When computer algorithms for artworks can match art historians, accuracy will match precision

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Title picture

Biker and Son, Poster art. credit: Flickr.com, Moriza

When art historians evaluate an artwork, they ask and answer questions such as the time and place where the artwork was done, what school of art the artist represents as well as his influences, and the artists his work has influenced. Asking a computer using an algorithm to do this would be very difficult. This is a field where human intelligence is very much required. Yet, computers and computer algorithms can still help us novices evaluate a work of art.

Algorithms have been developed that demonstrates computer ability to perceive and understand art the same way expert art critics would. The algorithms work on the composition of colors and easily measurable artistic qualities of an artwork.

Computers as art historians: Good job done!

In a recently published experiment in the ACM Journal of Computing and Cultural Heritage, using approximately 1,000 paintings of 34 well-known artists,

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researchers showed that a computer was clearly able to identify different art styles and even little nuances between art schools using only visual content. The results obtained were largely in agreement with the perception of art historians and dwarfed what one can obtain from untrained humans in the analysis of artworks.

A similar algorithm that was designed to place artworks in particular artistic periods using artificial vision algorithms also gave outstanding results. The computers were able to “understand” images and also differentiate between artistic styles based on low-level pictorial information.

Low-level pictorial information encompasses aspects such as brush thickness, the type of material and the composition of the palette of color. Humans on the other hand perform art analysis more abstractly. They employ medium-level information which differentiates between objects and scenes in a picture and the type of painting, and high-level information that takes the historical context and artist’s knowledge along with artistic trends into consideration.

Computer algorithms for arts not yet fully explored.

The future is stillborn as to the scope and extent visual algorithms can be used in evaluating works of art. At least, when it involves broad artistic differentiation, usually amongst art schools and periods, computer algorithms can beat an untrained human in arts analysis but fall short in precisely dating art periods or styles. According to Miquel Feixas, one of the authors of the study that was published in the ACM journal, “it will never be possible to precisely determine mathematically an artistic period or to measure the human response to a work of art, but we can look for trends.”

This is not the only technique that has been expended towards paintings. Physicists sometimes use ion beams to determine paintings and painting authenticity. This is the first time though a machine has gone one step better than humans, whether trained or untrained, in evaluating and analyzing works of art. It is hoped that this work will also open the way for further work in developing image viewing and analysis tools, classifying and searching for collections in museums, creating public information and entertainment equipment and to better understand the interaction between humans, computers and works of art. Digital technology will not replace art historians at all, just as software has not replaced human mathematicians, but with digital technology, art historians have an arsenal that makes their work stand out with more precise accuracy.

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Conversion exercise in decimal and binary systems, part 2: fractions

In part 1 of these exercises, we treated whole numbers or integers. This second series will deal with fractions.

Fractions are divisions of numbers, as distinct from whole numbers. 2/3 is a fraction as well as 0.342. Most times, fractions are written as the latter, with a decimal place because it is more intuitive.

converting binary fractions to decimals:

Let us take a binary fraction like 0.1001 base 2 as recurring example. Note that the decimal point makes that number a fraction. The place values of binary fractions are determined starting from the decimal point and we count starting from negative 1 (-1). That is, the first digit after the decimal point has a place value of 2 raised to minus 1 or 2^-1. The second digit has a place value of 2^-2, the third a place value of 2^-3 and so on and so forth accordingly.

Therefore, to convert 0.1001₂ using the expanded notation to base 10:

0.1001 = 1 x 2 + 0 x 2 + 0 x 2 + 1 x 2 

= 1/2 + 0 +0 + 1/16

Then make all the denominators the same

= 8/16+ 1/16
            = 9/16
            = 0.562510  

Alternatively, you could convert the fractions to decimals and then sum up the decimals although that route might take a long1er time.

Another way is this:

1. Place the decimal point to a position at the end of the last digit. It is now an integer
2. Count the number of places you moved the decimal point and denote it as n.
3. Convert the integer to decimal or base 10.
4. Divide the result in (3) to 2ⁿ.
5. Produce the decimal from the fraction.

