Monday’s Math Puzzle

Mathematics is one of the essential emanations of the human spirit — a think to be valued in and for itself like art or poetry.

Happy Monday, wherever you are!

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“Mathematics is the supreme judge; from its decisions there is no appeal.” –Tobias Dantzig

Thursday’s Math Puzzle

“People tend to think that mathematicians always work in sterile conditions, sitting around and staring at the screen of a computer, or at a ceiling, in a pristine office. But in fact, some of the best ideas come when you least expect them, possibly through annoying industrial noise.” 
― Edward Frenkel, Love and Math: The Heart of Hidden Reality

 

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“God used beautiful mathematics in creating the world.” –  Paul Dirac 
Happy Thursday, wherever you are! 

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Wednesday’s Math Puzzle

“The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.”  ― G.K. Chesterton

Happy Wednesday, wherever you are! 

 

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Tuesday’s Math Puzzle

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Mathematics may not teach us how to add love or how to minus hate. But it gives every reason to hope that every problem has a solution.

Happy Tuesday, wherever you are! 

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Monday’s Math Puzzle

Mathematics is one of the essential emanations of the human spirit — a think to be valued in and for itself like art or poetry.

Happy Monday, wherever you are! 

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“a drunkard may not know which number is larger, 2/3 or 3/5, but he knows that 2 bottles of vodka for 3 people is better than 3 bottles of vodka for 5 people.” 
― Edward Frenkel, Love and Math: The Heart of Hidden Reality 

Live your beautiful Life! While there is Life, there is Hope! 

 

Why mathematics?

“Mathematics is the music of reason.” –  James Joseph Sylvester

 

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“Where there is no mathematics, there is no freedom.” 
― Edward Frenkel, Love and Math: The Heart of Hidden Reality

Happy Thursday, wherever you are! 

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What does it take to learn math?

 

“Mathematics cannot be learned by watching someone else (teacher, tutor, peer) do it — you need to do it yourself. Relate to trying to help a friend who has a serious problem: a text message 😦 vs. meeting your friend face to face.
Be responsible for your learning. It is too easy to “validate” your poor math test mark on the fact that you, and a few of your peers, agree that the “test was too difficult” or that the “teacher did not give enough examples to practice.” 
You studied hard and failed a math test. What do you do? How you deal with failure is a major key to success!
You work on a math problem and you cannot get the answer. When do you give up? Relate to persistence, grit.
Math makes you think and discover truly interesting things, You realize that it’s very little about talent, and a whole lot more about working hard. Don’t lead a shallow life, reflect often on people and things that surround you. Whatever you truly care for (parents, friends, sports, hobbies) requires your energy, dedication and lots of time.
Do not waste your time. Reference to the 10,000 hours myth (and how, by age of 15 or 16, some kids spend that much time playing video games). Imagine where you would be if you spent 10,000 hours doing math!”

 

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Happy Tuesday, wherever you are! 

How maths helps us understand why music moves people

Elaine Chew - Professor of Digital Media, Queen Mary University of London

“Music is known to provoke the senses, give pleasure and sometimes move people to tears. Surely this has little to do with mathematical models which are so frequently associated with cold and rational logic. So what can maths tell us about this powerful phenomenon closely connected to the emotions? Can mathematics help us measure what’s sublime or ineffable about a piece of music?

Music evokes strong emotions such as frisson (goose bumps), awe and laughter – and has been found to use the same reward pathways as food, drugs and sex to induce pleasure. A shiver down one’s spine or an uncontrollable guffaw when listening to music is most often a case of the music defying your expectations. Expectations can be defined in two ways: schematic – knowing how a genre of music is supposed to go – or veridical – knowing how a particular piece of music unfolds.

On one end of the spectrum, a performance or a piece of music that does just what you’d expect runs the risk of becoming banal. On the other end, music like that of PDQ Bach – which uses tongue-in-cheek egregious violations of known expectations – makes many people laugh.

The craving that comes from musical anticipation and the euphoria that follows the reward have both been found to be linked to dopamine release. As a result, performers and composers alike play with listeners’ expectations, often going to great lengths to carefully choreograph their expectations, and then sometimes breaking them, to provoke and heighten emotional responses.

Playing with expectations

In tonal music, which is almost all of the music that we hear and can be thought of as being based on a scale, the note sequence sets up expectations, then suspends, fulfils, or violates them. For a simple example, sing the first three phrases of “Happy Birthday” and stop at the end of the penultimate phrase.

Anticipation for the resolution to this musical cliffhanger creates a palpable knot in the gut. This hollow feeling can be further intensified by delaying the final phrase. The release is evident when the final phrase is heard and ends happily on the most stable tone.

Two things are at work here in this miniature example: tonality and time. Tonality provides a framework through which expectations are formed – and the play on time, the delaying of expectations, uses the framework to create a musical cliffhanger and titillate the senses.

Where maths comes in

Expectations can be modelled mathematically and time can be measured – so the shaping of both expectations and time can be described in numbers. Over the years, in my research lab, we have developed models and computer algorithms for quantifying tonal properties and expressive parameters in music. Many of the tonal analysis algorithms are based on what is known as a “spiral array model”.

The spiral array can be plotted in 3D to allow us to visualise the dynamic evolution of musical keys and spot when the notes and their timing combine to do something interesting to tug at our emotions.

As music is heard, the notes can be mapped to the model, duly weighted and summarised as points inside it. Movements in the space inside the model allow listeners to see deviations from expected tonal behaviour.”     Read the original article.

 


 

Happy Sunday, wherever you are!

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Tuesday’s Math Puzzle

“Take the challenge of your life.
Reach out to your goals.
There is no limit to what you can achieve.”
― Lailah Gifty Akita

Happy Tuesday, wherever you are! 

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“But in my opinion, all things in nature occur mathematically.”
― René Descartes