Our Boston Mensa Writing Group formed in 2008. Right from the beginning, Michael Coughlin joined us. Michael was well known in Cambridge, Massachusetts from the 1970s, participating in the music scene as a recording engineer. He adored all styles of folk music, especially fiddle music. Michael wanted to write essays about the theory of music and frequencies – how music varied from culture to culture, how it changed over time, and how humans reacted to it.
Michael was active in Boston Mensa beyond our writing group. For example, he was a regular at the New Mensans parties, welcoming new members with a smile.
The more our Boston Mensa writing group met, the more we realized how varied Michael’s interests were. He delighted in explaining to us why our novels about time travel were impossible. He helped us with in-depth research on near-light-speed travel and on telescopes. He showed off his own experiments on TV antennae of various shapes and sizes. He dreamed of creating a YouTube channel where he explained them to the world.
If a writer had a question about how radios might have worked in the 1920s, for a story about historic Alaska, Michael was right there with all the details and intricacies. If an author was writing a science fiction story about aliens, Michael had great insight.
Michael was fascinated with language. He continually honed an essay on how languages could be optimized by creating new letters which represented sounds. He was waiting for it to be just right before publishing it. He could definitely be a perfectionist.
He wrote an essay about what it was like to be part of the big smallpox vaccine push in New York in the 1940s. He was in the final stages of editing that one.
He loved visiting local museums and researching their statues. He wrote an essay about an Egyptian statue pairing at the Boston Museum of Fine Arts. He wrote another essay about a bronze Amazon statue at the Harvard Museum.
When the pandemic hit, our interactions grew. We set up weekly 2-hour Zoom meetings so everyone in the group could remain motivated and creative. Michael was there every single week. He would offer ideas, suggest constructive feedback, and was a wonderful part of the conversation.
Michael was always supportive, happy to listen, and had a great easy-going nature. We could tease him incessantly about time travel and he happily let us give our point of view, before calmly letting us know it simply was impossible.
Michael loved taking photos of cats and always carried a pocket camera to capture stray cat images. In fact, it was a camera I gave to him that had a shutter issue. Michael figured out how to fix it. He could fix pretty much anything. We’ve given him countless iPhones, laptops, and other devices over the years, and he always enjoyed fixing them up. He especially loved taking a Windows computer and installing Linux on it.
Michael passed away in his home in July 2022 at age 82. At the time, he had at least six different writing projects that he was working on. He was immensely excited about getting them published soon. He had just published his essay on the Bronze Amazon statue in the Boston Mensa Beacon, and another essay on time travel was in the review stages at the Mensa Bulletin.
We all miss him immensely.
Note that I checked in with the Cambridge Police and the Office of the Chief Medical Examiner on August 15th, 2022. They let me know that Michael’s legal name is James Michael Coughlin, and that they had found cousins of his who transferred Michael’s body to a funeral home. Legally, the office was not able to tell me which funeral home. I have not found any funeral home listing for Michael. It could be that Michael’s cousins do not have any intention of holding any ceremony and that they will not be posting an obituary for him. I will definitely update this page if I find any listing for Michael in the coming days.
In 2021, Michael Coughlin made a concerted effort to organize some of his thoughts about melody and music. He had wanted for years to write a series of essays about stringed instruments throughout history, how they were tuned, how their notes harmonized, and much more. He decided to tackle just one tiny aspect of this set of thoughts.
Michael felt his main challenge was how to explain this complex topic to a person who was new to music. He struggled to find ways to make this easy to understand. He kept putting the project aside and then returning to it.
Here is the essay from 2021. Michael was a brilliant, talented person, and it shows in the variety of interests he held.
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What makes a beautiful musical melody? With few exceptions, each note is consonant with the note before it and after it . After the invention of the lyre and harp, when two notes would be played together to tune the instrument, it was discovered that consonance is mathematically related to the length of strings and the tension they are stressed with. In recent times this has been expressed in terms of the frequencies of notes. Two notes are consonant when the ratios of their frequencies are small whole numbers. A ratio of two to one is the most consonant and is named the octave. Next is three to two, named a fifth, and four to three, named a fourth. As the numbers in the ratio get larger the notes are less consonant. If notes are not tuned precisely then they will not be ratios of small whole numbers — they will be ratios of large numbers so will be dissonant instead of consonant.. With numbers as large as five and seven things start to change from consonance to dissonance.