Place the decimal point at the end: 0.1001 becomes 1001.0

Count the number of places you moved the decimal point, n: 4.

Convert the integer to decimal: 1001 base 2 is 9 base 10.

Divide the result by 2ⁿ i.e 2⁴: 9/16

Produce the decimal equivalent of the fraction: 0.5625 base 10.

converting decimal fractions to binary

Decimals fractions can take two types, the fractions whose denominators are prime factors of 2 and those which the denominator is not. Denominators of the earlier type have terminating binary fractional equivalents while the latter have binary fractions which do not terminate and this is important when doing the conversions.

Time to stretch your legs? Credit: Wikimedia commons.

Let's take the 0.5625₁₀ decimal as an example before we try some other exercise with a fraction without a decimal point.

The technique is:

1. Multiply the decimal fraction by 2.
2. If the result is less than 1, place a 0 after the next decimal point else the result is greater than 1, place a 1 after the next decimal point and remove the integer part of result. If the result is equal to 1, place a 1 after the next decimal point; you have reached the termination point for the binary fraction.
3. If (2) has not terminated, go back to (1).

Decimal to binary fraction. Terminating.

Fraction	Result
0.5625	0.
0.5625 x 2 = 1.125 > 1	0.1

The result of multiplying the fraction by 2 is greater than 1, so I added a 1 to the next decimal place after the decimal point. The binary fraction, (or the result) is not going to terminate. So, let's continue. But first, I will take away the integer from the fraction.

0.125 x 2 = 0.25 < 1	0.10
0.25 x 2 = 0.5 < 1	0.100
0.5 x 2 = **1.0 = 1**	0.1001

By repeating the steps above, we arrived at a doubled fraction which is equal to 1. The binary fraction has terminated to arrive at 0.1001₂ as the result. It's simple, right?

Binary fractions that do not terminate are fractions whose denominators are not prime factors of 2. A denominator is the number under the dividing line in a fraction. Let us say in 2/3 the numerator is 2 and the denominator is 3. Converting this decimal fraction to binary will not terminate, though you might end the manipulation when you get a repeating pattern. Let us take 2/3 as an example.

A decimal fraction producing non-terminating binary fraction.

Fraction	Result
2/3	0.
2/3 x 2 = 4/3 = 11/3 > 1	0.1

The initial multiplication by 2 results in a number greater than 1. We place a 1 after the next decimal point, remove the integer in the fraction and continue.

1/3 x 2 = 2/3 < 1	0.10
2/3 x 2 = 4/3 = 11/3 > 1	0.101
1/3 x 2 = 2/3 < 1	0.1010

Note that the last row of the table is a repeat of an earlier row. The result is a repeating pattern: 0.101010... Binary to decimal system conversions and vice versa are fun. I find myself doing them sometimes even while listening to music. You can do the same. Gottfried Leibniz wrote an article about 300
years ago on the usefulness of binary arithmetic. You will find the discussion on chinese figures of fuxi interesting.

conversion exercise in decimal and binary systems, part 1 :whole numbers

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Conversion exercises in binary and decimals. Part 1: Whole numbers.

The decimal numeral system, the numbers that start from 0 and end at 9, are of everyday use in our lives. Sometimes we tend to think that all other systems play a little roles because we do not use them or see them in action.

Well, the binary numeral system might appear to be of more importance than the decimal system; especially if you are talking to someone who is conversant with electronics, computer languages and logic. They can also be of importance to you. Unknown to me, until I read a wikipedia article on
binary numbers , the Ifa priest makes use of this system in divination. I do not recommend though that you learn geomancy or divination because you want to understand the usefulness of maths.

Birds sitting on powerline. Each bird is a 1 and spaces a 0 in base 2.

