I talked with three professional mathematicians who didn't know Math is real. There's English Majors--which that's all they do--who can't read Charles Dickens. There's people graduating High School with 4.0s and have taken calculus who can't do simple 1st grade math. 54% of Americans read below a fourth grade level. There are experts on Husserl who work at McDonald's and men who barely passed college tenured at Yale.
A perfect example of what's wrong with our world, is we have CAD and Dynamometers, but physicists don't use them. Instead, they erase data points, and use basic calculus and well behaved curves to do their math. That and people with College Majors in Math believe Math is subjective, and people who are explicitly studying to read English, cannot read Dickens. That's what's wrong. And people in the leading edges of science are actually pontificating on whether a whale is a fish. They really don't know what a fish is. It's that bad.
There's also students who get perfect SAT scores, 4.0 GPAs, juggle three tasks at a time for 12 hours a day, have glowing recommendations from teachers and professionals, but because their college admissions paper doesn't sound like a blog post, they get denied at every school. Despite the essay being written lucidly, with perfect structure, no purple passages, good grammar and spelling, in simple and plain enough language, as they talk about something like a Non Profit that they started and how they're leaps ahead of other students their age.
Another thing, an actual school faculty told one of the best and most professional teachers in their school, that Reading and Writing are not a Twenty-First Century skill.
Category: Analysis
Why Prisoners Learn Faster than College Students, BetterU Response
I actually relate to this. I was in Jail, I read To Kill a Mockingbird, War and Peace and the Bible. I read War and Peace twice. Loved every minute of it. To Kill a Mockingbird I read three times. The Bible I read along with a Radio Ministry called Through the Bible with Jay Vernon McGee.
But, even now, I'm the same. I just learn obsessively. Something I want cracked, I think about it--I'm a little slower than other people, but can focus like a laser--and I don't stop until I understand it. I listen to teachers--YouTube videos--read books, take notes in the form of poems and stories. And I have a very accurate metacognition that will scan my work for faults.
A Novel Idea
I had a similar idea to this, but it was much different. Kind of an alien invasion, where a super race of Extra Terrestrial Terrans--who are smarter, stronger, and more beautiful--come to Earth, and take it over. And I would have one of their families who shipwrecked on Earth, but they never told their children, and the child grew up among us, and was super beautiful. And she had to stop them. Kind of like a Superman sort of deal, you know? But, they're just smarter, better looking, and stronger. Like, they can grow muscle fast, they have a mean IQ of 150--that's the middle of their bell curve--and they're super beautiful, and also very coordinated as is what happens in upper echelons of intelligence. But, they hate our earth because our people aren't smart enough to understand the objectivity of mathematics, or understand the objectivity of ethics. It'd be a cleansing of them because they're too stupid to understand morality, science, aesthetics or law. And they sent sages to the Earth, to test them to see if we were advanced enough. And we failed. But, she has to prove to them that humanity has intrinsic value, even if they're too dumb to understand morality, aesthetics and truth. The whole conflict would be around habitable worlds, that it's a lot of resources to make a world habitable for humanity, and if we advance too far, we could destroy an entire planet, and that would be the Terran's reason for doing it. There'd be all the races in the Terran forces, as they advanced beyond racism, but they'd just be more beautiful, and the racism would be against ugly people as there'd be a way to determine intelligence based on facial features and muscle and bone density, which are metrics for beauty. And the protagonist is only 172IQ. About one standard deviation above the norm for her race, so equivalent to a 120 IQ.
“Mathematics Are Made Up”
That's not true. We didn't make up mathematics. Mathematics are a language, that describe the way the world works. Yes, the language is made up, but the things they describe aren't. Like any language, it requires context to fully understand, and through context we describe the real world. Math is also a form of logic, and like language, there's true and false statements and valid and invalid methods of reasoning to further principles. A math problem, that relates to no context, is like a novel, that it's fictitious, but still the logic works, and is proven to work.
A Little Bit of Set Theory
So, if I have a pair of glasses, I have one frame, two lenses, two earplacers, four screws, and two nose rests, and two arms.
All together, that would be like this:
1(x)=1+2+2+4+2+2
If I'm talking about the the number of individual sets of components it's:
1(x)=1+1/2(2)+1/2(2)+1/4(4)+1/2(2)+1/2(2)
If I want to take the screws as two sets it's:
1(x)=1+1/2(2)+1/2(2)+1/2(4)+1/2(2)+1/2(2)
So forth. That's how set theory ought to work.
