The War Between Music And Mathematics
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- Опубліковано 7 лют 2020
- Ted Gioia, author of Music: A Subversive History, talks about the 2,500-year-old tension between music and mathematics-from the Pythagorean tuning revolution of ancient times to the algorithms of the current day. For more information on Gioia's research into music history, see tedgioia.com/music.html.
Ted Gioia is truly a treasure of musical knowledge and history. I've started reading his book A Subversive History Of Music and it's an enlightening if challenging read.(There's a lot of information to digest.)
I remember a lesson in a college music class where we were assigned to dictate the pitch and rhythms of music from Appalachian folks...{I think our teacher wanted to see how we would react to music that could not be accurately written out}...Thank you Sir!...another Fantastic video
More advanced mathematics (e.g. Fourier transforms) can handle anharmonic ratios and even continuous sound spectra, including random noise. We need to understand this to design sound reproduction and transmission equipment. This is not to say that the intellectual input of a composer can be reduced to a systematic procedure (an algorithm) and few mathematicians would think so.
This made me think of Thelonious Monk (no bad thing) and his implied quarter notes, which don’t really exist in our western scales but did exist in his head and were realized through his hands. But… they still made beautiful mathematical sense. There is something very exiting about hearing a piece that makes perfect mathematical sense. I think for every piece it needs to, one way or another. But if you want to kill it then just ask yourself why and you will have poured your bucket of water on the flames. The difference is in the hands. The human element. Monk had the touch. The feel. And most of all the vision. An algorithm can figure all that out easily enough, cause its only math and even musicians can manage that, but it can’t take a breath and then play the piece in a unique, today only way.
The drummer I work with says it best. He holds a masters degree in jazz drumming and can play in perfect time to something approaching 400 BPM (seriously). But as he says the most memorable moments in his musical career have occurred when everybody in the band went slightly off time here and there for the phrasing, in unison. Now, try getting an algorithm to do that!
I have thought of this recently - the idea of "hits" being written by algorithms. Regarding Pythagorus: I had a conversation recently with a drummer about how I was at the beach trying to understand the "bpm" of the Gulf of Mexico as I was seeking inspiration and writing. We started talking about musical notes (how I naturally by ear I tuned my guitar to about 435hz rather than 440hz (modern standard tuning for A) and how there have been orchestras that have played in 435hz as standard A tuning in history. Some symphonies in Europe tune to upwards of 446hz or so because of the musical illusion that "higher pitch equals louder and more emphatic in nature." As a songwriter I believe "the notes between" are where the magic is - just how you said, the bending of notes in the blues. (Yes!!!) A church music director recently looked at me sideways when I said that often I played "In Tune" when I was technically "out of tune" (mathematically). I've also believed in the importance of going outside with an acoustic guitar and "tuning it to the moment." All this to say, my drummer friend said he heard it put this way: "One day, someone said there was 12 notes and we've been stuck with that ever since." It's so true! There is a "universe" of music between those 12 notes! Selah
Also, on the fear of mathematical reductionism - I've concluded within myself that an algorithm can never replace the human experience it takes to write and share / create music within a community of people. Songwriters are not dependent only on their ears and "hearts." So, while the songwriting process can be explained and replicated mathematically, (maybe why there is so much "bad" music out there), the songwriting process can never be legitimately "taken" as long as we are "human." Even producers, there is a magic that happens when they twist the compressor knobs beyond themselves and achieve something magical. As long as we are humans who value and understand "meaning" there will be songwriters and artists who call us back to our humanity and create opportunities for reflection of whatever current state of affairs that there is. In my view, music is exactly the tool that will bring humanity back to and through this rapidly expanding technological revolution. We do not need to be afraid. Just like time, music will always have deep spiritual messages for those with ears to hear, and while there is a science that could replicate the magic of a song - the ultimate "magic" of music is more spiritual, relational, and based in the context of human / human and human / divine interaction. - I suppose it could be argued that a pseudo-process of all this could be initiated via algorithm and that the results could potentially foster genuine connection as I mentioned above, however even still, there will still always be the songwriter, poet, artist, who will also be perfectly capable of the process, because it is innate to the artist. If such algorithms push the boundaries of what we know as music today, then ultimately it will only act as an inspiring force for the next generations of poets and songwriters. Great topic! Love your work - thank you!!!!