I took the above picture because the positions of the birds is a good example I can use for the positions of the 0s and 1s in a binary system. If you represent a bird sitting on the power line with a 1 and an empty space a 0, the picture will produce the binary number: 10110000100110100110 base 2. Alternatively, if I represent each bird to be a ten in the decimal system, I will oblige your indulgence and make it number 90 base 10. So, for the exercises, we'll try converting the 90 base 10 to base 2 and then 10110000100110100110 base 2 to base 10.

From base 10 to base 2 (or from decimal to binary numeral systems):

A simple system of converting from decimals to binary is to divide the decimal number by 2 and if there is a remainder, place the remainder, which will be a 1, at the rightmost bit position but if there is no remainder, insert a zero. Then divide the resulting decimal number again and continue placing bit positions based on whether or not there are remainders until we arrive at decimal number 0. Then write down the 1 and 0s on the remainder column, starting from the bottom of the column such that the bottom is the leftmost bit position in binary numeral system. Your work is finished.

Let's show this with a table using the birds sitting on the powerline, or decimal number 90.

Converting 90 base 10 base 2.

Result : Decimal number % 2	Remainder (leftmost bit position)
90 / 2 = 45	0
45 / 2 = 22	1

Note our technique. Taking 90 and divide it by 2, we get 45 with a remainder of 0. So we insert 0 in the remainder position. Because the result is not zero, we continue the division. The second division, i.e 45 divided by 2 gives 22 remainder 1.

22 / 2 = 11	0
11 / 2 = 5	1
5 / 2 = 2	1
2 / 2 = 1	0
1 / 2 = 0	1
	1011010 base 2

This dividing and inserting remainders continues to the seventh row when the result becomes 0. When you write down the converted number in binary, from the bottom, taking 1 as the left most bit, then the next is 0 and then 1 and until we get to the last remainder, 0, we get 90 base 10 converted to 1011010 base 2.

From base 2 to base 10 (or from binary to decimal numeral system):

This time, we'll convert the bird positions in binary,10110000100110100110 base 2 to base 10. How many positions are there? Let us count: the leftmost is a 1, then a 0 and counting from there we have 20 bit positions.

There is a system of binary to decimal conversions that uses bit positions and successive additions of their face values and place values to get to the result. The face value is the literal value for a bit position and the place value indicates the bit position, counting from the right starting from 0, to which we raise the number 2. 101 base 2, for simplicity has three (3) bit positions, with the rightmost bit 1, having a face value of 1 and a place value of 20. The next bit position has a face value of 0 and a place value of 21 and the last a face value of 1 with place value of 22. This simple system of conversions adds up the face and place values thus: 1 x 22 + 0 x 21 + 1 x 20 = 4 + 0 + 1 = 5 base 10.

If we apply this technique to a binary number with twenty (20) bit positions, how enormous the multiplications and additions that have to be done, and furthermore, mistakes will surely creep in.

There is a simpler technique, and it is very elegant. In fact, this technique, which I found while reading the wikipedia article on
binary numeral system was what prompted this blog. I just was impelled to share it. It is called the Horner scheme.

These are the steps to apply the scheme:

1. Create a prior value and give it a value of 0.
2. Multiply the prior value by 2.
3. Take the leftmost bit in the binary number and make it the Next Available Bit. Add the result of (2) to the Nest Available Bit.
4. Let the result of (3) be the value of a box you will call, the Next Value.
5. Now, assign the Next Value to the prior value, or make the Next Value be the value of the prior value.
6. Provided there are still some bits that have not been manipulated in the binary number, or the next bit still have some candidates from the binary number, go back to (2).
7. If the binary number bit positions is exhausted, then the result of the conversion is the value of the Next Value box.

We can illustrate the Horner scheme with a little table using the 20 bit positions of the birds sitting on the powerline representation.

Illustration: Horner scheme for 10110000100110100110 base 2.

