5, 6 and 7, to define the broad location of a point within the cube, then repeat the process as above to define more digits and more accuracy in specifying the location of our chosen point.

If you would like to experiment with n-dimensional numbers there is an Excel spreadsheet available from the link below with conversion functions for this number system.

2-dimensional Numbers

The picture below shows a 2-dimensional number. The first two digits of the point shown would be 13.

Below is a graphic representation of a 3-dimensional number.

The Travelling Salesman Problem

Solution to the Travelling Salesman Problem (2010)

The Travelling Salesman Problem is a famous problem in mathematics.

Given a set of cities, the problem is to find the shortest route to visit all cities without visiting any city twice.

A ‘brute-force’ approach of testing every possible path results in an extremely large number of tests and is impractical to compute for more than a few dozen cities.

The solution I have developed seems to find the optimal solution in all cases.

I have tested this in computer simulations.

Travelling Salesman Problem Simulation

The solution is algorithmic and is as follows.

1. Select a starting city.
2. Choose the shortest path to another city, and take this path.
3. Remove the starting city from the set.
4. Repeat this process until all the cities have been visited.

Proof

1. Start with the set of all line segments connecting individual cities
2. Select a starting city
3. Select the shortest segment that has the starting city as one end of the segment.
4. Remove all other line segments ending at the starting city
5. Continue to the point that you have connected the starting city to
6. Repeat this process
7. The final solution set will contain the set of the shortest line segments connecting each of the cities
8. This path should then be the shortest path to travel to visit each of the cities.

Pictographic Numbers

Pictographic Numbers (2010)

‘Pictographic Numbers’ is a pictographic number system in the tradition of the number systems of ancient civilisations such as the ancient Egyptians.

Different graphics pictures represent different quantities.

Due to practical limitations I have used uppercase English letters to represent the quantities in this work, however there is no reason that graphics symbols could not be used such as a picture of a goat, a house or a bag of wheat.

This number system has a number of interesting properties.

For example, addition is actually simpler than the standard Arabic number system.  All that is required is to concatenate the symbols in the two numbers together, and simplify the number if appropriate.

Below are download links for an Excel worksheet for conversion between Decimal and Pictographic numbers, a Word document with descriptions of the algorithms for performing arithmetic with these numbers, and a set of possible graphics symbols to represent different quantities.

This number system is not intended for serious use.

Pictographic Numbers Worksheet

Pictographic Numbers Algorithms

Pictographic Numbers Graphics Symbols

Money and Inflation

Consideration of Inflation (2016)

Inflation is probably the hardest problem in economics. This is unfortunate because lack of inflation is critical to the successful operation of an economy.

Despite some views to the contrary, it appears that banks do not create money.

A bank’s balance sheet is shown below

Assets

Loans due from customers

Deposits with other banks

Cash held

Liabilities

Customer deposits

Amounts owed to external parties including overseas

Net assets

Shareholder’s equity (i.e. shareholders’ share of the assets)

If the banking system uses the following procedure, then banks do not create money.

1. Customers and the shareholders deposit cash in the bank.
2. The cash is held within the bank and recorded as an asset on the balance sheet.
3. The customer’s deposits are recorded as a liability on the bank’s balance sheet.
4. The bank lends some cash out. This loan is recorded as an asset on the balance sheet.
5. The assets of cash held within the bank are reduced by the same amount so total assets do not change.
6. In practice cash is not held inside the bank vaults but is deposited with other banks including overseas banks and the Reserve Bank of Australia (in Australia).

Money then, (in Australia), is created by the Reserve Bank of Australia on behalf of the Australian Government.

Money is created when the RBA prints notes and sends them to people for government salaries, pension payments and other government payments.

In the modern day, obviously this is usually a direct credit to the customer’s bank account but the same principal applies.

I would suggest the following relationship:

money created = government payments – taxes collected –

net new govt borrowings

= budget_deficit – net new government borrowings

‘Government payments’ includes all government payments including salaries, pensions, payments to suppliers etc.

An increase in the volume of money in the system should, in theory, lead to increased prices (inflation) as there is more money to be spent on the same goods.

I have performed some visual correlation analysis on this model and unfortunately it was not a particularly good fit. This is an area for further investigation.

Interest Rates and Inflation

Conventional economic wisdom states that low interest rates generate inflation.