I believe your drummer friend might have oversimplified the answer. While one can experiment with microtonality, it is challenging to find beautiful sounds except for a few exceptions. In reality, our music is more based on heptatonic scales, and the 12-tone system arises from the intervals that result from it. I hope that musicians of the future will find a way to create truly beautiful music using microtonality, but I think we still haven't found the right path yet.
please make more of these videos. They are fucking amazing!
Great as usual. Reminds me of a specific part of your How to Listen to Jazz book:
"The African tradition conceptualizes music-making as the creation of sounds. You may think that music-making is obviously the creation of sounds, but that's not really the case. The Western performance tradition of the last two millenia has been shaped by practitioners who conceptualized music as a system of notes -- of discrete tones, tuned in scales with twelve subdivisions. Back in the days of Pythagoras, Western musicians had to choose between creating sounds and playing notes -- and they opted for the latter. But African musicians never got enlightened (or is corrupted the better word?) by Pythagorean thinking. They followed the other path -- creating music that drew on infinite gradations of sound, and not just twelve notes in a scale."
African music is made of discreet onsets of sound in time. Usually there are 12 onsets per cycle. The most common bell pattern has 7 onsets in the space of 12 and follows the same pattern as the major scale (whole whole half whole whole whole half). The polyrhythms played by supporting drums often follow the ratio of 3/2 the same ratio as a fifth in harmony or they use 4/3 the same ratio of a fourth in harmony. Furthermore, the subtle variations off of the metronomic time are very precise, not random, so there must be some math (probably fractals) that defines them. I don’t understand why he thinks African music has more sounds than European (europe has gongs, jingle bells, timpani, etc). African music is full of rules and logic. Bell patterns in Africa are equivalent to scales in Europe. Polyrhythms are equivalent to harmonies (they are just a much lower frequency).
@@johnnygraves8741 MIND BLOWN! Thanks for pointing out this incredible connection between the common 12/8 African bell pattern and the major scale. Wow.
@@johnnygraves8741 Another interesting note- this is the ascending major scale that corresponds in the way you pointed out. If we apply this concept to a descending scale, the result is the Phrygian mode! (So this is nearly a very clean explanation for the existence of minor, a question I’ve pondered.) Really fascinating to consider all the implications of this... for example, the prevalence of Phrygian mode in Spanish music, Spain having been occupied by the Moors for many hundreds of years.
Well I think it's businessmen who want to reduce music to algorithms. We mathematicians are more humble. Pythagoras was just obsessive. He had one of his followers killed because he spread the existence of irrational numbers outside the cult. Leibniz had just invented calculus and probably imagined he could do anything. Wouldn't you. Descartes thought he could prove the existence of
God after he invented analytic geometry. But really, just getting bird movement right in animation has been really difficult. Managers always think their machines can do more that they can do. People who try to reduce life to algorithms insult life and algorithms. Mathematics is an art. It is as beautiful as music.
Timbre is another essential aspect of music (I would say specifically of modern music) that can't be notated.
electronic music with noise, non-diatonical soundscapes and non-linear filter overtones is just the revolution you speak about.
Great presentation!
Thanks so much Ted for this presentation. Among other things, it made me think about Bartok's use of the " Golden Section " within some of his pieces: .618 and .382.
I learnt so much from this, thanks!
Great video. Well done.