Prior Value	x 2	+ Next Bit	Next Value
0	0 x 2 = 0	0 + 1 (the leftmost bit) = 1	1
1 (the previous Next Value)	1 x 2 = 2	2 + 0 = 2	2
2	2 x 2 = 4	4 + 1 = 5	5

We started with a prior value of 0, multiplied it by 2, got 0, then took the leftmost bit as the Next Available Bit, which is a 1 and added it to the earlier result to get a 1 which was placed as the Next Value and then transferred to the prior value. Since there were still bit positions remaining, we continued by multiplying the prior value by 2, adding it to the next bit which is a 0 to get a 2 that was placed into the Next Value box. Continuing this algorithm for the third row resulted in a next value of 5.

Horner scheme for 10110000100110100110 base 2 continued

5	5 x 2 = 10	10 + 1 = 11	11
11	11 x 2 = 22	22 + 0 = 22	22
22	22 x 2 = 44	44 + 0 = 44	44
44	44 x 2 = 88	88 + 0 = 88	88
88	88 x 2 = 176	176 + 0 = 176	176
176	176 x 2 = 352	352 + 1 = 353	353
353	353 x 2 = 706	706 + 0 = 706	706
706	706 x 2 = 1412	1412 + 0 = 1412	1412
1412	1412 x 2 = 2824	2824 + 1 = 2825	2825
2825	2825 x 2 = 5650	5650 + 1 = 5651	5651
5651	5651 x 2 = 11302	11302 + 0 = 11302	11302

So far, we have calculated for fourteen (14) bit positions starting from the leftmost bit. I am sure you have realized how elegant Horner's scheme is compared to the earlier one that depends on face and place values? Especially if your bit positions are in the high numbers. Man, am I breaking out in sweat? Yet, the job has to be completed.

Horner scheme for 10110000100110100110 base 2 continued still.

11302	11302 x 2 = 22604	22604 + 1 = 22605	22605
22605	22605 x 2 = 45210	45210 + 0 = 45210	45210
45210	45210 x 2 = 90420	90420 + 0 = 90420	90420
90420	90420 x 2 = 180840	180840 + 1 = 180841	180841
180841	180841 x 2 = 361682	361682 + 1 = 361683	361683
361683	361683 x 2 = 723366	723366 + 0 = 723366	723366

So, finally, when there are no bit positions remaining, we arrive at the value of 723366 base 10.

Try out some exercises at home. You'll soon using this scheme yourself.

I will like to end this blog by noting that the Horner scheme is the conversion from base 10 to base 2 using division by 2 and noting remainders in reverse.

I leave this as an exercise for you to compare both methods. This underscores a trait in mathematicians that I admire very much: they have an open eye for patterns, even the queer variety. They have a knack for knowing what works most of the time if it has worked once in their life. They have an amazing memory recall system. I know it because I have experienced it myself.

Surprisingly, ancient India used binary numbers and applied binary to decimal conversions prior to 2^nd century A.D, more than 1500 years before their discovery in the west.

My next post will cover fractional conversions, conversion exercise in decimal and binary systems, part 2 : fractions.

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THIS BOOK IS A GOOD CHRONICLE OF HOW VERSATILE MATHEMATICS IS AND CAN BE IF WELL UNDERSTOOD AND APPLIED.

If you are asked to mention one element in nature that is ambidextrous, I am sure that water will be one of them. The late Fela Anikulapo-Kuti sang about the varied uses that water can be made us of in one of his songs.

water is used in manufacturing various liquid beverages

How we can’t do without water for washing!

Elements aside, one subject in life that is as versatile and can serve a trillion uses to human needs, that is as old as man itself, remember my post on counting?, is mathematics. One branch of mathematics that is prime to modern civilization, without which man would never have dreamt big dreams which have revolutionized science and technology, is calculus.