If multiplying it by two pairs of glasses, you just do this
2(x)=(1+2+2+4+2+2)2
If you want to combine sets it's just:
1(x)=1+1/2(2)+[(2+4)/(2+4)]+1/2(2)+1/2(2)
Little Reigns
“Some bold adventurers disdain
The limits of their little reign,
And unknown regions dare descry:” – Thomas Gray, Ode on a Distant Prospect of Eton College
Please, mathematics makes sense. You're just not smart enough to understand it. Please... know your limits. The derivatives are finding the limit to the area underneath a curve, and averaging out the total slope. So, when you download a file, it could create an X/Y graph, through the curve based on bytes and time, and the total file will relate directly to the area. That's how calculus works, and a derivative is a shortcut to build a similar curve, to get an approximation--or it just takes the actual raw data of the curve itself, and gets its area, or the curve. It's an exact science, and makes perfect sense. And it takes geometric series and infinite sums using secants to do this. And this is important, because in things like energy waves on a stove, or even a car driving on a dyno machine, it gets us measurements we can actually use to understand our world.
Please... don't say this kind of thing.
Yeah, you can't lawyer math. I mean, you could, it'd actually make better understanding of how evidence relates to things in a courtroom, but definitely, this is just stupid. We need a little faith, and a little bit of a leap to the conclusion. That's how division works. Without it, we can't have math. Division is the most important operation, because it kind of guesses the right answer, based on the obvious pattern.
On Metaphysics, Logic and Descartes Argument
[ How can you have] a syllogism? What can a syllogism prove, if there are no axiomatic or tautological statements? From the foundation, you need to build and settle your logic on what's true. Having a syllogism isn't going to work, where you invalidate all true statements.
But Descartes said, that since all he could know was that he thinks therefore he is, and since he was often wrong, he couldn't be God, but there had to be a God outside of Him which ordered reality, therefore, there had to be a God to establish proof, and therefore, since God is good, He allowed us to trust our senses about that proof.
Like I said, we need tautologies and axioms to make sense out of logic. You didn't follow my or Descartes' argument.
Again, why have a syllogism in the first place, if you can never establish a truth claim?
We're arguing on the being of being, which is a metaphysical presumption, and you brought up Descartes, which his argument was that since he got things wrong, he couldn't be God, but there had to be a God to establish and order existence. Since, he found that he could make false claims, something bigger than him had to establish the truth of those claims.
And God is good, because we see there is good. Without God, there can be no good. As then it's humanity's judgment, and we've established humanity cannot be God, from even Descartes, that we get things wrong. Therefore, a being more powerful than us, i.e. God, needs to order what is Good and also what is true. But, good is self evident as is truth, as all things relate back to tautologies, of either being true or false. And I observe good, and I observe truth. And since I see good, I know God is good, and we can therefore trust our senses. Therefore, God exists, and we can know reality is real.
[If we're] basing it on the axiom that reality itself is real, then the organizational framework of reality, that it makes sense [is the proof of design]. There's a lot of structures that appear in physics and nature that are directly related to geometry--they have to be--and by number, which inherent in that organizational framework is proof of a design. And how we get to the God of the Bible, is that if there's good that can be seen outside of human judgment--and I'm pretty certain there can be--then we need to find which God best represents it. And I think the God of the Old and New Testament, reflect what we do know about the good. That ultimately there must be judgment by means of a sword, but also grace for those who truly want to receive it, and better themselves.
[I]t's just what the laws of nature prove, that there's a design. At some point, you have to look at it, and it makes sense.
I think your problem is, you want to stay at step 1 too much, and never move beyond it. But, generally, there's sense in the universe, based on the laws of physics, and their geometric construction. And X = X is the foundation of logic, so you're basically trying to undo logic, while telling me to prove something logically. So, that's kind of nonsensical, and if your doubt is like that, then that's doubly why I believe in God, so X does equal X, and so there's sense and coherence to the universe. And not my own mental faculties, or the whims of experts.
As far as the God of the Bible, like I said He is good, and sometimes there needs to be a sword to purge the Earth. It's a very dense theological argument, which I can see from the get go you're not willing to have.
But, generally, there has to be punishment for sin, and if you took the Old Testament, everyone would be put to death. If it's stoning for breaking the Sabbath or dishonoring your father, or being a part of a nation that is not Israel, that's the whole point, is that we need Grace so we aren't slain. And we need to trust on God's goodness, and His definitions and not our own, as I've clearly established--and so have you--there can be no knowledge without Him.
And you're moving to the point, where you're saying X=X can be put into doubt, and that's generally why I'm a little leery of people like you, and believe in God, because you do invalidate X = X. Which a Syllogism relies on X = X as much as anything, as if X doesn't = X you can't move to the next step of the causal chain. You're stuck in infinite loops of trying to prove ontological existence, and metaphysics. Not moving to the assumption of reality, which you need for any basis of science to begin with.