I get the point here but so many people are scared of “reducing” things to maths. Maths does not reduce anything. Maths just describes what is in nature in a formal way. What is reduced is our intellectual ability to describe most of the subtleties of nature in formal systems. Actually it is proven that all formal systems are flawed. So we don’t need a revolution against maths. We need to show math how great and rich musical nature is, and challenge it to describe it, so we can then go into richer details and challenge again. This way, maths and music will grow together. Make peace, not war
well, it does reduce it, because it has no language for the essence of music: spontaneous, irrational emotion. It cannot formulate that, so it leaves it out of the equation. It's like the difference between looking at a mathematically correct map of Mount Everest and actually being on Mount Everest. The experience of being there will be shockingly different from the experience of looking at the map, because the mathematically correct map has left out so much other information that cannot be described using map logic.
There's a brilliant term originally coined by Nassim Taleb and later used by the political-economist Mark Blyth, "intellectual yet idiot." Basically it's really smart people doing really smart things arriving at really dumb conclusions. You have economists who craft brilliant mathematical models of the economy. They begin to dogmatically believe in their model, until one day everything comes crashing down when inevitably the unpredictable happens. As you said, all formal systems are flawed. But society has fallen into scientism, and believes too dogmatically in its mathematical abstractions, it forgets that models are only approximations of reality. I agree about making peace, not war. Mathematics and modelling are highly important, and always will be. But I think it deserves some pushback, because we've been far too uncritical for far too long, and therefore we've turned it into dogma, not science.
Ted, glad to have found your channel! I've been digging your writing for a while (Birth and Death of the Cool is a favorite) and loved the Beato interview. Also been sharing your great article on fake spotify artists. I hope you don't mind me sharing a few thoughts in reaction to your ideas here.
I think your point here has a lot of merit, but I'm not sure I buy your argument with respect to Pythagoras, tuning, and a so-called "African" music. I'd urge you to reconsider-some would see it reductive and relying on stereotypes, and at the very least it's somewhat overgeneralizing and not very accurate with regard to musical history (at least as far as I'm aware - happy to be corrected if I'm mistaken here).
Pythagoras was supposed to have studied in Egypt (which is in Africa) and his theories and ideas were also very influential on Islamic scholars such as al-Farabi and ultimately Arabic music (of which a significant portion is African).
The pentatonic scales favored specifically in much sub-Saharan African music are also clear expression of Pythagorean ratios (regardless of how they are derived, most likely from acoustical resonance and not as a direct influence of Pythagoras), while European music from the Renaissance onward is largely based on both Pythagorean and non-Pythagorean "Just Intonation" ratios based on 5:4 (thirds, non-Pythagorean) and not just 3:2 (fifths, Pythagoras' approach).
Meanwhile, Arabic and Turkish music, which was distinctly influenced by Pythagoras and the scholars he influenced, is some of the most microtonally variable music on earth and uses both precise ratios and many forms of expressive intonation of the type that you reference in the blues. So clearly the hypothesis that adopting Pythagoras's ideas leads a loss of the full range of pitch expression is not supported by the historical record or musical practice.
I always like your writing a lot-you're an insightful writer and creative thinker-and I think the overall point you're making is still generally valid. There is undoubtedly tension between different aesthetics, precision and mathematical rigidity, and it's very clever to draw a connection between this as an aesthetic tension and the current role of computer algorithms in the music business. But the presentation of a tension between the discrete tone system of "European" Pythagoras (not really European) and a supposedly continuous "African" approach (supposedly non-Pythagorean) is suspect. The tension you describe does exist and the manifestation in the history of American music is entirely correct, I think, but drawing a line to Pythagoras as a direct contributor seems misleading and distracts from the more important points you're making-at least for this reader :)
An alternative possibility might be that a focus on developing complex harmony reduces the opportunities of melodic expressiveness with respect to tuning, as the more voices there are the more potential there is for conflict. This is arguably congruent with the evidence that jazz became less variable/expressive with regard to intonation over time as the harmonies employed become more complex (compared to the blues). One can certainly argue that BAM retains to this day an inherent give and take between melodically expressive intonation and harmonically mathematical intonation. This is still only a hypothesis, but seems to me more grounded than claims about the influence of Pythagoras.
