Once I read about something of geometry of flowers. The article said that a key element of it is said to be pentagonal.
Fibonacci sequence, a famous mathematic, is said to be ruling over their geometry. Anyway, at a first glance, I can’t identify the relation between Fibonacci sequence and the geometry of plants and flowers, nonetheless I can feel they have certain mechanism of forming their shape, mechanism which may possibly be represented and/or modeled by mathematics.
Here is the recurrence relation of Fibonacci Sequence (Numbers). F0=0, F1=1 and Fn=Fn-1+Fn-2 for n>1 So, you see, pasts (term: Fn-1+Fn-2) accumulates in the present (term Fn). It looks to me of one of mechanisms of growth.
Also, a fact to be noticed is that Fibonacci Sequence has certain relation with Golden Ratio. The ratio is found in something that has beautiful shape.
Unfortunately, it is impossible for me to figure out how that mathematics reaches pentagonal. (There may be certain theories which were proven well by some academics or professional scientists)
Here I took pictures of several flowers which I found in a park nearby to explore a little bit into the geometry of flowers. You may find some pentagons there.
Cherry Blossom: Japanese like this very much in heart. But however deeply we love it, most of us can never be aware of its divine relation with mathematics without being told. Anyway, I can have Cherry Blossom party (Hana-mi). This is ——–, OK, the leaves look like vertically stretched pentagon, it seems. the “flowers” may contain something of Fibonacci, isn’t it?Azalea flowers. Japanese love this as well as Cherry Blossom.I don’t know the name. They were emitting fluorescence in the real siting though unfortunately picture can’t express it.Oh, Tanpopo!(Japanese for Dandelion) Can you properly pronounce “Tanpopo”? Sorry, today is about geometry of flowers and plants. So, can you find Fibonacci or pentagon there? I think in this picture there are some pentagons.
Debussy’s rêverie, Beethoven’s Moonlight Sonata & Für Elise and Sometimes I Feel Like a Motherless Child (Jazz Piano), I like their melody lines.
I have been long thinking of why I can identify those quite impressive and beautiful or “cool” melody lines. A melody is composed of multiple notes sequenced in a specific rhythm (length) to each. If I hear some of the notes arranged in a different rhythm, the melody will never be the one I can identify. Or if those notes are all changed to different pitch yet with the same length, then again, the melody will be different.
Maybe, the first note still reverberates in one’s consciousness or simply in one’s memory when the second has started ringing. Whenever a note starts ringing, relation between past notes crystalizes, a relation between fading past and emerging present that gives one an identification of the specific melody.
I just expressed it with a word “reverberates”. But that may not precisely convey what I am feeling with the mystery of melody.
Imagine hitting the piano keyboard of the first note and then 2nd, 3rd, and 4th, successively until the final note. You may identify or say, gain the slight impression of the specific scale if not being a well-trained musician. Then, the next is G major scale. As done with E minor, imagine doing the same practice.
The impression you have will be different from that of E minor although there are some notes that are the same from each other. Therefore, the relation between notes in a single scale might matter.
The first note then the second and the third follows, when you hit the 7th one, in your consciousness, all the past notes are still affecting the 7th in a degree and superimposing something over the 7th note that has just been heard thereby, 7th becomes something unique, as one of the notes in a specific scale.
OK then, what is the relation with physics? Yes, my crazy illusion says; the quantum particle with 4 dimensional theory of Einstein, 4 dimensional means 3 dimensions of space plus 1 time axis, might be like music notes. Because of time axis as one of 4 dimensions, any particle, its present appearance is affected by its pasts. So, I can’t help stopping an illusion that the time is successive single time points like clock pulse of digital system. (Oh sorry, this is a kind of mischievous.)
Why major and minor?
Major scales or chords express some kind of positive feeling. Minor scales or chords express some kind of negative feeling. For instance, let’s compare C and Cm.
C Major = C You can hear the sound at the site below.
You may feel some sort of feeling of upper tension with C while with Cm somewhat with lowered tension; negative or depression or sadness.
Chords and Scales will never disappear because they are just simply combinations of sound notes. And human can identify them as major or minor even if human achieve the life in which only happiness prevails. If such a negative of sadness is not necessary for human, then in a long-long future human will lose its capability of identifying minor scales and chords when human succeed to build civilization where only happiness rules. OK? Uuuuu, that sounds somehow wrong, isn’t it?