The problem of tuning a lyre or harp was solved early on by tuning pairs of strings in ratios of 3/2, 4/3, and 2/1. A collection of seven notes tuned this way was found to be particularly useful. After a thousand or two years this musical scale of seven notes was named the Pythagorean tuning. Unfortunately this does not exactly match what a singer wants to sing. But it comes close. The harpist can change the notes that are out of tune for each song.
Multiply the fraction 3/2 by itself four times. Also add 4/3
4/3, 1, 3/2, 9/4, 27/8, 81/16, 243/32
divide by 2 to make the fractions be between 1 and 2
Or start the Pythagorean scale at the high note and tune down 1/1, 8/9, 27/32, 3/4, 2/3, 16/27, 9/16, 1/2
Of the many musical scales that have been used to improve on the Pythagorean, one called the just diatonic scale has had the most influence. It uses intervals with small whole numbers. First written about around 130 AD by Claudius Ptolemy of Alexandria. it was also investigated by prominent musical theorists such as Gioseffo Zarlino and Hermann von Helmholtz. It is not favored by composers for orchestras since there are still small changes needed to keep everything in tune with a large number of instruments and key changes.
A comparison between a Pythagorean scale and the justly tuned diatonic scale.
How does this work out for frequencies? Musical notes are designated by letters. Let the first or lowest note in the scale be ” C “. The notes in a scale would be C D E F G A B. So the sixth would be ” A “. The pitch frequency of the note A was defined to be 440 Hz by an international conference in 1939. The pitch of the sixth note in the above Pythagorean scale is 27/16 times the first, so C would be 16/27 x 440 or 260.74 Hz.
Classical music has a requirement that any melody can be played at a different pitch by starting on any note. No problem for singers. For musical instruments five extra notes (flats or sharps) needed to be added to the original seven to attempt this. But it is still not possible to be perfectly in tune with the Pythagorean scale or the just diatonic scale. Many attempts were made to create such a well tempered scale and about two hundred years ago it was decided to use a compromise named the equally tempered scale. Easy to do with a guitar; much harder with a piano. The pitch of each note was given by multiplying by a factor of the twelveth root of two (1.059463). So if the note A is 440 Hz then A# is 440 x 1.059463 = 466.16 and B is 440 x 1.059463 x 1.059463 = 493.88 We lose the idea of using the ratio of small whole numbers but this compromise comes very close to sounding like a justly tuned diatonic scale and that scale can be played starting on any note.
Let us return our attention to the ratio of small whole numbers. The singing voice and certain other musical instruments (violin, trombone, Hawaiian guitar) do not have the limitations of the harp family. The singing voice can change the pitch of notes by any ratio. It is not limited to using the pitch of only a few harp strings. Around 1960 Warren Creel and Paul Boomsliter experimentally measured the pitch of familiar melodies produced by expert musicians and found they chose rational intervals but in combinations that did not match any conventional scales or temperaments. The instruments they used were a monochord with a six foot long string tuned with a steel rod like a Hawaiian guitar and a reed organ with a selection of keys tuned to confirm the measurements discovered with the monochord.
Start with a series of fractions 3/2, 4/3, 5/4, 6/5, 5/3 … these are intervals from the just diatonic scale. Add a few more fractions that don’t seem to be used as much 7/6, 8/5, 7/4. What Creel and Boomsliter discovered was that these intervals were only part of what was used to play music. They needed to be combined in other patterns. Start with one note in a series. Multiply by each ratio to have a selection of pitches to choose from. But then multiply all by another ratio to have a different selection. This is repeated several times. Unlike conventional musical theory that has notes related to a tonic pitch, Creel and Boomsliter found that what could be thought of as the tonic pitch changed as the melody progressed.
