A Question To Think About
Is Mathematics a Discovery or An Invention
I believe that mathematics is a highly specialized language created to empirically explore and explain the existence and the phenomenon of the physical environment…
Languages were invented and evolve to meet the special challenges of interactive communication.
I believe that mathematics is not monolithic or immutable and, like other languages evolve to meet challenges, so too does mathematics evolve to meet the special challenges of exploring and explaining the ever evolving physical environment.
What do you think…
02/17/2023 @ 7:36 am
crispr quantum!
(off the cuff I’d
anticipated
a Surf City joke)
02/17/2023 @ 7:54 am
TGIF…
02/17/2023 @ 8:21 am
hahahahahahahha hah. math.
Right brained here, so can barely understand your math explanation. In high school they made me take algebra two years in a row and both times I failed. Today, I can’t balance my checkbook, so I don’t. So far, ok 🙂
02/17/2023 @ 9:55 am
Suzanne:
There were times when Einstein couldn’t figure out when it was time to eat or go to the toilet.
02/17/2023 @ 2:16 pm
Language is a limiting factor on the ability to communicate. If you don’t have a word that everyone agrees describes the thing you are trying to discuss, you simply cannot communicate with each other about that thing because you don’t know what you’re talking about. This is one of the central themes of Nineteen Eighty-Four. Orwell knew what he was talking about because his wife was working as a government censor censoring newspapers and radio broadcasts.
Mathematics is a symbolic language in which each symbol has a specific meaning that must be described in words in order for the formulas to have any meaning at all, except for the operands, which are universally understood and require no additional explanation.
Without the definition table that describes the meanings of the symbols being used, higher mathematics is indecipherable, which makes mathematics a meta-language that allows you to express thoughts in a compressed format.
Within the current intellectual context, we are seeing a sudden and dramatic divergence between the English we grew up with and the language the younger generations now speak.
One notes an increasing use of abbreviations and catchphrases in which familiar words acquire unfamiliar meanings which means that the generations are having increasing difficulty communicating across the generational barrier. This is one of the causes of the developing collapse of this civilization, to wit, that the language we are familiar with in unfamiliar to our grandchildren, just as the language the founders of the Republic used is often misunderstood by our generation and the ones after.
A review of the misunderstandings, both accidental and deliberate, of the wording of the Second Amendment, illustrates this quite succinctly. Whether you like it or not, and without either approving or disapproving of the Amendment itself, the right to keep and bear arms was reserved by the Second Amendment to the PEOPLE not to the milita, as it is often suggested. The radical reading results from a misunderstanding of the basic nature of the colonial militias which were quite different from the National Guards and the Reserves.
02/17/2023 @ 7:10 pm
“Mathematics is a symbolic language in which each symbol has a specific meaning that must be described in words in order for the formulas to have any meaning at all…”
Alan;
Are you suggesting that mathematics is a form of hieroglyphics? Symbols as ‘written’ communication of spoken language?:
02/18/2023 @ 8:34 am
Is mathematics the hieroglyphics of science and technology?
Mathematics was/is ‘invented’ to communicate what we know and learn through the observation of the physical environment, which extends from the core of the earth to the outer reaches of the universe, and, in so doing, ‘discover’ new ways to use and apply it.
02/20/2023 @ 9:53 am
Yes. Mathematical notations area meta-language. In computers, at the machine language level, current technology is limited to on and off, zeroes and ones. (Quantum computers will have four or more variables, which might be expressed as minus one, one, plus one, plus zero, to super oversimplify the process.)
Computer languages then utilizes the machine language via a symbolic system in which large numbers of instructions are referred to via aliases, to the point where it is not impossible for humans to write the code needed to define and invoke operations on the basis of a command language.
The parallels between mathematical notations and computer languages is self-evident. Curiously, mathematicians don’ make the best computer programmers for higher level languages because those higher level languages are programmed via human languages, note binary notations.
02/18/2023 @ 9:19 am
Alan,
We have reduced the behemoth mainframe computer to the size of something that you can hold in the palm of your hand…
Virtually everyone in the industrialized free world owns or has access to a cell phone which, in my view, is the greatest technological achievement in communication known to humankind. Yet, the ability and capacity to communicate effectively has not improved beyond the era in which human language itself came into being…
This could be the result of ignorance, stupidity, or intellectual lethargy and the so-called intergenerational communication gap but the deficiencies and inadequacies are clearly there, standing out like the flashings of a neon sign.
The ‘founding fathers’ were well aware of the fact that the democracy would not long survive without the benefit of a well educated and well informed populace and yet what made it into the Constitution was the ‘right of the people to bear arms’ not the right of the people to be educated….
Apparently, fear of slave revolts and indian uprisings was a stronger incentive and motivation than fear of the political exploitation and demagoguery which could befall an uninformed and undereducated citizenry…
02/20/2023 @ 9:43 am
Actually, the greatest fear the founders felt was toward a resumption of hostilities with England, a fear that was realized in the War of 1812. The leaders of the Republic had reasons to fear England, and France, although France was castrated by the Napoleonic wars.
02/18/2023 @ 11:05 pm
In college I was around people who could have answered this for me. Now I’m not. My own HS math got to advanced algebra/trig, and I don’t remember my trigonometry (though if I looked it up I would probably understand it very quickly). I never took calculus. I can’t answer your question to my satisfaction.
One thing I do know from my own field of sound is that engineers use it but it’s a language you need to speak or you get lost immediately. I also think it’s sometimes a way of looking at things where other ways would help more with some audiences. I think that a lot of what happens with math can be explained mechanically but that people don’t. I find that I’ve had to figure a lot of things out for myself, not from reading but from reasoning. I’m still doing it, even at my age. I’ve noticed, and I’m repeating myself because I’ve certainly said this before, that people in technical fields often have no clue how to talk about that field to people who aren’t in it. They slip into jargon because they’re too used to it, forgetting that the terms they’re using are not common English. Or sometimes they are but no one explains that – like the term Frequency. Frequency is a term for how frequently something that alternates goes back and forth per second.
