/sci/ - Science & Math

I'm honestly not sure if picrel from the monk that wrote over Archimedes is real or not. But if it is, then it is evidence this doesn't just affect individuals, but has societal consequences. We all forgot how the Calculus part of math worked on a civilizational level.
But why tho? Is it that math itself fails somewhere in that area, so there is something deeply wrong with our understanding? Or is it that our brains are not sufficiently well adapted to truly understand that area of logic? Both? Something completely different?

>>15648451
Just use infinitesimals like everyone secretly does and then calculus will be algebra, too.

>>15648505
i just use 0.00000001 in my equations

>>15648505
Fair enough, but I wasn't talking about personal problems with Calculus, rather a cultural phenomenon. Which seems to repeat even, if you subscribe to the evidence pictured above.

>>15648544
why would anyone forget it? it's so much more simple of a concept than you think. if we really did lose knowledge of it, then it simply means that no one passed it on to future generations, and it resurfaced when people cared enough about math to start discovering new concepts

Personal hypothesis: calculus is actually more scary to the ones who understand it than to the ones who don't. It deals with infinites and infinitesimals. The singularities the lie at the edge of mathematics, and so at the edge of our understanding.
It is the border that separates order from incomprehensible chaos. And so if you don't actively force yourself to periodically use it, your mind will automatically trash most of it to protect itself from exposure in a very Lovecraftian way, as you unconsciously observe the unknowable singularities to be dangerous.

>>15648549
Most graduates actually forget it to the point where they don't understand the very basics, unless they work in a field where they have to use it.

>>15648559
am i missing something?
>integral calculus is adding up lots of small areas under a function
>can be found by adding up the height of each point in the function
>differential calculus is finding the angle of a point in a function
>can be found by sampling two points that are very close to each other, and seeing what their angle is
it's not complicated at all. why would they forget it? it's not like chemistry where you need to actually memorize all kinds of things. calculus can be figured out logically by using small measurements

>>15648557
Mind you, I am not suggesting the great old ones live in equations. I am merely proposing that an unconscious reaction based on primal instinct exists, that affects memory in an adverse way. The implications of this do be spooky though, and would explain how our whole species can just forget knowledge about something that is at its heart purely logic.

>>15648566
I appreciate you contributions, but you are missing the point. The fact is that they do forget it.
The >why would they forget it
is the thread topic. Just ask any postgraduate who is not working in math or physics if they can still "do calculus".

>>15648580
okay, my guess is that they forget it because the teacher didn't teach in an intuitive way. they were taught to use limits from day one, instead of truly understanding what calculus is. every time i see people complaining about calculus being hard, they act like they've received a revelation whenever i tell them that integrals are a bunch of squares under a curve, and you can add them up. by the way, lots of people don't truly understand what functions are either. i felt enlightened to find out that the X correlates with the Y in a coordinate plane when working with functions. no math teacher ever taught me that

>>15648601
>received a revelation whenever i tell them that integrals are a bunch of squares under a curve
kek
Sorry to hear about your functions experience, that's just sad man. But wouldn't this mean the teacher who can't explain what calculus is in an intuitive way don't truly understand it either?
I have held the opinion for a long time now that too many actual brainlets are handed degrees to be honest.
But I also have observed that the majority of people who learned Calculus at some point did forget most of it, with samples from all over the world, at a rate which isn't explained solely by this problem. So unless to handing-degrees-to-retards situation is way, way worse than I dared to imagine, another explanation is in order, hence the thread. I could be wrong though, but I kinda hope I'm not.

>>15648612
>But wouldn't this mean the teacher who can't explain what calculus is in an intuitive way don't truly understand it either?
i guess so. people can know how to do things without knowing the WHY behind it. why do we use circles (specifically radians) to solve trigonometry problems? if you understand that, then you can suddenly teach trigonometry in a whole new way.
>I have held the opinion for a long time now that too many actual brainlets are handed degrees to be honest.
let's be real, thank affirmative action for that

>>15648544
Precursors to infinitesimal calculus were not forgotten, e.g. the Greek method of exhaustion kept being used, it was developed into the method of indivisibles, Fermat's adequality, etc. leading to calculus.
They were considered less rigorous than more direct constructions, and proofs using these methods were considered merely suggestive of their result.
This changed with time as people got more comfortable with symbolic manipulation and the ontological status of mathematical objects in general.