The count of the modern uses of calculus is endless, but I will attempt to mention some uses that will cover every faculty that man has endeavored to spend money and effort in his research endeavors. According to a professional resource on calculus,Calculus and Analytic Geometry by Thomas and Finney, Economists use calculus to forecast global trends, oceanographers use calculus to formulate theories about ocean currents, meteorologists use it to describe the flow of air in the upper atmosphere, biologists use calculus to forecast population size, medical researchers use calculus to design ultrasound and x-ray equipment for scanning the internal organs of the body, psychologists use calculus to understand optical illusions in visual perceptions and finally, drug companies use calculus to determine profitable inventory levels. The list can go on and on; I just have to stop here.

But whether calculus can help you to lose weight, or survive a zombie apocalypse, that is the subject of a book by Jennifer Ouellette, The Calculus Diaries: How math can help you lose weight, Win in Vegas, and survive a Zombie Apocalypse. You can get it from the Amazon.com bookstore online, or even Barnes and Noble.

The varied applications of calculus aside, the history of Calculus is laced with colorful characters lilke Isaac Newton, Baron Leibniz, René Descartes and Pierre de Fermat. The book also presents in vivid details how calculus can fit into your daily life; how you can use calculus to even calculate the stats on your blogger and Facebook Insights dashboard.

According to the reviews posted on the Amazon.com page for the book, I read that Jennifer Ouellette writes with a touch of humor, beauty and elegance. That her stint as a science writer and in physics gave her much material and experience to brace this daunting subject. She covers the basic principles very well. So if you are a student preparing for undergraduate degrees and you think an understanding of calculus is essential to your success, then you should lay hold of this book.

But the subject, calculus, has already defined the readership for the book, right? Don’t be in much of a hurry. Readers who are mathphobic, or afraid of mathematics, can even enjoy reading it. It doesn’t come with much mathematical formulas that could be daunting, one of the negative sides according to another reviewer but the writer did her majors in English and understands what mathphobic concerns her readers might and would surely face.

Why not get a hold of this book. I’d recommend it myself. I followed a link to her website and just subscribed to her blog feed.

So, for those who want to brave the world of calculus, I’d recommend the book:The Calculus Diaries: How math can help you lose weight, Win in Vegas, and survive a Zombie Apocalypse




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PATTERNS CAN EVEN BE FOUND ON THE SIMPLE HANDS OF A DIGITAL CLOCK.

When scientists discover new things they are aided most times by the patterns or models on which those objects are based. Calendars, for example the Gregorian calendar, were based on patterns drawn from natural observations, and so for so many scientific examples, like gravity, relativity etcetera. The list can go on and on.

I like to pretend I can be an inventor. Pretense or make-believe, where one works towards it, can lead to undiscovered treasures. So in my make-believe in looking for patterns in everyday objects like license plate numbers, colors of clothes people wear, shoe sizes at the market and telling the time, I search for factual patterns, hoping to make a sale.

Voilà, I did succeed one unholy day. That day was the tenth of October, two thousand and ten or when written in numerals, 10/10/10. It’s not everyday that the date and time gives you a pattern, and by the way, those do not look like patterns, just chance coincidences, so I decided to concentrate on the time.

Another eureka! It will surprise that when you copy and paste the hour hand on the minute and seconds side, you can get a pattern for every hour of the day, whether counting by 12-hour or 24-hours?

Let’s start from one o’clock in the morning. You will always get to the time: 01:01:01, that is one minute and one second to the hour. Another is 02:02:02 or two minutes and two seconds to two o’clock in the morning.

 

11

11

11

I noticed that every hour can be copied and pasted on the minutes and seconds side.

13

13

13

Even when the hour is close to midnight.

22

22

22

I really cannot find any functional value of this patterns except for the fact that they possess some aesthetic value. Also, I find much delight waiting for the next pattern to appear on the digital watch embedded on my handset.

There are times though when the patterns do not really make good matches on the hour, especially when you want to flip the hour.

For example, at one o’clock, when you flip the hour and paste it on the minutes side and then flip the minutes and paste it on the seconds side, sometimes the patterns follow but sometimes they do not.

01

10

01

The one o’clock hour do follow beautifully, but these pattern is followed until six o’clock.