There’s also the question of how thoroughly they understand it. One thing I can tell you from experience is that a lot of technical explanations are not explanations at all, they’re naming of a phenomenon with a basic description but no explanation as to cause. This can absolutely happen in math. I’ve used logs before in a statistics class but I have never really grasped what they are or why people use them. I know it’s a weird relationship involving exponents but I don’t speak that. This is also true in much simpler things. If I pull a tuning fork out of my pocket (I’ve been substitute teaching on the side locally in elementary school and I’ve found that tuning forks fascinate children), hit it on my heel and hold it up, unless you’re damned close you don’t hear it. If on the other hand I touch the ball of the fork to a wall, you’ll hear it. If I ask people why – not little kids, adults – someone is going to say it’s because the wall amplifies the fork. What that means is that the wall makes the fork louder. That’s already obvious. Phenomenon named but not explained. What’s really going on is that to hear you need to move air, a fork is too small to push air but if you touch the fork to the wall it shakes the wall and that moving wall pushes enough air to hear because of its surface area and its ability to vibrate. Some people with basic math have been told that the wall amplifies the fork and they know how to repeat that but it doesn’t equal actual understanding.
02/19/2023 @ 2:49 am
“…Some people with basic math have been told that the wall amplifies the fork and they know how to repeat that but it doesn’t equal actual understanding.”
Kosh;
That’s because the explanation that was communicated to them was incomplete and hence, inadequate.
My guess is that they weren’t taught what they repeat by a mathematician (or an audio engineer, or even a musician) who likely would have been able to reflexively provide a more comprehensive and thus, more accurate response.
02/24/2023 @ 6:11 pm
Trust me, I’ve heard some of this kind of answer from audio engineers. They’re so in their own language they don’t even realize they’re not speaking laymens’ English. I’m not sure a lot of them would know how to translate all those concepts into English because they’ve never thought about them.
Audio isn’t alone in that. I’ve probably told this story before, but
When Jonah was maybe ten or eleven, the head of his camp complained about his bladder control. He was in a camp full of people with cerebral palsy so this was an odd thing to complain about but, just to be safe, I took him to a pediatric neurologist in Indianapolis, the closest big city to where we lived at the time. The neurologist explained that the only way to do what was wanted to was put a catheter up the urethra to the bladder and empty it externally periodically. However, the risk if you didn’t empty it fast enough is that as the bladder tried to urinate its walls would thicken and eventually it would send urine back to the kidneys, and urine is toxic to the kidneys.
Jonah asked me: What did the doctor just say?
I said something like:
The doctor says the only way to control your peeing would be to put a tube up your penis into your bladder, which is a sort of bag made out of muscle that holds your pee, and we’d to empty it from the outside. If we don’t get to emptying it and the bladder tries to push the pee out it gets exercise so it gets stronger and eventually it could accidentally push your pee back to your kidneys, which is where your pee came from. Pee is poisonous to kidneys so that could get you sick.
Jonah was able to reach a conclusion from this but what was surprising was that the doctor and his nurse looked at me like I’d just landed from Mars. They told me they had no idea that this could be explained to a child. This was a Pediatric Practice; 100% of their patients were children. That the children didn’t understand what was going on was considered normal. it certainly is in my industry. Consultants often notice that some of their clients don’t understand what they’re doing, particularly a church board. And then they don’t understand why the church would sometimes go with a trunk slammer. Why not? You’re both offering magic and his magic is cheaper. My attitude is it’s up to you to learn how to communicate what you’re doing and why in ways they understand. Curing diseases your customers don’t know exist won’t get you credit for doing so from your customers. They’re not psychic.
So I say: Learn To Translate or figure out how. I’ve had to figure it out because I’ve never come across a place to learn it and frankly I do it better than I think an outside source would. My arrogance perhaps but it comes from experience.
02/24/2023 @ 2:37 pm
Democracy Dies in Darkness (WAPO)
Jesus, international news videos early on profiled Ukrainian children and broke my heart. Apologies for my off-topic lapses. I get all choked up inside. What good is even basic arithmetic … when an egregious immature near schizoid faction of our electorate continually attempts to usurp our God-given nation and heavenly cause. Heck, what was the U.S.S.R would not have jumped the gun if it were not for our U.S. insane insurrection of 6JAN2020. Right when we’ve embarked upon a new dawn-era of empirical miracles. Longevity. Cures. Peace, tranquility…would the word be quantumnisity? Sustained imagination like right and wrong, good and evil. Harmony and harps. Improved holistic statistics with no dread of intercontinental ballistics. For sure: the mathpath is existential; fundamental to logistical humanism. I certainly remain enthralled with the magic of search: e.g. [sic] *’… there are currently 10,824 bird species in the world …’ *(Flocking Around)….
02/24/2023 @ 11:33 pm
“Learn To Translate or figure out how.”
Kosh,
Most lawyers don’t understand your maxim.
Many don’t get that the best clients are the ones who know what you’re doing and can understand and appreciate why you’re doing it…
I have always had a knack for the translation of relatively complex concepts and explaining them in common language….
That’s one of the reasons and motivations I have as a teacher…
I teach law to people who, for the most part, have no interest or desire to become lawyers…
02/24/2023 @ 11:45 pm
“For sure: the mathpath is existential; fundamental to logistical humanism. I certainly remain enthralled with the magic of search…”
JP;