However, I would suggest an argument for the opposite effect.

When interest rates are very low, this stimulates companies to borrow money and invest in new productive capacity.

The problem with this is that, a few years later, there is excess productive capacity and goods in the economy, which pushes prices down.

Through this mechanism, low interest rates may actually generate deflation, not inflation.

What is money?

Consideration of Money (2016)

Having considered inflation, it is worthwhile to move on to the more general issue of ‘what is money?’

In past centuries, when money may have been fully backed by a commodity such as gold, money was simply a receipt for a certain quantity of the underlying commodity.

In the modern world, money is simply a digital record in a bank’s computer system and a small number of physical bank notes and coins.

Modern money is a form of points system.

Bank accounts record the number of points that an individual has.

Physical banknotes and coins allow a person to give points to another person.

In this world, why should money have value? After all, businesses are willing to accept money in exchange for real tangible assets.

It is sometimes argued that ‘confidence’ is the reason that money continues to have value.

However, confidence would evaporate quickly if there was no tangible reason for money to have value.

I suggest that there is only one reason that money continues to have value, and that is because the Commonwealth Government is willing to accept (and in fact requires) money as an item of value in payment of taxes and for government services.

Because the Commonwealth Government will accept money as payment, people require money and money circulates through the rest of the community as an item of value.

Foreign Exchange Rates

Consideration of Foreign Exchange Rates (2016)

Exchange rates are set by how attractive a country’s goods and other assets are to foreign investors. If foreign investors value the assets of a country they will be willing to place a high value on exchanging into its currency.

Factors affecting this desirability:

• The domestic bank deposit rates.
• Rental and dividend yields, current asset prices and the projected outlook for asset prices.
• Political and economic stability of the country.

Asset Prices

Asset Price Model (2016)

Fundamentally the value of any investment asset, such as a share, property or bond, is the Net Present Value of its future cashflows.

Individuals may form opinions of the likely value and range of the future cashflows for the asset.

These estimates will be based on imperfect information, as human beings have a finite capacity to absorb and process information.

Also, an interested individual must select a discount rate to arrive at the NPV of the asset’s cashflows.

This discount rate may be based on the investor’s personal attitude to risk, and also the degree of variability in the possible future cashflows.

Existing holders of the asset may be tempted to place offers of the asset if the recent trading prices of the same or similar assets are well above their personal valuation of the asset.

Potential buyers may be tempted to place bids for the asset, if their personal valuation is well above the recent trading prices for the asset or similar assets. This will only occur if the investor has sufficient wealth to place a bid, and is not constrained by other factors such as having a higher-priority use for their funds.

Trading occurs when bids and offers overlap, until there are no more overlaps for the trading day.

Economic Growth

The Law of One Price (2009)

The phrase ‘the law of one price’ has a specific meaning in economics, however I would like to propose a new meaning for this phrase.

Many industries in Australia are dominated by a small number of large companies.

There may be many reasons for this, but one reason is that large companies receive discounts for buying in bulk.

This effectively makes it impossible for small and start-up companies to enter industries and compete, as they are hampered by having to pay higher prices for their input goods and services.

My proposal is a new law, that would make it illegal to offer discounts to customers for ordering in large quantities.

This law would give small and start-up enterprises a fighting chance of success.

This idea is not as radical as it might sound. It is really just an extension of laws that came in 100 years ago to prevent the formation of monopolies, and to prevent competitors from colluding to set prices.

There are a number of benefits of monopolies and oligopolies, such as cheaper prices for consumers due to economies of scale.

However innovation and full employment would be assisted if small companies were allowed to flourish.

Commercial Activity Rules

It is probably the case that agricultural productivity has been one of the main sources of the wealth of past civilisations.

However I would like to suggest another possible important reason.

This is that wealth of past civilisations could have been created by the laws of commercial activity, i.e. what is allowed and what is not allowed in business activity. We will probably never know what lead to the wealth of the ancient Egyptian civilization but here are a few suggestions for commercial activity in the modern day.