05

50

05

But at six o’clock, when you flip 06 at the hour, you do not get a translation for the minute hand.

Notwithstanding, from ten o’clock, the pattern starts to make another connection.

10

01

10

 

11

11

11

And this connection continues until the fifteenth hour.

15

51

15

And breaks up at the sixteenth hour, when 16 cannot translate to the minute when you flip the hour readings. But at the twentieth hour, our pattern continues again.

20

02

20

 

23

32

23

Looking for unbroken patterns on flipping the hour hand is not possible, but the start and continuation of the patterns can create a good aesthetic graphic display.

As I said before, patterns in nature if one cannot find the functional value yet, can serve for their aesthetic value and also as a time killer, to kill the boredom. When I do find another pattern in nature, I’ll surely be blogging on it.

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IF ONE GREEN BOTTLE ACCIDENTALLY FALLS DOWN…

We all love nursery rhymes. I do remember, as if it was yesterday, the rhyme about counting ten green bottles on the wall, subtracting them by one until all the bottles on the wall have fallen down. I think it is a skill children learn about subtracting and how to count backwards.

Counting has always been with man since he knew how to acquire things. When one discovers that he has started accumulating material objects beyond the singletons, then he develops the innate ability to be able to remember how many they are, if one is lost, which it was and plan towards acquiring more. That is counting. While counting, one also develops the innate ability of naming the things counted so that he can group them together for remembrance and memorization. Therefore, a man possessing goats, yams and lands, names these things and counts each of them so he can distinguish all of them while being able to group them as his properties.
The simplest way of counting, which we all learn even from infancy, is to count by watching others. Then we express this ability with our lips. This is what some call recitation. From recitation, we decided to develop the number system so that counting can be done easily and quickly. Numbering can be done through tally or writing out numerals depending on whatever system one desires.

If you visit the market, you will be astonished that counting is a skill traders practice and have learnt to master. They have to know the totals of what they possess. They count as if by rote, even while sleeping, while walking and eating. They count the cash they have, the goods in the store, the debt they owe, the number of times the relative or girlfriend who comes to solicit for funds come every month. They have learnt to count so well that this skill has become a personal sin.

I think that is why from counting, they have also learnt to calculate.
Without the ability to calculate, we wouldn’t find a meaning to what is being counted. If you are counting forwards, do you wish to do addition or multiplication? Do not forget that multiplication is addition done in groups. Some count by adding one to the things before, some in groups of five i.e in multiples of five; some can also count backwards, doing subtraction or divisions.
Calculation makes it possible that you can predict the outcome of future counting. For example, if you know you have x goods in the store and you sold y number of them, by calculation of the subtraction, you can predict the outcome of a future count of those goods taking y from x.

Calculation also helps the counter understand the outcome of past counting and design appropriate counting projects. By calculating our counting, we can derive patterns from them due to repeated counting. For example, I have found that while counting the sum of the license numbers of Nigerian plate numbers that every time the sum is a multiple of 3, I can juggle the numbers so that they can fall in ascending order. Imagine a plate number is LH855KJA, the sum of the numerals adds to eighteen (18), which is a multiple of three, so I can rearrange the numbers as 666, then take one from the leftmost number, six (6), and add to the last six to derive a number that falls in ascending order: 567. Quite some maverick practice, but it works when you find pleasure in counting and numbers.

Abacus, one of the earliest mechanical calculating devices

Counting and calculation has been as old as man itself. A short history of counting involves when we counted by recitation and with the fingers. A mechanical calculation device, the abacus, was thereafter invented to aid in faster counting and calculation.

William Oughtred, the inventor of the slide rule

A Scottish mathematician, John Napier developed logarithms in the sixteenth century. Logarithms made it possible that multiplication and division were converted to addition and subtraction respectively, thereby making counting and calculation of numbers more easy, especially for very large numbers. William Oughtred, an English Mathematician, built upon logarithms to invent the slide rule, a mechanical calculation device, for logarithms.