The following chart illustrates this. The vertical scale is frequency ratios in cents and fractions. Three generations of pitches are plotted horizontally. The left hand axis is marked every hundred cents and the corresponding Do Ray Mi Fa Sol La Ti Do syllables are indicated. The horizontal green lines mark the pitch of piano keys or guitar frets.
The first generation of ratios is 1/1, 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4, and 2/1. A collection of these notes is plotted as horizontal lines with their pitch values shown in cents. Next on this chart the second generation of ratios is 3/2 or 3/4 times the first generation. A third generation would be 3/2 or 3/4 times the second generation or 9/4 or 9/8 times the first. This is the same idea of producing the Pythagorean scale applied to more than one note at a time.
Music exists in major, minor and modal forms. Creel and Boomsliter discovered that using different ratios to change to the second generation made the melody change musical modes. To quote Warren Creel (1976) “Our experiments in Albany indicate that music in a major mode uses 3/2 of the first generation as reference note for the second. Music in a minor mode uses 6/5 of the first generation as reference for the second. Music in a blue mode uses 5/4 of the first as reference for the second.” Warren also states that several more generations are needed using the ratio of 3/2.
Creel and Boomsliter theory is a very radical departure from older theories. As a melody progresses each change of pitch is a ratio of small whole numbers, so it is a consonant interval with none of the out of tune beating of equal temperament. But notes that are several steps apart can have pitch ratios that are made of large integers. They need not come close to the notes of the equally tempered scale. Perhaps even more important such melodies can not be written as ordinary sheet music.
Composers of “modern” microtonal music frequently use equal tempered scales with any steps besides twelve. These are doomed to be out of tune.
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Fractions with small integers and corresponding cent values
A quote from the Catgut Acoustical Society — “Warren Creel and Paul Boomsliter worked together closely in the field of auditory perception and organization, studying pitch relations and durational effects in tonal perception, sensation, rhythm and cadence in language which they studied through music and poetry with related psychoacoustic studies, including animal experimentation. Starting in the early 1960s, Warren worked as a research associate in the Department of Surgery, Albany Medical College”
Paul C. Boomsliter and Warren Creel, “Extended Reference an Unrecognized Dynamic in Melody”, Journal of Music Theory, Vol. 7, No. 2 (1963), pp. 2-22″;
Warren Creel, “Musical Intonation For Fiddlers”, The Catgut Acoustical Society Newsletter, Number 26, November 1, 1976
In 2018, Michael Coughlin shared an essay with the Boston Mensa Writing Group about “fonetics”. It was Michael’s dream to revamp the English language (and all languages, really) by using new symbols to represent sounds. Part of his obsession was to present his case in a very specific format. He wanted the lines to wrap in exactly the right place. He wanted each character to be presented just the way he saw them.
We helped Michael again and again with formatting ideas, but he just never was happy with the end result. The only format which he was even remotely satisfied with involved a JPG image of his essay, so he could wrap each line exactly where he wanted. Having a JPG-only solution then posed problems for a number of reasons, such as how a visually-impaired person could “read” it.
Michael put this project off until he figured out a solution. Sadly, he never got that opportunity.
Here is what Michael was working on. We can share in his dream that the English language become easier to use. First I will show the JPG versions which he preferred. After that I will have the raw text, which might be harder for some display systems to show properly.
Image version of Michael Coughlin’s essay on fonetics:
Next, here’s the text version of this same essay by Michael Coughlin. Depending on your browser / device, you might not be able to see all the characters properly. For example, Michael used as a description the symbol less-than (<) with I and greater than (>). This combination means “italics” to most web browsers. So work had to be done to prevent this type of issue. This is exactly the issue Michael was having with his project.
* * *
When I was ten years old I discovered a disturbing aspect of the study of the English language. The alphabet had three extra unneeded letters (C, Q, X) that could be replaced with other letters. Worse yet many letters needed by the English language are missing. We say the alphabet has five vowels -- A E I O U -- but the English language uses three times as many.