1. Every seller must advertise the price of their goods and/or services on an internet website.
2. Every customer must be charged the same price for the same item or service.
3. Negotiation of prices is against the law, see point 2.
4. Cross-subsidising of products and services should be illegal. This occurs when a product or service is sold at below cost price and this is paid for with inflated prices on other items, or through selling down the business’ capital base. This situation involves some customers being ripped off to benefit others, while businesses can also not compete fairly. These practices should be outlawed, with a requirement that the selling price of every product or services must reflect the cost in producing it.
5. Monopolies exist in some industries where a large market share is necessary for any operations at all to exist. Examples include payment services and banking. There is an argument that the general public may be charged excessive prices in these circumstances because there are very high barriers to entry, and it may be necessary for some regulation of selling prices to occur. In the example  of payment services, it is necessary for economic efficiency that these not be charged at excessively high rates.
6. Supply contracts of more than 12 months should be banned. This would allow both the customer and supplier to seek alternative arrangements as their business conditions change.
7. Companies should be required to publish a list of key staff members and their contact details on their website to allow new businesses to seek new business more effectively.

The aim of these ideas is to make commercial activity more accessible to young people, and to increase the total wealth of the country through greater economic efficiency.

The Wealth of Nations (2010)

I would propose another observation – could the wealth of nations be due to the weather?

While obviously factors such as natural resources, agricultural productivity etc., and are major factors affecting economic output, there may be other factors at work.

Specifically, countries with cold weather tend to be rich while nations with hot weather tend to be poor.

Examples include the scandanavian countries, which have the highest GDP output per person in the world, and the countries of Africa which are generally poor.

I have done some analysis on this issue and it found a correlation r-squared of 16% between the average summer maximum temperature and the GDP per Capita ranking of the country.

In other words, this analysis is suggesting that on average 16% of the cause of the economic output of a country is determined by the weather.

This is quite a significant result given the myriad of factors that influence the economic output of a country.

There could be many possible reasons for this relationship, some of which could include:

• Higher agricultural productivity in colder weather.
• The need to build stronger houses in colder climates.
• A general attitude to working hard to stay warm in colder weather, and to relax in warm weather.

Full Employment

Part of the Reserve Bank of Australia’s charter is the pursuit of Full Employment in Australia.

Economists argue about the level of unemployment that indicates full employment.

A better guide would be the number of applications for each job opening.

Full employment is one application for one job.

Not 200 applications for one position, which is not uncommon.

I would argue that the laws that govern business and economic activity are a key determinant of the provision of jobs within Australian society.

Much work needs to be done before Australia reaches any kind of situation of full employment.

As an example of some changes that could be made, in many industries is it extremely difficult to establish a new business. This industry structure leads to wealth being held by an established group of participants and makes it very difficult for those outside the industry to win a place in the industry.

I would suggest a new law requiring business-to-business contracts to be published on company websites and banning confidentiality agreements, to allow new entrants a chance of competing (after a 3 year delay to enable the value of the contract to be utilised).

These suggestions have two goals – to give young people a chance of getting established in an industry, and to increase the total wealth of the nation. This doesn’t include contracts for personal services.

Business regulation has a number of goals

• To prevent individual groups being overcharged
• To benefit entire society through transparency and other tools. This does include any individuals that could be negatively affected in other ways.

Suggestions for third-world countries

Here are some suggestions for the economic development of third-world  countries.

1. Be ruthless in eliminating public officials’ corruption. Where one person has something they don’t deserve, another person suffers. This can be eliminated by imposing severe, widely-applied penalties for corrupt acts. For this to be viable, government officials must receive adequate salaries, so that they can support themselves without receiving additional payments.
2. Try to build high quality roads and rail services. This will enable the economy to be productive.
3. Ensure that government administration and the legal system is fast, simple, fair and efficient.
4. Impose appropriate business laws and taxes to prevent the wealth of the country accumulating into a small number of hands.
5. Don’t discourage foreigners from setting up businesses in your country, instead encourage it. They will take a share of the profits however they will provide employment for the local population, bring in valuable skills, and contribute to building the wealth of the country.
6. I would not recommend that you sell off your land to foreign companies or individuals. If you to this you risk becoming slaves in your own country with no assets or agricultural productive capacity.
7. Ownership rules for land are extremely important. Some countries have banned citizens from accumulating large parcels of land. The idea behind this is to ensure that every citizen has their own means of food production. However these laws probably have the opposite effect to the one intended. The system the results from these laws is one of poverty and subsistence farming. A better system would be to have a smaller number of citizens owning large parcels of land, where they could engage in large scale efficient agricultural production. This system also frees up citizens to work in higher value-adding industries.
8. Don’t be too generous with setting an early age for your retirement pensions. An overly generous pension system will bankrupt the country.
9. The concentration of business activity is a very important determinant of the wealth of a country. If business activity is concentrated in a few large businesses they will charge (high) monopoly prices and transfer wealth from the general population into a small number of hands. The USA found it necessary to bring in anti-trust laws around the year 1900 to break up monopolies and prevent this from happening. Regulations to impose minimum wages can also help prevent problems arising from monopolies. At the other extreme, having a large number of small businesses is generally associated with being a poor society. Business regulations should be set to prevent either of these extremes arising.
10. Determine which agricultural products grow better in your country than anywhere else in the world, grow these crops and export the surplus.
11. The process for obtaining government licences and permits, and the legal system, should be as fast, simple and cost-effective as is practical. This suggestion also applies to developed nations.