Calculators which are electro-mechanical devices successfully replaced the manual devices above and eventually, they have all been usurped by the computer. The beauty and sweat of man’s efforts to count and calculate efficiently is embodied in the computer. Thanks to the computer, the absolute impossible, for example, genotyping living beings, is possible. Every single gene in the human body can now be counted and understood.

So, even if all the green bottles fall off the wall, you and I will still be counting in some other way, either through an app on a mobile device or a computer game.

Talking about games, I intend doing research on games that can aid in numerical ability in the nearest future.




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SPECIAL PEOPLE AND WHAT IT MEANS TO BE A DISJOINT SET IN HUMAN ABILITIES

A set is a collection of things where each thing in the collection is supposed to be unique. A collection of students in a class where each student has a distinct name is a set. As respects human abilities, a collection of the skills humans possess can be likened to a set because each individual, with a name, can be the set itself and the abilities and skills that individual possesses the objects or the elements of the set.

In brief, your abilities are a collection where each ability is unique within you and the control for each of them resides in your nervous system.

Usain Bolt showing off his lightning pose.

The set for human abilities is finite. This is because the abilities or skills follow biological, chemical and physical principles which of themselves are constant, well defined and unchanging. What is infinite is the ability of individuals to enhance these skills. A good example is Usain Bolt, the fastest man on earth. Running fast is a skill which many persons possess but they possess it to varying degrees. Because the focus is on the generality of skills and not the specific, “Fast Runner” skills is a single element in a set. This observation is pertinent because a set can be the element of or contain another set.
Therefore, we can visualize a universal finite set of human abilities which I choose to call the UniversalSkill.

What is a disjoint set? If two sets do not have any common element(s), then they are said to be disjoint. That means disjoint sets do not intersect. In human language, they do not share anything in common. They are unique. Some examples are the set of local governments in Lagos state and that of local governments in Imo state.

We humans can be likened to disjoint sets if an individual possesses skills or abilities that are common only to him or herself.

In a situation where people are interdependent, is this possible? I think it is not, but the possibility could arise in some situations. There are cases of people who are termed mavericks or eccentricities because they have a way of doing things that are common only to themselves. It turns people off, not so? Such persons are usually thought to be self-centered, people who refuse to share what they have, who refuse to participate in the master mind network of intelligent persons, hiding whatever they have as to discoveries and research.

I think someone who tends towards the disjoint should be a superman or superwoman. I wonder how such a person can survive? If you look at the situation closely, a disjoint set is expected to know nearly everything that he needs to in order to solve his problems; he should not rely on anyone but himself. He should be a closed object, impervious to intersection. But is that possible in a networked interdependent world?

I was watching a game on television, football precisely, when my mind drifted to these thoughts. I was so bent when I realized one point: special people are persons like you and I. They did not fall from some planet. They share the same skills and abilities like all of us but they have so practiced and trained themselves over the years on these skills that they have fine tuned them to a high degree of sophistication.

The implication is that there is no special person who can claim to be a disjoint set. Special people are persons who have been helped by all of us to succeed. A good example is Jose Mourinho, who is presently coaching Real Madrid. Without the support of the players in all the teams he’s coached, the management of those teams, the media, his coaching crew, FIFA, and time and experience , he would not have honed his coaching skills to the high degree of sophistication for which we admire him today. Same also for Lionel Messi, Cristiano Ronaldo and so on.

On very close observation, one should realize that as the set of special persons intersect with other sets, these other sets who are unknown and mediocre, help the special persons to solve problems which are of a less important degree so that the special one can concentrate on solving the problems that are more important and more abstract.
That is why special people are paid better.

On the other hand, one contribution of having disjoint sets in leadership positions is that they tend to increase the level of powerful nucleuses in a region. These are the men called Great, but of what use is a Great person where he is unapproachable, narcissistic and highly selfish? What use is an autocratic to the survival of the greater society? Surely no one appreciates any of these so they need violence and force to succeed.

