@mike808 I can’t even begin to figure out what point you’re trying to make even if your pics were accurate. Regardless how big an asshole our current president is what sort of asshole even goes to an inauguration in the first place
@TheFLP I ended up taking calculus without ever having trig. Boy did that make that class hard. Similar issue with accounting and finance. I took finance first and had to teach myself some accounting to pass that class. Oops. Makes it harder… but then again math can help you figure out interesting things - like it would take about 35 years to walk to the moon presuming you could build a staircase to get there (stolen from the internet - I did not check their math).
@blaineg It’s like teaching yourself trig without a book or tutor while taking calculus. The other stupid thing I did was take physics while taking calculus. That would have been a heck of a lot easier if I had been done with calculus first. I also took anatomy and physiology as a first semester freshman - I had placed out of bio 101 - had mostly cut throat juniors in there. In there I learned how to memorize, a skill I hadn’t had to use prior to that. Rough freshman year. Calc, physics, bio, english (english was easy but time consuming).
In school I generally managed to get my prerequisites in the proper order, and for six years or so my “career” followed logically from what I studied in college.
And then I found myself working in an accounting firm. Nothing in my educational or work background was even remotely related to accounting, so I’ve been backing my way into it for 18+ years. I still can’t shake the feeling that if I took an accounting class today I’d come to an ignominious end.
(Meanwhile, I just managed to spell ignominious correctly on the first try, which surely screams “liberal arts degree.” Probably haven’t used the word since high school.)
@TheFLP I did the math. Got lost at higher order geometries, set theory, and matrix calculus. Then did some accounting math (cost-basis manufacturing, projected income escrows to realized sales for subscription income on crazy commission and discount schedules). Now I do crypto work and explaining the difference between authorization and authentication duality of passwords (or keys), with a bit of quantitative security with sone risk & control modeling on the side.
Explained to my son (in pre-calc now) the notion of doing all that ‘trig stuff’ in polar coordinates and he about lost it when he figured out it made everything just simple rational numbers (a bunch of easy fractions) for sin/cos/tan/cot/sec/cosec. He sure was mad at having to do it ‘the hard way’ for class. I chuckled.
@MagnaVis And then it became a challenge that said “…and you thought doing those high hurdles in PE was gonna be hard. Watch THIS!” There is a poetry to math. Unfortunately, once it went beyond iambic pentameter its beauty became quite elusive to me. Solving for X is easy.
Well, the 2 is familiar and so are the letters, but none of them spell “cat.” Someone told be there was a cat involved here somehow! Where’s the darned cat?
If I could’ve gotten my arms around the maths, I would’ve loved to have gone into the field of Physics. It’s magical. It actually is poetry in motion.
@LaVikinga@MagnaVis the little ‘i’ at the front is for ‘imaginary’. So imagine a cat. And there it is. Ta Da!
If it isn’t, try again. I’m a bit fuzzy on the details, but I think it’s probably a random thing.
Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
(By Edna St Vincent Millay)
The poet is overdoing the argument, of course, to make a point.
By her standard, anyone who has gasped on wonder at a mathematical concept has seen this beauty.
And anyone who has, in mathematical naivete, appreciated perceptual beauty (according to varying tastes), has appreciated the incendescent perfection of some mathematical relationships.
And I would have picked Gödel, not Euclid;
but that choice would have been tough for the poet (1892-1950), who was probably never aware of his work. The poem was published in 1922. Gödel’s great achievements appeared in the 1930’s.
(Some think Gödel’s work was the most important conceptual work of the previous century; in his later years Einstein is said to have not retired because he so valued his daily long conversations with with Gödel.)
Mathematics is the most beautiful universe I have ever been near.
And I, or anyone who has valued and practiced it, or tried to, knows so little of it, and so little of what it is or can be, even to such tiny creatures as we are.
Mathematicians often tend to think that even physicists and the like have no idea what math really is; and these mathematicians have a point.
But do mathematicians know what math is?
I think not; or perhaps they know only the tiniest fragment of a single strand.
I expect we will someday know uncountable choices of alternative, rigorous, and valid logics that are now so far beyond us.
And even then, we will know only the tiniest portion of a single thread of mathematics.
It probably all began (as a human practice) with counting. Many animals can count, to a degree, in a rudamentary fashion.
Geometry probably began with land boundaries and measurements.
Where does it begin in our universe? It feels transcendental and eternal and beyond mortal concerns.
Let a mind make an abstract distinction. And then define it and refine it unto a state of being rigorous.
And then make another. And …
And try to find a valid relationship between these distinctions.
And keep going.
And one is walking on the path.