It took a long time for me to realize that we did not have an English alphabet, but used the Roman alphabet for medieval Latin instead. How many letters were missing? The more I looked, the more I found, and the more confusing the subject became.
The answer was not to be found in any of my schoolbooks, or the books in the children's library, or the books in the adult public library. It was only when I searched in the largest textbook store in New York City that I found a good answer. I needed a book on the topic of phonetics. I did not need to study this subject to graduate from high school or college, I just wanted it to answer a simple question that any child might ask.
How many letters does a real English alphabet need?
This is something a ten year old can understand, but adults will have trouble with.
So can the computer help with this puzzle? Now we can write all the main languages of the world with the Unicode characters we have on our current operating systems, a big change from the days of green screen CRT monitors. We even have the International Phonetic Alphabet (IPA) characters available with some type fonts. These show up on web pages about languages between / / (or [ ] when being more fussy). Regular spellings can be quoted with < >. With the IPA we can write down any language even if it has never been written before.
Lets try that with English.
The first missing letter I always think of is <TH> which is neither T nor H. We need ð from Icelandic or Old English. But wait, ðere are two <TH>s. So we need θ from Greek.
English uses stressed or accented syllables. ðis just means important syllables are longer and louder ðan oðers. An unaccented or unstressed syllable frequently uses one of two special vowels, ə or ɪ. ðese are ðe most common letters in English but don’t have ðeir own symbols.
Now we have enough new letters to show a true fact about English ðat everybody knows but nobody can write. ðə definite article <the> is almost always unstressed and pronounced ðə before words ðat start wiθ a consonant but as ðɪ before words ðat start wiθ vowels. It’s a similar change as ðɪ indefinite article <a an> = /ə ən/.
Anoðer missing letter is needed for words like ship -- ʃip so we can distinguish it from words like sip and use ðə right number of letters. ðere is anoðer letter ðat goes wiθ it, ʒ, to distinguish bays from <beige> = /beiʒ/.
Now we have what we need to describe one of ðə strangest parts of conventional English spellings. Words like church and judge. Church starts wiθ a t. Judge starts wiθ a d. Sometimes ðə t or d gets put in at ðɪ end of syllables but not at ðə beginnings of words. Church is really tʃurtʃ and judge is really dʒudʒ.
But wait, it gets worse. ðese pairs of letters in speech actually only take up ðə space of one letter. So we need to have symbols showing ðey are squashed togeðer. ʧurʧ ʤuʤ. Now we don’t need to use j for ʤ, we can use it as it was originally intended a few centuries ago, a variation of i which was pronounced <ee> in Latin.
Here’s more of ðə story of <the>. It's ðe before consonants, ðɪ before vowels and <thee> /ði/ when its accented, someθing ðat doesn’t get written but does get spoken.
ðə letters M and N are nearly ðə same. M goes wiθ P and B and N goes wiθ T and D. But ðere is anoðer letter ðat needs to be used wiθ K and G. So we need ŋ for words like <ink> = /ɪŋk/.
Finding ðə new letters we need for all ðɪ English vowels is very difficult. We changed all ðə names for ðə letters a few centuries ago and didn’t change all ðɪ words and spellings. ðə first letter in ðɪ alphabet is ðɪ worst. In Latin it is called “ah”. ðə English name of A actually goes wiθ ðə Latin letter e. ðɪ English name of "I" starts wiθ “ah”. ðə main ways of pronouncing A vary wɪθ where people live. ðə IPA uses different type forms of letters for different sounding vowels. <Fool> becomes /ful/ and <full> becomes /fʊl/. ðose two different vowels need two different symbols. Likewise for O. ðə word <so> = /so/ but <saw> becomes /sɔ/. A word wɪθ only two letters should be written ðat way.
Dealing wiθ A E and I is quite a problem. Would you believe e should always be pronounced <eh>? No? Neiðer did I at first. It's a foreign conspiracy started by ðə Romans and Etruscans. ðɪ oðer version of E gets ðə symbol ɛ so we can write <bait> as /bet/ and <bet> as /bɛt/.