Of course there's only so much one can explore in a short video, it's naturally a bit limiting and one doesn't expect the same rigor as a scholarly article. The topic of the role of notation is a whole can of worms on its own that would merit several hours' worth of videos - one aspect the deserves more attention is that notation by design requires a degree of precision that is not inherent in the general idea of composition, and that Western ideas about composition have been highly influenced by this arbitrary and unnecessary requirement of precision. Of course there has been some modern reaction to this with stochastic/aleatoric practices and notation, but the general idea is so deeply ingrained as to seem "natural" and inevitable to Western-trained musicians.
Anyway, just some thoughts to consider perhaps.
Fun fact for those who don't know, the concept and term "algorithm" is named after the Persian scholar Muhammad ibn Musa al-Khwarizmi, who is credited with inventing the idea that zero is a number and wrote the first treatise on algebra (also an Arabic term: al-jabr wa-l-muqābala, i.e., “reconstitution and equation.”) Presumably, he was also influenced by Pythagoras.
Great post, Brian. Thoughtful, considerate, adding value to the discussion.
Loving your work, I was wondering what books on music / jazz history do you recommend reading.
Very good and well researched.
Wonderful!
Thank you Ted 🙏🏼
Awesome,I'm so glad i found you,you've had me thinking all day...this is kind of my latest muse..don't ask just play..lol.thank you
Math is a tool that describes, it doesn't create.
Everything is math as a musician and a carpenter I can see math in everything and when you can blend the math with the soul or consciousness you get art …. Sculpture and Mechanical design are the same
Fascinating
Excellent and insightful. It would be helpful to point out that mathematics (here, arithmetic representations of music) and algorithms (rigorously defined logical procedures for music) are not the same thing. However the idea that music as a human art always transcends and eludes both arithmetic representation (e.g. Pythagorean approaches to scales) and algorithms (e.g. AI approaches to musical aesthetics, composition, or performance) is important.
Thought provoking!
Music, being waves of vibration (and contextual absence of vibration), is, of course, something that behaves in a way that math describes very well. If all that existed were these waves and humans describing the waves as best they can through math, there wouldn't be much to discuss. It's just not that complex.
It's when we use these waves to create where we find we need more than to just describe. When we use our voices or instruments to create sound, we stumble onto what pleases us and then we try to create more of it and even pass it to others to recreate and enjoy, and maybe even change to something else that pleases.
In the era before we could record musical sound onto devices capable of replaying it with fidelity, we found a way to jot it down onto paper (as Ted talks about). As one who dabbles in music composition via pencil and staff paper, I commonly find myself unable to truly notate what I hear in my mind -- and that's following a predefined 12-note scale where I mostly compose diatonically. Even when I chromatically venture outside the scale of the piece, I know I am composing within a larger taxonomy that I cannot escape.
I love African music, but I have never tried to notate it. On watching Ted's video, I tried to conjure up in my mind how I could possibly notate that. Some of it, yes; but much of it, well, there's no way to do that on paper.
I am not so sure that music can challenge mathematics, since there is no sound that cannot be described mathematically. But I take Ted's point (if I understand it correctly), that if we are to progress in music we must break free of the constraints of classical music notation. (I find myself a little worried about offering a criticism of a musical process that produces notation of, for example, Mozart or John Williams scores!) I wonder if we are already moving in that direction? Much of commercial music today is composed by humans using computers with software that grabs samples from prerecorded instruments (including human voices), and where the composer can optionally use a keyboard to set the pitch and sequence of the sounds. Controls can bend sound and filters can do other very strange things to it. To a very large extent, composers using these tools can create music that cannot possibly be accurately notated. Indeed, many of these composers are illiterate when it comes to classical notation; even so, some of them are creating amazing music, free of the classical constraints of notation.