This is my working definition of a special person: Someone whom the society has helped to succeed more than others by solving his less abstract problems so that he’ll ensure the survival of the greater society or of other persons in the society by solving their more abstract or sophisticated problems.

Can we make some nominations from Nigeria? There are so many: Chief Obafemi Awolowo, Tafawa Balewa, Doctor Nnamdi Azikiwe, Wole Soyinka, Chinua Achebe, Professor Chike Obi, etcetera. Unfortunately, all these names are from older generations.

It’s so difficult making a nomination from my generation. Can anyone help me out?
I promise to send a prepaid recharge card credit to anyone who nominates someone for the position of special person, according to the working definition above, who is below forty (40) years i.e an individual of our generation, someone born after 1970. Read my lips. Send your answers to my twitter account or my mailbox: nnaemeka.david@gmail.com; note the dot between both names.


follow me on twitter, @emeka_david

Even the Mona Lisa smiles behind the blackboard.

Beauty that is rare like a painting of the Mona Lisa can be found behind the blackboard, in front of a mathematics equation.
I had the “Oh my, what beauty!” experience while solving a well worn mathematics problem a new way. The problem: simultaneous equations in two or more variables.
I’m sure you do remember the age-old technique of solving simultaneous equations in two unknowns.
First, chose one of the variables as the one to exterminate. Multiply both equations, numbered of course, by suitable coefficients so that the variable that will be exterminated becomes the same in coefficients. You then subtract one from the other, giving you an equation in a unique unknown. Finally, you solve the unique unknown. Your answer for this single unknown can then be used to find the second unknown variable using one of the simultaneous equations as template.
Hmm! Very long process that!
Matrices is easier. That is where the beauty lies. Take the value of the second order determinants for the two unknowns; call this the raw determinant. For each unknown, replace the column for that unknown by the column for solution to the equations. Take the value of the determinants for each unknown whose column has been substituted. Then to get the value of that unknown, divide the value of the determinants for the substituted column by the raw determinant.
Easier. Faster. More energy efficient.
Don’t believe the above line until you get equations of more than two unknowns. I saw the Mona Lisa smiling behind the blackboard and it was a matrix blackboard with blue markers.
I’ll be taking calculus with my students tomorrow.

The Eternal Question: who is God?

I believe God exists but how do I perceive him? The eternal question that is mind bothering and so intriguing is: how do you perceive something your senses realize, yet if your senses realize it, how come it was not perceived?
To perceive is to understand, and to realize is to know. I realize God, I know God exist but I cannot perceive, I cannot understand him. That is the most daunting frictional force that plagues and burdens me. Who knows the answer to that question; who knows who is God?
I cannot get any help from l’hôpital, newton, russel etc. not from anyone. Will I go to the grave with tears in my eyes, asking myself everyday: who is God? Why does he not allow me to know him to the fullest as I wish to.
The Infinite Eternal Question is: Qui est Dieu?
Hello Universe, who is God?

Finding contentment while searching for roots

Don’t get me wrong – I am not advocating a cure all technique. I found contentment or peace of find while looking for the roots of a quadratic equation. I’ll like to share it with you.

Suppose you are given a quadratic equation of the form: ax² + bx + c = 0. In a given quadratic equation with double roots, α and β, one is constrained to work within the confines of given formulas like the sum of the roots and the product of the roots. Whatever other complex derivations you desire, whether in creating a new quadratic equation or playing with the roots, you must work within the confines of the sums and products.

That was what I was doing when I realized one simple truth: if I do this regularly, looking back at my resources, the sums and products of the roots, and only these, in order to create new equations or derivations, teaches me one thing: contentment. I have no other choice. I have only sums and products and no other resource to get to any other equation I desire. I have to control my desires and wishes, be satisfied with what I have before building or deriving anything new.

I wish someone else has a story to tell. Have a class on Tuesday. Been teaching my students matrices. We’ll have determinants next week.