Happiness exists when Unhappiness exists. Oh it sounds somewhat like genuine proverb.
OK, I am not saying unhappiness is vital rather wondering if human can be in a state of infinite happiness, maybe the answer is NO. Even one is being in a state of happiness, the one can still identify the “beauty” of musical material that is composed of minor scales and chords. So, maybe we do not necessarily need to associate minor scales and chords with such negatives. They are just simply of beauty indeed and surely, although minor is sometimes applied to compose songs or music which are aimed at expressing some sorts of unhappiness.
Chords and Scales of Major and Minor
However, yes however, I have to say. I can’t eliminate a thought that the meaning of the fact that both Major and Minor exist would probably is happy history and sad history will continue happening especially such a thing like war and peace.
Major and Minor are categories of how human feel when they hear the music composed with those chords and scales. It is quite difficult to build a theory for feelings of human indeed and there are no such things like equation. Human behavior is often associated with evolution, “survival of the fittest”. And human consciousness is said to be crystalized in a way that the resulting consciousness leads the human to the fittest. Then, why does Minor remains as part of consciousness?
Probably, minor is used to express such things as sad love story, farewell, nostalgia etc. Or in a long future, will human be able to eliminate anything those sorts, completely thus minor will be no longer the fittest?
Only happiness exists. Is that possible? I think it means a devoid. Existence means contrast. Happiness can be contrasted with its opposite unhappiness. or maybe my wording is wrong. Happiness is ok but what should be its opposite. Happiness and ?????
OK, returning to the topic, Melody line and chord progression in a music – Time in physics -. In the sense of physics, negative and positive will be like plus and minus of electricity. There, any vector that makes thing directed to such things as happiness and sadness, is found or not, I wonder. But each specific series of notes in a specific combination like musical notes or melody will be like quantum particles acting throughout 4 dimensional time and space across the time expanse from past to present. But in physics, how to distinguish happiness and sadness. Is there any hint in survival of fittest? I mean, something that can lead things to the fittest means happiness? But I am quite sure “not”, though I can’t find any scientific or logical explanation. Anyway, ignorant confusion though.
Whatever. It surely is some kind of happiness, to be able to feel something through music whichever minor or major. So, please stop launching rockets and listen to music then happiness comes.
We are all exposed to so many negatives; criticized by others, be considered valueless by others, given a harsh downgraded in qualification by senior executive, failure of business, you name it. Or even sometimes you have to tell your once a lover goodbye. But you see in any of those there is no such things as killing people with rockets. And at least I can have just a short private time when I can listen to my favorite music, minor or major, that are beautiful to me.
By the way, is it a kind of hint to a breakthrough in modern physics which looks to me stacked that quantum put in Einstein’s world would be like musical melody? (Sorry, this is a monologue.)
Finally, if you like, listen to one of my favorites.
I am thinking of “Combinatorial Explosion”. The term is used in mathematics or computer science, it seems to me. So, I just freely trying to expand my ignorant imagination with this word.
1 Heart and 1000000 spades
When human predicts future or unexperienced, combinations are to be set. Nature will never simulate (predict) things rather it just built the world as it should be along with the progress of time whether or not it is favor to human. Or does have nature certain Algorism? If that is the case, combinatorial explosion will never happen. Only an absolute single combination should always be obtained. But that’s not true. Because our knowledge is not perfect while maybe nature is. Boltzmann once said nature always shifts toward the highest probability state. Let’s just think about picking up a card from a single bag where 1000000 of ace of spades and just 1 ace of hearts are put in. And then consider the probability of picking up the ace of heart. Once you miraculously have picked it up, the probability doesn’t matter. As long as any degree of probability exists do we have to consider it will anyway happen no matter how small the probability is.
Combinations continuously change along with the events happened.
Pi, its infinite lower digits or similar, such random may cause unpredictable and therefore be the source of combinatorial explosion. An event has happened. The next will follow. Then the cycle continues. So, each single event determines the ultimate destination of the whole.
It’s like that nostalgic talk of Murphy’s law.
If the time is infinite (putting aside Law of Entropy) any small possibilities should surely be existing anywhere in its infinite time span, like that ace of hearts, then because of its lowest entropy it always be the beginning for everything.
