ARTWORK by Murray Young
Most of these works are mathematical, dealing with fascinating, important and useful concepts; my hope is that these works stimulate an interest in those concepts yet can also be enjoyed by anyone who has no interest in Mathematics whatsoever. The artistic quality here is mediocre at best; I have known at least four people who are better artists than I am so this is not false modesty. The best part of these works are the ideas they play with, ideas to do with music, imagination, culture and philosophy as well as mathematics.
THE DIGITS SET
- One is the One (One)
- Two Much Not Too Soon (Two)
- Charm (Three)
- Hedera Helix (Four)
- Safety in Numbers (Five)
- The Paragon of Numerals (Six)
- Cyclic Power (Seven)
- Eight to the Bar (Eight)
- Fire Beast (Nine)
TESSELATING THE EUCLIDEAN PLANE
The nine works in the Digits Set each features a single digit carefully designed so that it interlocks with itself and can be replicated in every direction infinitely tiling (i.e. covering) the two dimensional Euclidean plane with no gaps or overlaps.
1. ONE IS THE ONE – ONE. July 11, 2015. 30.4 cm by 30.4 cm
The second work I attempted was an early version of this work, completed July 5, 2015. After a few days I completely re-did the work and this is the result. The border numbers in this piece are all binary numbers. The Binary System, used internally by computers, uses just two digits, 0 and 1, rather than the ten digits used in the decimal system. An explanation of the border numbers:
- 10011101100 base 2 = 1260 base 10. 1260, unusually, has the same digits as the numbers whose product is equal to 1260, i.e. 21 x 60.
- 10001 base 2 = 17 base 10. 17 is a Fermat prime, that is a prime of the form (2 to the power 2n) + 1. A prime number is one with only two factors, itself and one.
- 110111 base 2 = 55 base 10. 55 is the tenth triangular number, which are numbers that count the objects that can be positioned to form ever larger equilateral triangles.
- 11011100 base 2 = 220 base 10, and 100011100 base 2 – 284 base 10. The factors of 220 are 1, 2, 4, 5, 10, 11, 22, 44, 55 and 110 which sum to 284. The factors of 284 are 1, 2, 4, 71 and 142 which sum to 220. These are Amicable Numbers.
- 10101 base 2 = 21 base 10. 21 is the eighth Fibonacci number. Each number in the Fibonacci Sequence equals the sum of the previous two, starting with 1, 1.
- 1111111 base 2 = 127 base 10. 127 is a Mersenne prime, that is, a prime one less than a power of two, first analysed by Marin Mersenne (1588 – 1648).
- 1101111011 base 2 = 891 base 10, the eleventh octahedral number, representing the number of spheres in an octahedron formed by close packed spheres.
- 11100 base 2 = 28 base 10. 28 is called a perfect number so it is equal to the sum of its factors (1 + 2 + 4 + 7 + 14) if you don’t count itself as a factor.
- 10111111 base 2 = 191 base 10. 191 is the tenth palindromic prime. It reads the same backwards and forwards, and has only two factors, itself and one.
- 1000000 base 2 = 64 base 10. 64, unusually, can be expressed with three different powers – eight squared, two to the sixth and four to the third.
- 1011000 base 2 = 88 base 10. 88 is divisible by the count of its divisors. It has eight divisors (1, 88, 2, 44, 4, 22, 8 and 11) and 8 goes evenly into 88.
2. TWO MUCH NOT TOO SOON – TWO. July 12, 2015. 30.4 cm by 30.4 cm
Many things can be said about two (e.g. it’s the only even prime) but this is not the place.
3. CHARM – THREE. July 14, 2015. 30.4 cm by 30.4 cm
The title is a reference to the irrational expression ‘third time is the charm’ i.e. that if bad things happen twice the third incident will be favourable.
4. HEDERA HELIX – FOUR. July 9, 2015. 30.4 cm by 30.4 cm
Hedera Helix is the name of an ivy commonplace in Europe, and Ivy can be read as the Roman numeral IV which means four. Four is the first non-trivial perfect square, and many other things.
5. SAFETY IN NUMBERS – FIVE. July 16, 2015. 30.4 cm by 30.4 cm
A safe prime is a prime number of the form 2p + 1 where p is also a prime (i.e. it has only two factors, itself and one). Five is the smallest safe prime.
6. THE PARAGON OF NUMERALS – SIX. March 7, 2017. 30.4 cm by 30.4 cm
Six is defined as a perfect number, hence the paragon of numerals. A perfect number is a number that is equal to the sum of its factors (not counting itself as a factor). Six equals one plus two plus three. In William Shakespeare’s ‘Hamlet’ (Act 2, Scene II), the phrase ‘the paragon of animals’ is used by Hamlet to refer to humans.
The early version of this work was completed July 17, 2015. A substantially better version was completed about two years later. In that new version the background consists of the number 1.61803 . . . which is phi, the golden ratio, a number with rather extraordinary properties. A second number, 6.28318 . . . is also visible, this time in red. This is tau, equal to two times pi. Some argue that tau, rather than pi, is the more significant number of the two since the circumference of a circle is tau times its radius rather than pi times its radius.
7. CYCLIC POWER – SEVEN. July 21, 2015. 30.4 cm by 30.4 cm
The smallest cyclic number is 142857, obtained by dividing one by seven and getting 0.142857 142857 . . . Multiply 142857 by two and you get 285714 which contains the same digits as 142857 and in the same order, but this product starts with a different digit. Multiply 142857 by all the numbers from 2 to 6 and the same thing happens, so it is called a cyclic number. There are an infinite number of cyclic numbers. The title of this work is a parody of the phrase ‘psychic power’.
8. EIGHT TO THE BAR – EIGHT. March 4, 2017. 30.4 cm by 30.4 cm
The musical phrase ‘eight to the bar’ refers to refers to an unusually fast and challenging improvised solo passage, and therefore usually something impressive or worth paying attention to. An early version of this work was completed July 22, 2015:
9. FIRE BEAST – NINE. July 27, 2015. 30.4 cm by 30.4 cm
Chinese dragons, also known as fire beasts, come in nine forms, they have nine attributes, nine children, and 117 (i.e. 9 x 13) scales. This work plays with the concepts of top and bottom and can be viewed both upside down and right side up.
According to The Kidd 