1. I think all knowledge begins with look and listen. And we draw conclusions from it, that what I see, in mathematics, and the geometry of it--and I'm not the first to say this--is a design in the inherent structure of the universe.
2. Well, x can = y. But, you need x to = x first, as that's the fundamental groundwork of logic. If it's not, then there's no way to ever move from x to y.
3. It is a dense theological argument. You're not going to understand it. But, generally, sin causes suffering, and there needs to be judgment against it. Which without God's judgment, it falls into man's hand, and man judges incorrectly. As, we're arguing the very basic basics about logic and how to prove I have hands. That's the context. Which, you can't even get there. That's utterly specious, is what I'm telling you, but also why humans cannot establish what's right or wrong, or what's good from evil, or even that there is good and evil. Which I personally observe, and see the God of the Bible best represents what I witness to be good, and has the best solution to what's evil.
4. You can call it special pleading, but it's actually your stubborn disinterest in grasping my argument.
Also, there are no universal principles, only principles drawn through context. You don't put an honorable man in prison, but you do put a murderer in there. But, you don't put a soldier who murdered in there, unless it was murdering an unlawful agent.
You understand?
So there's nothing to special plead. God destroys sinners. He gives grace to those who desire Him and want to change. And you need Him, to understand what's lawful and not. As He's smarter than we are. And His law is indeed self evident... but so are the most difficult constructs of Geometry. It can be too difficult for people to understand, so we need to trust on God.
[D]esign is [also] self evident. In the rudiments of mathematics and the way geometry fits together, it proves a design.
If x doesn't equal x, there can be no logic at all. That's what you're failing to understand.
I think in the theological world--which again, you're not going to understand because that's always been the thing you couldn't--I think there is a nuance. There is both good and evil. Humans can--the most intelligent--discern some of it. Not all of it. Just like humans can't determine all of science. But, we can understand it. And so we need God to arbitrate, and ultimately judge. Even more than that, empower His people to live according to what's right and good.
That's what God means in Hebrew is "Judge."
Why there's evil? I don't know. But there is, and the imperfections of this world are proof that it's not a safe place to put our hopes. And generally, there could only be evil, if God didn't judge. Men are awful judges of right and wrong--not all, but some people can't understand why calculus works, while some can, and others cannot understand basic empathy.
There needs to be a judge higher than man, and also a power by which Man uses to be righteous. As men cannot act righteously on their own accord. I've never seen it, actually, and the societies that least have God, seem to be the most immoral. And they lack peace. They may have pleasure, but they have no peace.
But, generally, the laws of quanta are self evident. We just don't understand it yet. And I'd say morality is also self evident--a genius like Confucius or Mozi can describe it--but say you do codify a perfect morality, what or who holds man accountable to it? That's the real trick... I do believe men can indeed form a perfectly rational moral system, but they ultimately--because of sin--will fail to do it. And also, the chances of them completing such a thing is slim to none, also.
Because men, and it's in the first three chapters, get tempted. That's why there will never be a perfect world, until God judges and uses the Torah to hold man accountable, through the Sword--Jesus is going to war at the end--and without this, without God's power, and without God's authority, man is incapable of ever arbitrating himself. Specifically, when someone does sin, who is going to forgive them? As all men sin, and naturally all men create suffering... who's to forgive these men? Who's to restore their conscience? Are you going to kill them when they make a mistake? Then you're affirming the Old Testament, which I know you don't want to do. Or are you going to just torture them in a cell? Which you essentially make hell through that edict, and I think only God should have the authority to torment someone so.
So, ultimately, it's God's judgment, not man's, that's the new dispensation of Grace in Christ Jesus, man is not the authority, man is not creating utopia, because that's a bloody endeavor on its own, that can only make suffering. Man will fail. And that's why we need God.
American Decline
I think it started with Vietnam. It just shook the public how wrong we were for starting that war. The laxing of morals caused by the Free Love movement. And that sowed seeds of distrust in the public officials. It came like birth pangs. Timed more frequently with each wave. Then the Drug War got people used to unwarranted search and seizures. Then Reagan said “Greed is good”, which set the Republican platform. Then Columbine made people leery of guns, and made schools more restricted. Then 9/11 shook the public’s trust and made it too security conscious. Then the Patriot Act made us warm up to giving up our privacy. Then Obamacare passed, and ruined our medical system. And then Benghazi turned people weird, because it turned American politics into a circus. And Jodi Arias, and Jerry Sandusky shook the nation, making people feel constrained around children. And then the Freddie Grey killing, made people suspicious of the police. And then in 2015 the Woke thing began, with the safe spaces, and people started questioning free speech. And then COVID did the most damage, that was Trump’s fault. Then January 6th and George Floyd tore the country into two factions, and all the rioting that year. And then the Alex Jones Lawsuit confused people on the legalities of free speech. And then Western Europe started punishing people for memes. Now we have a whole litany of things Trump’s single handedly responsible for. Deregulating the market, allowing BlackRock to buy everything. Shutting down the country during COVID. Then in his second term, unilaterally demolishing the East Wing of the White House. AI becoming a huge thing. Defunding public welfare programs. Using people with half a trillion dollars to cut said programs. Trump invading Cities with the National Guard. Getting rid of Public Broadcasting. Discontinuing the Penny. And making threats at our allies. The unrestrained nature of ICE and its conduct in overreaching its jurisdictional boundaries. And then Trump threatening Greenland and Iran turned the whole world against us.