And as the time is infinite (if so) nobody can identify when a beginning begins like uncertainty principle. Then, the movement of nature should always be in orderly manner which graduate from the lowest probability to the highest. In this regard, no matter how small the probability is, it should happen anyway.
The point is combination should be as much elemental level as possible say elementary particle. The story of the ace of hearts does not contain any perception of time and sequence of events. Each single event affect any of succussing events.
Oh, I am losing my composure. Is there any probability that he gives up the idea of the war by the end of June 2023 saying that “I was badly wrong”? Even if he does, the world will never forgive him perhaps therefore the probability is calculated as Impossible. Anyway, this problem can never be solved by science.
It’s just the very Combinatorial Explosion, isn’t it?
Is the world entering a state of Combinatorial Explosion as there are lots of conflicts Energy, Environment, Food Supply, Demography, you name it, emerge? As the probability is within the time-space of elementary particle, our world and life will be of absolutely unique yet there are infinite numbers of another time-space set, I think with infinitely little confidence. (Oops I said it!)
I tried this subject “Combinatorial Explosion” this time. The result is the combinatorial explosion in my thought therefore at this point I better to stop thinking about it, it seems.
In a cave, they found strange fish. It does not have any eyes. Scientists observed that a long period of cave life deprived it of eyesight because in the cave there is no light therefore any visual device is meaningless.
In the near future, human will be deprived of faculty of writing statements because of AI.
Artificial Intelligence. It will bring us darkness of consciousness as like fish in a cave, don’t you think? Novel, poetry etc will soon be created by AI. Then will a situation follow in which nobody wants to be novelist or poet? Because, by the knowledge of a fact that real human writes them can one come to wishing being another author.
Will a world that is ruled almost by AI bring something new and better to human or it merely bring bad degeneration or retrogression? To what extent anything of so called artificial should be developed?
Sisyphus may abandon his toil of bringing the stone leaving the task on artificial Sisyphus.
Excess artificial leads to devoid of mind and spirits and most importantly emotion.
Pleasure is good thing for human unless it is given through dangerous drag. Pleasure given by such bad thing is “Artificial Pleasure”, we may call it perhaps?
With the emergence of practical AI, further the definition of human is getting difficult i.e. what does exactly form the meaning of human? Anyway, too much extreme will never be rational so it’s better to stop talking about it at this point.
I do not want to be like fish in a cave. However badly clumsy I am, I want to use my own system to an acceptable extent, the extent that can identify the meaning of human.
Please note that the talk above is just a lament and murmuring of an absurd man who is not convinced of the value of AI.
Good morning! Dr. Hypatia. What is the topic today in our classroom? How about observing stars we all together tonight then, please tell us about their movements in mathematical manner. Or shall we talk about Diophantus’ theory? ”Arithmetica” Dr. Hypatia, you are respectable “scientist”, who are still reminding us a spirit of scientific approach to everything.
Hypatia: I came to know her just a few years ago on some YouTube contents.
And then I have been so admired at those stories on her that this time on this science monologue, I can’t help writing about her eventually. Although I have just a few knowledge about her.
Alexandria, the place of a Big Bang of human knowledge: She was living in Alexandria in late 4th century to early 5th century.
Don’t blindly believe things without deeply meditating on by yourself! It is reportedly said that she often said something like that.
Her science and philosophy, that were destroyed by violence.
Stars in the sky, standing next to next we all there, all spirits huddled together, among those who are standing there, found is she I believe. Her spirit, with an astrolabe in her hand.
I have been admired at stories of revolutionary scientists who in their life were criticized as an outlaw, bothering the commonsense of the society such as Galileo Galilei. But in reality, it is quite difficult to be a person who tries to bring in an idea not exactly of revolutionary yet even of an improving something. They were courageous. And Hypatia was maybe I think one of those.
Now a days, world society looks shifting toward accepting new and revolutionary ideas than did in the era of Galileo Galilei. But in reality, the same expelling of new idea by conservatives actually is still being practiced of course in mild and gentle ways still exists, I believe.
I like star gazing. Whenever I look at stars, I can feel a kind of strength flows into my mind even if I am suffering from a negative thought caused through my daily life as I am not such competent person in my society. Dr. Hypatia, please give us the strength to carry on!
科学好きの独り言 Science Monologue 