I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
@f00l Nuts are good. And if you go with the Japanese theory of food shape being good for that part of the body (can’t recall the name for it) re:… walnut looks like brain so it’s good for the brain… then that’s a good thing!
Here is the problem with your argument, you state you hate math but so much of your everyday life uses math. Perhaps you don’t use trig or calc but you use math. If you want to say you hate math be specific. What kind of math and why. It’s like saying you hate all Democrats or Republicans you really don’t and if you do you have serious issues and let’s get you help.
I currently hate grading math - and the fall out from students who can’t add their grades to see if they need 450 points to pass and there are only 200 points left to earn You. Are. Going. To. Fail. Arguing with me about that doesn’t change reality. Hmm maybe it isn’t grading math I hate, just students who can’t do math. Also I hate teaching that bunch statistics - I have had to do that too. Ugh. Managed to figure out how to get most of them to turn their brains back on and pass, but OMG the effort involved on my part to pry their brains back open after they slammed them shut at the word statistics. I need to win the lottery but I don’t buy tickets as I understand that math and have no plans to voluntarily pay state taxes with my entry (AKA put a match to my $2). Once with a retired plumber I explained it to him, in a simple way that he appeared to understand, and then he said, “yes but if I feel lucky that changes the odds”.
When I discussed math with non-mathematicians, or with persons who were not confident about mastering the concept under discussion (or who had no mental approach or discipline for the subject), the trick for me was to find metaphors, examples, and illustrations that “spoke” to the other parties.
This was often difficult, and sometimes took time and creativity - I happily got several people thru calculus and beyond (pre-med and economist and similar types, and the mathematically curious).
I would just keep trying and trying different approaches until something clicked thru their heads from the latest attempt at explanation. These were mostly friends or fellow students from other disciplines, and I was “willing to the task”.)
Anyone who needs to actually understand some area of math needs to learn how to read it and to mentally take it in and play around with it, tho.
(Asking for assistance in an area one needs to understand/master is fine, so long as one does all one can without assistance [which means using online help and doing a lot of hard mental work alone, first;
and one sharply limits the time&patience-cost of the requested assistance.)
It’s mostly about developing strong mental discipline to the task of learning in that area.
And about being willing to read and re-read and re-read alone, and forcing one’s brain around the specific thought or chain of reasoning repeatedly, until one gets it well enough to move to the next statement.
Spending hours (or days) on a single statement or sentence is no waste of time or proof of incompetence, given the personal intent of mastery.
All mathematicians do this, in some areas of subject matter.
Also, non-mathematicians sometimes think all mathematicians can explain “all math”.
Well, only if the mathematician is recently familiar with that area, or the area is pretty elementary and common to anyone in the field. And if that mathematician has the patience and the skill/facility for explanation.
Mathematics requires only tightly rigorous definitions of conceptual objects, postulates or axioms, theorems, and proofs/counterproofs of relationships.
Because no external evidentiary data or experimentation is required, the current knowledge in the field is enormous; said to be many times greater than, for instance, the knowledge base of physics.
(I read this stat somewhere a while back, but have no backing data and I’m annoyed that I don’t remember where I came across it.)
I do know that cooperating mathematicians who work in very closely related areas of investigation sometimes needs days or longer even to explain to each other most basic and simple structures and directions of their various ongoing works.
And they often resort to using metaphor between themselves as a time-saver, while intellectually “forgiving” metaphor along the way, for the “flaw” of not being rigorous within the topic under discussion.
Even the various small sub-subfields are just that enormous, and the knowledge within is just that tightly packed.
The language is as compact as possible.
So the simplest and most obvious implications from a single statement can take days or centuries or millennia to unravel, and are never finally explored.
There is always more.
Math students start out, in naïveté, wanting to "know all of math”. (And - subjective human corollary - “know all of all possible math”.)
Those who stay in the field learn much about mortal limits, time, and tide;
in the same way we all do in the areas each of us would master.
@f00l When I took grad stats, after semester 3, I got the highest grade out of 60 plus students, including 8 or 10 of them getting their PhD in psychometrics (I was in business but taking the stats in the psych dept because they were higher quality classes than the other choice) the guy who taught my first two semesters ran into me and asked me if I was changing my major (since I beat out all the folks in psychometrics by almost 2 percentage points). I said something along the lines of, “Are you out of your mind? I am so glad to be done with 20 hours of homework/studying a week”.
That term had been made worse because I had to teach myself matrix algebra to survive that class and I had never even heard of that. And I got very, very lucky. I found in the old stacks the actual textbook he was teaching out of. That gave me an advantage. I lived in terror someone else would do what I did and look for a multivariate book taught this way and then recall the book from me. Never happened fortunately.