I'd say that once you have algebra, calculus with infinitesimals is not that far of a leap. It's not a coincidence that we ended up inventing calculus right after we got fully comfortable with plain algebra.

>>15648647
Precursor argument acknowledged, that is a fair point.
So do you have a way of explaining why the second pic (that is supposedly plain Calculus with different notation) got completely forgotten? It takes a societal level of not handing down this knowledge to happen. Or do you think it's just simply not as portrayed? (And count it among the precursors, or as simple sensationalized nonsense?) If so, why?
>>15648646
>thank affirmative action for that
The systematic dumbing of the population is much more than forced mixing of populations, but I get your point. It's also a bit offtopic.
Pic unrelated, but I'm phoneposting and browser is forcing me to upload a file.

>>15648667
>It takes a societal level of not handing down this knowledge to happen
i did a little bit of reading, and apparently math fell out of favor at the time of archimedes. his work was definitely copied many times for us to still have access to it, but it was clearly not being used back then. maybe no one cared to use it

>>15648694
So, unironic dark ages argument? Workable, and this hypothesis
>>15648557
>>15648572
also works as an underlying reason for the cultural force driving a whole civilization to abandon higher math, especially the described spooky part. (Yes, I know it was muh religion, but religion is always shaped to represent a group's more basic beliefs and instincts.)

>>15648710
So in this case, I would argue that the fundamental attribute of the human psyche that drove a civilization to burn scientists as witches is the very same instinct that makes the majority of people who don't use it forget calculus. And it has to do with an instinctual fear of the unkown, which gets proportionally amplified when it encounters the unknowable (mathematical singularities).
(Yes, this is kinda a psych thread. Sorry not sorry.)

>>15648451
If you don't practice calculus, then does it really matter that you forgot it? It probably means that, like 99% of the population, that you don't need it in your daily life.

>>15648721
eh, i still think that people who were able to learn calculus at some point are smart enough to not be afraid of it

>>15648751
>smart enough
I would suggest this is not a conscious fear, but a side effect of the same instinct that saved our ancestors' arses from the predators. You can't really overwrite it indefinitely l without actively working against it, in this example taking the shape of practicing calculus, or forgetting it as a result of not doing so.
>>15648737
So how come these people don't forget complex numbers when not using them? Or matrix operations?

>>15648667
>So do you have a way of explaining why the second pic (that is supposedly plain Calculus with different notation) got completely forgotten?
Many Greek/Roman texts have been lost to time (the Romans didn't contribute much to mathematics anyway, despite their engineering prowess), and the Greeks' geometric approach to mathematics didn't lend itself to symbolic manipulation and algebra, which in my argument is almost a prerequisite for an easy grasp of calculus, so anything pointing towards calculus from the Greek was primed to be lost to time.

In a sense, this is a dark age argument, which some people don't like. But it's a brute fact that some works were lost and rediscovered later through the Arabs.
You mention the Archimedes palimpsest, which was lost until it was found in the 20th century.
But its contents were not entirely lost. Next to the the Method was his work on floating bodies, also lost, but Archimedes' principle never stopped being known. Likewise, Greek calculus knowledge kept existing in the form of exhaustion, a method treated with a degree of suspicion.

And you don't have to appeal to dark ages, it's just that the sum of active human knowledge does not grow linearly over time, but undergoes periods of expansion, when new ideas are invented and applied, and contraction, where only the most fruitful results are compiled and kept.
Contraction is not a perfect process, so some workable knowledge can be lost in the process if it is too cumbersome to express in the framework of the age, or if the framework itself is too cumbersome to transmit.