Your comment is very thought provoking and lucid.
I find myself writing using scales and developing chords and melody progressions with my main instrument, guitar. But what I get really excited about is using modern effects pedals and synth programming to achieve micro tonal variations and modulations that I've never heard before. Using these effects processing tools can leverage the good side of the algorithmic influence so that we can achieve new sounds and, ultimately, a new form of art like Jazz or the blues. Algorithms freak people out because they fear being replaced and ultimately rendered obsolete. And there's no more uncomfortable a feeling than having a computer express the human condition better than the human can.
But the human artist will remain at the center of creativity. Successful artists in the future will leverage the novelty of AI and algorithmic sound processing with the raw power of traditional instruments(and voice) to create new sonic landscapes which reflect the reality we all live in. Sort of like how Radiohead took historical rock and classical influences and synthesized them using modern effects processing and made music which reflected the era and seemed to predict a future of an overly connected technological society.
They took it as far as linking the uncanny beauty of Paganini's music to the big D himself... I always find labels funny and I like Math Rock the most. Artists who are willing to explore the deepness of rhythmic and harmonic overlaying, explicitly based on math and its so called Sacred approach. I have Tool and King Crimson in mind right now. But it is also worth mentioning the more cynical and aesthetically idiosyncratic approach of Maestro Zappa (Zappadan 2021 in full observances, Dec 4 to 21) of the promotion of radical use of Rhythm over melodic conventions, in what he brilliantly describes as Statistical Density (see The Black Page, Zappa in NY 1978 release, marking Zappa's forced "sabbatical" 77, one of the only years in his career w/o a release, because of WB and the famous lawsuit that ensued, other were 1980 and 1990).
Brilliant
Speakin about "war", "music", and "revolution" ,...Sir Mr. Gioia you really really need to do one one about Django Reinhardt and Sinti guitarists of today. Discovered your Channel a couple hrs ago when I was supposed to be sleeping. I got the butterflies watching. I think I know what you stand for. I'm really no one to talk, but I feel that there's a possibility to fortify "jazz". I know it sounds crazy. But I really love the videos i've seen so far. You should check into Christaan van Hemert's channel. He's "formally" taught in violin, but he's teaching jazz guitar the Sinti way, and there's others with the similar approach. There's been quite a few that have expressed opposition and dislike in his method, I've witnessed for the 3 yrs i've been learning from him. I have a feeling this might and could be that spark for that "African Revolution" you're talking about.
Great video. Algorithms are great and have been used explicitly since Xennakis most notably, but even back to Schillinger. If you think that's weird, just wait 'til you hear about set theooy. :P
Music for me is about creativity and emotion. The act of making and enjoying sounds. Of course you can _describe_ any aspect of music mathematically. You can recreate, maybe even create it algorithmically. But that doesn't mean that music _is_ math. Also, we can automate any tedious and hard work away with technical solutions. That's fine. But why on earth automate something away that we thoroughly enjoy and that gives our lifes meaning like composing, improvising, and playing music?
It was not only Africa! Even in Europe the classical trained musicians (most of them) rejected the enormous traditions of european folk. Where scales, tunings were not respected by the traditional instrument constructors. And that what is great about the old recordings, where you can listen to isolated villages players with no training at all playing. Simple and humble people keep it simple and pure. Thats why when you listen to a work chants "Cantar Alentejano" of south Portugal you can relate to African tradition. Or the bag pipes of north Portugal you can see the exotic characteristics of the islamic traditions. That people keep the traditions and ways of doing from the old days.
How to practice and play in African system? What do we must read or exercise?
Tangent Comment- Pythagoras played the Lyre and has been said, in some circles, to be related to Apollo (his son, possibly). Apollo was given a Lyre by Hermes and became a virtuoso of that instrument which was also Pythagoras's main instraument. Pythagoras's name is said to have been derived from Apollo's alias Pythios. So, if you want to believe in "fantastical thoughts" Apollo & Pythagoras could be the main influencers of western music... 🤔
I like to think of an Al-Gore-rythm as the former vice presidents inability to keep the beat on a nightclub dance floor.
