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.
It has recently been found that an equipment went off an alarm of ERROR state and then does not proceed with water filling operation for bathtub. The ERROR code says, its temperature controller has got malfunction. EcoCute: Heat Pump Water Heater, the equipment is called. ——- Then, I contacted the service office of the manufacturer. The customer service personnel said that the production of the controller had long been stopped therefore its spare parts are no longer available. (Because the equipment is somewhat around 15 years old.)
Then, I attempted to pursue the service personnel further to seek an alternative temperature control device, saying “is that possible?”. Because, I am a sort of engineer and I understand that temperature control for water is not so difficult rather the technology, if I call it so, but anyway, is now a days of quite primitive and simply basic & matured one.
I am quite sure that it is not so difficult to find alternative parts and then assemble them together so that the same function is achieved. Of course, they have to make some adjustments so that the alternative can be installed in the very present EcoCute. That’s just a matter of engineering. But the service personnel blankly said “No sir, that’s impossible. Now the whole system should be replaced with new one.”
But temperature controller! Such a simple device! How can the alternative device not be found? There must be some alternative applicable to original system through just a basic engineering work!!! I tried to insist on, but —–, in vain.
How much CO2 will be emitted throughout the whole process of full system replacement. How much CO2 will be released to atmosphere if the temperature controller only is repaired or just replaced with new controller? Then how the difference will be.
Apparently, in the former, more of CO2 will be released than the latter. The manufacturer does not really practice sustainability, so I felt.
Maybe the company has to keep its personnel and increase its business performances; mainly the sales volume and profit.
My EcoCute looks intact in terms of its water tank, cabinet, piping, pump unit and electrical circuit, except for temperature controller. [Temp Controller] < [Whole replacement], in terms of CO2 emission.
Innovation, Economic growth, Conservation of the size of Economy, minimizing new production, maximizing innovation. Too much minimize may bring society a state of boring or depression, then no innovation and high entropy. But, too much “production” also may cause high entropy as well. And simply producing things does not necessarily mean innovation. If the similar products are continuously produced for a long period time, the state is considered as saturation; a kind of high entropy state. However, this time, replacing the unit fully is valued than replacing or repairing the temperature controller though the latter should highly be valued from the view point of carbon free society.
I see, the manufacturer would say, “Sir, we do repair it if the model is not so old for which repair parts are available”, without referring to those two ECO cycles. First of all, ecological cycle should always come first as it takes precedence over human. Ecological environment has created all the biological existence so far. Then after the dawn of human civilization, economic environment came. And both the ECOs have their own cycle respectively. Just a few decades of cycle the manufacturer takes for its economy does not match with that of ecological one, which does have rather longer time-cycle.
Anyway, now is it possible to find further controlled manner between the two sides?
EcoCute, the equipment. To produce the unit, if you have scientific and technological knowledge, you can design, fabricate and manufacture the whole in a small workshop, the whole process will take so much time though. Then, for industrial scale of production, you have to establish a factory and well organized people, energy of the process, subcontractors for parts production, help of transportation company etc. Once that industrial scale production scheme starts working, you have to feed it with continuous demand for new units, maybe overwhelmingly larger than it really is.
Is it possible to reduce new production while continuing repair work so that CO2 emission gets significantly reduced? Maybe reducing production of new units will kill the industrial scale production scheme. Then, the point is whether the manufacture can thrive on only repair work and just a few numbers of production of new units. (The number is quite limited comparing with the beginning of industrial scale production.)
Cars. Overwhelmingly frequent model-changes are introduced. If I say, it’s daily, that’s not so overstated remark, I suppose. Car makers have to keep its employees earned and to provide shareholders dividend while they are well aware of the state of saturation in terms of innovation, leaving CO2 in the air.
Can human overcome this paradox and guide its civilization to quite sophisticated and balanced state? Or else, is it a kind of unavoidable destiny of “Fall Of Civilization”?
Once I heard of Mirror Neuron. It is a kind of nerve, perhaps in my understanding. Mirror neuron, as it bears a word “Mirror”, it seems having function of mirror. Mirror reflects, especially when something that has its own consciousness sees its “reflection” on the mirror, the presence of the “reflection” causing feedback effect over the formulation of consciousness.
So, mirror neuron needs objects to be reflected, literally saying. But the device is not necessarily a real mirror rather is an imaginary perception of reflection that is taking shape in human consciousness (I’d rather say consciousness than brain) on any stimulation by any outside object it regards. For instance, human’s mirror neuron needs such outside object as other humans.
Without others human cannot shape itself, it suggests, I think. The reflection that is formulated through mirror neuron feedback process will not always be of positive rather be sometimes hater, anger, sadness, missing feeling etc. It sounds like to me something what Yoda said to Luke Skywalker.
Nevertheless, as long as others exist, our mirror neuron continues functioning, regardless of positive or negative.
Then, think about war. That means terminating the feedback loop with others. Don’t you think? Of course, exchanging fires seems somehow exchanging feedbacks but the final destination of war is to exterminate others, means cutting feedback. There only remaining are mounting dead bodies.
OK, sorry, my imagination has just overrun.
Maybe everyone has own problem in seeing the self, sometimes negatively, sometimes positively everyone sees the self. I am always trying to see myself positively but sometimes I face a situation that the more forcing me to see myself positive the further I’m getting negative. Anyway, scientifically also it has been proven that thinking positive leads human to positive manner and enhances its capability.
Obi-Wan Kenobi, one of apprentice of Yoda said, “Use The Force”. I am not saying Mirror Neuron is The Force. It’s just kind of metaphor for me.
Mirror Neuron has been and will further be an issue for researchers for neuro science and then utilized by computer scientists, phycological study etc.
Here I built a tiny SCRATCH program for short video image on my impression on Mirror Neuron. (For just killing time.)
Maybe some places on Earth, it has already been 2024, others have not been yet. Anyway, let me send this message on WordPress just slightly earlier than the start of 2024 in my time.
Wars are still there, environmental issues persist, anything that makes our civilization unsophisticated loams around, but at least I can be positive by reading through those blogs in this small cyberworld.
My personal life in 2023 was not so glorious but rather somehow of clusters of lessons. I must say thank you for all the blogs that gave me opportunities to think about things in a positive and creative way.
And I look forward to reading everyone’s blogs in 2024.
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.
科学好きの独り言 Science Monologue 