>>15648771
I can't stress enough that any counter-argument or suggestions on how to test this with large groups of people is welcome. To reiterate: the hypothesis is that a primal fear of the unknown (and unknowable) is the main factor in the phenomenon of people forgetting Calculus when not practicing it for years. There might be other behaviours that derive from this prime driving force, such as Anon mentioned in relation to people abandoning math in the "dark ages", but I'm not suggesting one necessarily leads to the other.
Idea: find out if there is correlation between postgraduates/dropouts slowly forgetting Calculus and finding the genre of cosmic horror quantifiably scarier than other types of media meant to frighten or inspire horror.

>>15648451
because calculus is hard and built around using arithmetic wrong

>>15648505
this works for the most part

>>15648737
Fair-ish point, but consider this: OP is wrong.

>>15648805
I disagree with algebra being a prerequisite for calculus. One could easily imagine advanced geometry being used to make the same conclusions in some "parallel reality". The other points are well put though.
The
>sum of all human knowledge expanding and contracting
is a completely different hypothesis, and it belongs to history and sociology. I can see it being the case due to environmental factors and periodical collase of societies though. Still, let's not complicate this with other stuff yet to be proven and widely accepted.
>>15648824
Is this a notation argument? Because there are 2 different notations on display here, are both of them just unintuitive? I actually considered this might be the case before making the thread, but I'm leaning towards a hard "no" now.

>>15648451
For the ones who want the TL:DR:
>I posit there is an evolutionary psychological reason for people to naturally forget parts of math that deals with singularities.
>The most popular alternative is that most people are just stupid.
So far both are equally valid, feel free to contribute.

>>15648451
Because the subject is taught incorrectly. Practically no one understands what it's used for in the real world, so almost nobody gives a conceptual understanding of it, and as a result it just becomes conditioned arbitrary rules stacked onto other conditioned arbitrary rules. for example, almost everyone has some idea of why pi shows up in so many equations, but if you ask people, hell, engineers, why e shows up in equations, probably over half wouldn't be able to answer.

>>15648710
It might also explain why, for the longest time, Religious orders also served as shelters for the knowledge of higher maths

>>15648451
Most people don't remember calculus because they didn't actually learn it in school. They memorized rules just to pass the next exam. Actually learning the material takes more effort than passing an exam. For everyone you encounter that remembers nothing about calculus, their understanding at the time they "learned" it was probably mediocre.

>>15648505
my book had the more rigorous proof for the chain rule, then for arc length just algebra'd the differentials. I have no clue when nigger-rigging differentials works and doesn't work.

>>15648451
>if you don't practice Calculus, you'll forget it in a few years if you don't have a photographic superhuman memory
>Why?
Taught by rote instead of intuition. Did you ever have to memorize integrals of trig functions and logarithms? I integrating and deriving polynomials is like riding a bike but the rest of it is just memorizing a series of steps and a bunch of patterns. It gets really weird in Calc 3.

>>15649329
It's easy:
>I have no clue when nigger-rigging differentials works
Always.
>and doesn't work.
Never.

Infinitesimal calculus only breaks if you misinterpret d^2x as (dx)^2

>>15648466
There was a time when most couldn't read. Took hundreds of years to get society to where it is now

>>15648451
I would guess for 2 reasons
1. Calculus and especially integration are a lot of rules and processes that require strict memorization, and you can't really intuit them from previous studies. You wouldn't figure out integration by parts on your own like you could figure out multiplication if you know addition
2. There aren't real world visualizations of it. This is true for complex numbers too. You can picture 5 apples vs 1 but you can't really picture the change in speed of a car in your head

>>15649391
well shit if its really that simple. I'll probably still hit some weird restriction/condition i won't understand in DEs this semester

>>15649136
this. i never learned anything in chemistry because i just memorized the material before each exam instead of understanding why electrons are ordered the way they are

>>15649573
>You can picture 5 apples vs 1 but you can't really picture the change in speed of a car in your head