Hope you get a chance to listen some of my compositions. Let us know what you think ? Classical Jazz ad more ! UnderGround 3000 or Jason Cremasco
Excuse me, but I suspect there's still space remaining between mathless music and inadequate algorithms. I would point to the example of the actual randomness of stochastic music vs the unpredictability but actual determinism of chaotic processes. The latter may be replicatable with deep learning. And would more closely resemble human creation than a particular algorithm could.
I don't understand what you are trying to say. Bending notes and imprecision has nothing to do with stepping away from mathematics. It's just as much mathematic as everything else in the world. It's stepping outside the bounds of western classical tradition.
Sonic Geometry: The Language of Frequency and Form:
ua-cam.com/video/FY74AFQl2qQ/v-deo.html
Here because of Beato
It is probably possible to invent new notation to handle bending notes and other tricks. The notation would likely end up looking ugly.
Well, there'is mathematics in music , if you make a structural analysis etc.There
is mathematics in a wooden table too because you can measure it.Then what's the difference between a table ( no offense to tables) and the music? Music is supposed to have emotional content while table is not( Stravinsky does not share this opinion, but that's another subject).If you use only a computer patching together different "samples"your abilities to express emotional content is very, very limited.Young men, learn to play an instrument and to express yourself through it!
The composer that plays with this line dividing maths and music the best is Iannis Xenakis.
The greatest samplers are also the greatest musicians. School yourself in the work of Madlib, DJ Premier, Bomb Squad, Beastie Boys, Dr Dre, then we'll talk! Every composer of any orchestral work will have to do the work of a sampler: how do I put all these patches of music together and make them work together.
@@sieteocho you do not understand composers work. Those mentioned by you are not really composers.
@@bossanovaboy You don't understand how arranging works. You've never written for the orchestra before and it shows. I've been writing since the Berlin Wall was standing.
@@sieteocho Ok I m glad for you. Just wanted to tell that rappers don't qualify to be composers. Have a great day.
12 tone music?
I don't think western classical music perfmorance is as mathematical as Ted says, nor is African music (or from other places like India) as non-mathematical as he says. But I agree that modern production where everything is autotuned to perfection is not what I want to hear.
All is fair in love and war
If Godel's Incompleteness Theorem applies to math, why not to music?
"People were probably threatened by this (Pythagorean music theory), but we don't have a lot of good evidence. Pythagoras was forced to go into exile, his followers were burned and had to go into hiding... nobody has linked this to the music, but...". I kinda lost interest in this lecture around this point.
jazz and blues, yay for those. i dont like the limitations of mathematics in soul expression. emotion does not translate into the dry mental language of mathematics, its the language of the spirit and cannot be measured. freedom for music and feelings. freedom from the tyranny of scales and notes.
African music is not pure magic. It has a more advanced mathematical structure called fractals. The subdivisions of a beat are not simple ratios, but are golden segments. An irrational number called Phi determines the length of time between two hits. This is called groove/swing.
prove it
(Yawn)...
m.ua-cam.com/video/YQ-w3bLK2Wk/v-deo.html
I could not DISAGREE more.
In Africa they bent their notes. This could be modeled with a graph over time of the pitch showing the rate at which the note was bent, the starting and ending pitch etc.
That’s the only example he gave in the video, but here’s another idea...
If you play drums and it’s “off beat” I’d argue that you’re actually on beat but just at a much smaller beat interval. A little late on that 1/4 beat? You weren’t on the 1/4, but you were on the 67/256th beat. Go to 512, or 1024 beats per measure or higher until you have intervals that capture your “off” beats
music isnt a science its art
The whole idea that musical intervals have to be pure simple mathematical ratios is obviously wrong. A perfect major third has a ratio 5:4 but a tempered major third used in keyboard instruments has the complex ratio of 81:64 yet it still retains the character of a major third. Its no good saying "its only de-tuned a little bit". It has become a complex mathematical ratio.