<I> is more of a problem. Its pronounced <ee> in languages ðat don’t fool around changing θings like English. We have a lot of words like <machine> ðat use it ðə old way. A small capital I is used for <pit> = /pɪt/ to distinguish it from <pete> = /pit/. An interesting case is <pity> which could be /pɪti/ or maybe /pɪtɪ/ depending where ðə stress falls. Unlike ə, ɪ can be used in boθ stressed and unstressed syllables.
I’ve saved ðə most confusing vowel for last. <A> has more variants ðan you can shake a stick at. So ðə IPA uses a whole bunch of different A type faces for completely different vowels. ðɪ old sound from Latin is just ɑ as in <bar> = /bɑr/, which is a different vowel ðan <bat> = /bæt/, and not ðə same vowel as <ask> = /ask/, ðə IPA doesn’t change ðat word. ðə symbols ɑ, a and æ are always getting mixed up boθ in speech and writing IPA depending where you are from.
One vowel ðat is in a class by itself is ʌ. You use it in words like <but> = /bʌt/.
Two oðer leftover letters are j and w. ðey are related to ðə vowels i and u but get stuck onto someθing else and don’t make whole syllables.
If single vowels are confusing, ðen θink of what to do wiθ diphθongs wich are vowels ðat start off one way and change into anoðer in ðə same syllable. ðɪ English name for I and ðə first personal pronoun is just such a case. It might start off wiθ ɑ, a or æ and finish off wiθ i or ɪ. I like to use ðə leftover j and write I as aj. Its ðə way ðey do it in Polish. Some people use ɑɪ instead. Two different ways of writing ðə same sound. Maybe ɑɪ means <ah> <ee> in two syllables instead. IPA transcriptions are somewat a matter of opinion.
Oðer English diphθongs are ɔj aʊ and oʊ.
Anoðer troublesome letter is R. It is pronounced or left out in different ways all over ðɪ English speaking world. Only people from Scotland can pronounce R. Everybody else just mumbles it. A word like <nurse> and a word like <word> doesn’t use ðə separate sounds of u o or r and needs anoðer symbol /nɝs/ /wɝd/. For unaccented symbols we need /ɚ/. Where I’m from we almost lose R at ðɪ end of words, but not quite, and not always. It depends on wheðer ðə next word begins wiθ a vowel.
wi naw kæn mɛʒɚ ænd kaʊnt ɔl ðə ɪŋglɪʃ lɛtɚz.
hir ðe ɑr.
p b t d f v s z θ ð ʧ ʤ ʃ ʒ k g m n ŋ r l
h j w ɪ i e ɛ ə ɚ ɝ o ɔ ʌ u ʊ æ a ɑ
aj ɔj aʊ oʊ
ðə lɝnəd ʧajnis ɛmpɝɝ kāŋ ʃī dì roʊt -- θɪŋgz ju stʌdid æz ə ʧajəd ɑ ðə lajt əv ðə rajzɪŋ sʌn; ðə stʌdiz ɪn jɔ mæturɪti, ə kandəl.
I’ve been working on an article for Lisa and Mused for years. It is not going well. The subject is complicated and has a vast literature. I want to summarize everything ever thought of in a few paragraphs. So I must take a bold step to at least get started even tho I can’t write logically flowing steps the way I’d like. I reserve the right to make radical changes, especially if you send me suggestions.
I still can’t find an easy way to get 64 characters per line.
Years ago my mother told me she did not enjoy science fiction stories about time travel. The idea was too impossible. How could I have a mother with such a limited imagination? I decided to think of a way to build a time machine and expand her horizons. After a while I realized all you would have to do is place every atom and subatomic particle in the universe back exactly where it used to be and travelling in the same direction at the same speed. Oh, wait a minute, that is impossible. It is even more impossible than anything I’d ever read of why a time machine is impossible. My mother was right!