Violence and economic development

Violence has been a feature of human history.

Economic development is one of the great cures of violence.

These is no violence in a region where the greatest worry is finding enough time to take the kids to the dentist and to get the BMW serviced.

Poverty

It should be an aim of modern society to totally eliminate poverty.

Technology is so advanced in the modern world that it takes only 2% of the population to produce all the food that we need.

If poverty cannot be eliminated in a state such as this then our economic and social system is fatally flawed.

United Nations Poverty elimination Program

I have a suggestion for a United Nations program to completely eliminate global poverty over the next 50 years.

This should be achievable given the modern technology that is available.

This program would have the following features

• It is important to respect the culture and traditions of individual countries. It would not be the aim of the project to turn every country into a developed Western culture.
• A separate plan would be required for each country.
• Agricultural productivity would be an important component.
• Every country needs to develop export industries.

Financial Regulation

The USA is known for having a strong anti-government attitude and desire to prevent laws and regulations from intruding into private life.

While this idea has its merits some regulations are necessary to protect the innocent and enable efficient markets.

Here are a few suggestions

• A requirement that all jobs advertised include a salary figure or salary range.
• A requirement that properties and businesses advertised for sale should include a price or estimated price range.

These regulations would greatly assist individuals in their search for a property, business or job.

It would also assist the entire country by facilitating more efficient economic markets.

Ironically it would benefit a large number of people and doesn’t really disadvantage anyone at all (including the seller).

Basic Society

If modern trends continue, the global population of the human race will reach a peak in the next 50 to 100 years, then start to decline.

This could lead to the global population gradually falling, until the human race comes close to dying out in around 900 years from today.

The document below contains some thoughts on a possible stabilised society at this time, termed ‘Basic Society’.

Basic Society

Physics

Physics (2010)

I am not very well qualified in Physics (first year undergraduate level) however I have a few thoughts to share for the interested reader.

1. There has been considerable investigation into the structure of atoms through the use of high energy particle accelerators in recent decades. It may already be the case, however it could be considered that the various particles that exit the atom when it is bombarded do not exist within the atom initially, but are actually created through the high energy bombardment.

According to E=Mc² energy and mass are interchangeable. This is normally taken to mean that matter can break down to release energy. However the reverse should also be possible.

It is possible that a high-energy bombardment creates matter that did not exist before the collision.

2. Gravity is still not well understood. I have a suggested model for gravity.

Imagine two spheres suspended in a fluid, and vibrating.

The standing-wave pattern between the spheres could create a suction affect, leading to the objects being drawn to each other.

3. I also have a suggested model for light.

Consider a photon of light as a parcel of high pressure moving through space.

This may already be the current model for light.

Computer Science (2010)

Here are a few ideas regarding Computer Science.

Massively parallel CPU chip

The original 8086 chip used 29,000 transistors. The latest 18 core Xeon Phi CPU from Intel uses 5,000,000,000 transistors.

This means that using a single chip of silicon, it should be possible to make a chip that has approximately 170,000 8086 or similar CPU’s on it, not allowing for connecting paths or memory.

This massively parallel CPU chip would have many applications that are currently filled by supercomputers such as weather forecasting and physics analysis.

Music

The world needs more songwriters and music composers.

There are many performers with strong voices however they sometimes seem to lack good material to sing.

Maybe some bands die out simply from a lack of good material to perform.