I'm not certain that a notated musical composition is an algorithm. I think you might be stretching a definition beyond its breaking point.
An algorithm is a sequence of logical steps. Exactly what a notated composition is.. First, Play this note, then this note, then this note, and so on.. I don't think it's stretching the definition at all.
This entire construct of a "conflict" between music and math is silly as hell. Mathematics underly music. Science explains stuff. Math explains stuff. Notation describes. You are not being threatened or limited by people writing down music or explaining how science works with sound.
There's a mathematician Marcus du Sautoy, who has very interesting insights into how artificial intelligence can contribute to creativity. ua-cam.com/video/9nhjwMAsvGE/v-deo.html It would be interesting to hear opinions on this.
Nobody cares...eat organic, listen organic. 🎊🎉🎀🎏
Euclidean algorithm may be used to effectively generate a variety of rhythmic patterns, which can be found in sub-Saharan
African music and world music in general.
Here's the link to the article describing Euclidean algorithm - cgm.cs.mcgill.ca/~godfried/publications/banff.pdf
So sad an idea that music could be reduced to an algorithm: stripping out our very heart from our very body. But some like that if this a sign of their big power - like Aztec priests... Fortunately, their results are still quite laughable (not to say vomitable) for now. But alas they're tenacious. Will they succeed as they did for chess and go?
Is this really true? Isn't African traditional music measurable by numbers? Perhaps the Europeans simply couldn't immediately grasp it because the intricate rhythms were unfamiliar to them. Today, we comprehend polyrhythms in a logical manner and appreciate the algorithmic aspect. The same could apply to variations in pitch and timing. Microtonality and groove deviations are also explainable nowadays. Isn't it a natural inclination to explore music on a theoretical level and understand it better?
This would be more correct and less compelling spoken in more precise terms.
Chinese had a system way before Guido
Overall I agree, but the next revolution won't be from Africa. It will be from India. Disappointed that you didn't even touch on that.
They are killing the human soul
I don't believe the 'revolution' has to come from Africa. There were other influences that entered Europe around 1900. The 'revolution' could and should come from any folk music that hasn't been tainted by dogma.
You are wrong. Math not equal algorithms. , in fact algorithms is related to computer programming. not mathematics
My friend, you misunderstand both computers and mathematics...
@@jmarvins Oh really , how come ? I learned algorithms major at uni.
@@jmarvins Oh , really , how come ? I learned algorithms major at uni.
@@gerykis And I am a graduate student in philosophy of mathematics. All computer science is a part of mathematics, a fact which can be seen from the origin of computer science thinking to begin with: Turing and Church developed their respective models of computation to work on the Entscheidungsproblem, which asked if there was an algorithmic method for determining if a statement is satisfied by certain conditions in a formal language. To do this they had to come up with a rigorous notion of algorithms, which led to the development of purely theoretical models of computation. Later these would be approximated by physical machines leading to practical computers. The point is: algorithms are a structural feature that shows a deep connection between purely mathematical/algebraic structures, purely logical formal languages, and actual discrete computations like those we use physical computers for. This shared connection between fields lies at the cutting edge of research in both mathematics and computer science these days (look up the Curry-Howard Isomorphism and the research that emerges from it, for example). To say that "algorithms" have nothing to do with math, only with computer science, is silly. It's like saying "saxophone doesn't equal music, in fact it only has to do with jazz, source i majored in saxophone at uni."
@@jmarvins Nice to meet you ! I'm not saying that algorithms is not connected to math . I'm saying not equal. You may say that everything is mathematics , I can't disagree . So basically I can agree what you states . However algorithm is more down to everyday life in my definition than what academics teaches