Making up a story about time machines creates many paradoxical ideas. The past has never gone away and the future has a short cut to visit it. Where does our imagination stop and reality start? The past does not exist, except in our minds. The future has yet to happen. What we see is what we have. And not only can’t we put everything back the way it was at some distant time, we can’t know exactly where everything was there in the first place.
Travelling forward in time presents a different set of impossibilities then going backwards. Actually it is possible to travel forward in time a little bit as shown by Einstein’s theory of the relativity of simultaneity. Global positioning satellites need to take this into account. Suppose you wanted to make a big trip into the future? Then Einstein’s paradox of the twins comes into play. Build a space ship that can accelerate constantly forever. This is, of course, not possible. But I think this idea is more interesting than the usual fictional space ship magic of disappearing from one part of the universe and instantly showing up in another. As this space ship travels thru the galaxy constantly accelerating at 32 feet per second per second, all the people on-board will comfortably experience the same force they do on earth from gravity. Makes filming the story very easy. The space ship will travel faster and faster till after only a few months it will be travelling close to the speed of light. The passage of time and the view of space will be radically changed. After a few years the ship can be anywhere in the galaxy or even beyond. Half way thru the trip turn the ship around and decelerate at 1 G. Then travelers can explore their chosen stars and planets at their leisure. Reverse the procedure and come back to Earth. Surprise. Time on Earth has gone forward much more than time on the travelling space ship.
The idea of a 1 G space ship was written about years ago and it didn’t catch on. Too bad since it might have been an educational lesson for the theory of relativity. What was not known at the time is that the universe is not as empty as it looks. The night sky looks really dark and black but we now know there is a faint glow of light at various wavelengths. When the space ship accelerates to interesting speeds this light becomes blue shifted and strong enough to destroy things. Also the universe is filled with unknown “dark matter” that could also collide with and destroy speeding space ships. Then there is interstellar ordinary matter of various sizes. Colliding with a grain of sand while travelling near the speed of light is a very bad thing. Never mind colliding with a rock or comet.
Time machines have nothing to do with “science” fiction. They are fantasy. Mark Twain had the right idea when he wrote “A Connecticut Yankee in King Arthur’s Court”. No machine needed, just a strong blow to the head to go back and then the right spell cast by Merlin the Magician to return. Time travel is an exercise for our memory and imagination. You can’t put things back the way they were. But you can look back and decide how things could be different so you might know what you should do when similar events show up.
The laws of Physics are the same for time going forwards and backwards. Maybe time does go backwards, sometimes, for a little bit. Time might not apply to subatomic particles colliding. Maybe time does not exist and can be replaced by rules of how parts of atoms bump into each other. Physicists want to compute the state of the universe forward and backward without limit. And also account for things that happen in the smallest possible spaces in the shortest amount of time, as well as the largest things we can see and beyond what we can see.
This is not a subject only for Physicists. Impossible time machine stories are a refection of how we perceive reality as well as the passage of time. In many stories, the hero goes backwards and creates a disaster that prevents him from returning to the time from where he started. Perhaps other events occur to cancel his actions, or he needs to do something amazing to happily return home. The author has decided that the passage of time actually cannot depend much on what we do. Our lives are fixed by fate and we must follow a path that we have little ability to change. At certain places and at certain times people have thought that way. Now that I have invented an imaginary impossible time machine, I can look at things in a different way. It is not possible to go back in time since all the atoms can’t be put back where they used to be. At least in the past the atoms were in a certain place at a certain time. Travelling into the future is a whole different situation. The atoms of the universe have never been where they are going to be. Our impossible backward going time machine can’t just shift into reverse to go forward in time. It must be able to calculate where everything is going to be to put it there. An impossibility piled on top of another impossibility.
We can do much more than cavemen could, not because we are more intelligent, but because we know more about the world and how things work and don’t work. Learning about what is impossible is as important as learning what is possible. Right now the science of Physics has not neatly connected the radical new ideas from the 1920s of quantum mechanics combined with general relativity. Thinking about time machines is another way to try to learn what time really is and how to keep track of it.