I’d say that's the whole of it, right there.
Analysis of “Ode on a Distant Prospect of Eton College” by Thomas Gray
Verses 1 - 2.
Imagery of the college.
Verses 3-4
Henry the VI established Eton college, and here we begin to see the beginning of the metaphor. What College is for, that the college rests in Henry VI's holy shade, and the college is for science.
Verses 5 - 10
Imagery of the college, and the Thames river, showing a peacefulness, separating the college itself, from the academic learning.
Verses 11-12
Here we have the first intonation of a tone, set in the negative. "Belov'd in vain", sets the tone, of a negative experience. The college's education was not as splendid as the college itself, and its beauty.
Verses 13 - 14
The college occupied his childhood, and he was yet a stranger to pain. He was not yet taught the ways of the world, by the college. His innocence wasn't broken yet.
Verses 15 - 20
There is a joy there, of the college, a certain nostalgia. Of the college itself, and not the academic subjects, which get separated in the poem.
Verses 21 - 26
The students play there, and those are his fondest memories. Of the students playing, and frolicking, and being freed from the rigor of the academy. He's free, to marvel at the thames, and the architecture of the college.
Verses 27 - 30
The idle offspring of men and women succeed, to chase the balls, and play catch. I suppose there were balls, then, which the students would play with.
Verses 30 - 34
Here we get the first intonation of the academic side of the college. Not the idle play, and activities, not the beauty of the landscape, but what you're here for. And "Bring constraint/to sweeten liberty" is a negative wording of it, to bring "constraint" and "sweeten liberty" these two are juxtaposed with one another, to make "Liberty" a negative concept.
Verses 35 - 37
Some bold thinkers disdain the limits of their "Little Reigns", the limits of their imagination, what is theirs to grasp. And they venture into unknown subjects, and dare to "Catch sight of them." Their minds aren't proper for it, though.
Verses 38 - 40
They run, though, into these subjects, to "hear the voice in every wind"; they follow the voices of their books, and learning, and their teachers, and "snatch a fearful joy." The things they learn are a fearful joy, because they half understand it, and can only make mischief with it.
Verses 41 - 42
Their "Gay hope" is liberty, and a world of liberty, but it's "Less pleasing when possesst."
Verses 43 - 46
Their movement is short, and forgotten as soon as they shed a tear, and their vitality is healthy, and their witty inventions are new. (Though this isn't true: this is being written around 1742, so the movements of the enlightenment were just beginning, and he's critiquing them a bit. The philosophies are half baked, and not full yet, and won't have their fruition until 1776, and the Colonies are getting rambunctious over this new doctrine. Also, intonating the French Revolution. Just a foreshadow of the events to come about 30 to 70 years later that will change the world.)
Verses 47 - 50
They truly aren't thinking about the concepts, and are lolled to sleep, and have thoughtless days, and easy nights. Their spirits are poor, and they don't truly understand what they're being taught.
Verses 51 - 52
They do not know that these philosophies will spoil them. They play, and are victims to its ideology.
Verses 53 - 56
They have no care beyond the ills of the day, or ills to come, nothing beyond today. Around them, cultured by this ideology, are "The ministers of human fate" "Fate" is a strong word. The tone of the text implies something fiercely negative.
Verses 57 - 60
And misfortune is "Black" and "Baleful". The consequences of their beliefs. And they stand in ambush, to seize their prey, and are a "Murth'rous band!" Why are they murth'rous? They're being radicalized by the university, ready to fight because of half baked ideas. They are innocent, at the one end, not knowing what they are being used for, but also getting radical, and ready to murder for the things they have been taught.
Verses 61 - 64
The fury of their learning, shall be a passion, that tears, and it is a vulture of the mind. It brings disdainful anger, pallid fear, and shame that skulks behind.
Verses 65 - 70
Or they will be occupied with finding love, and not swept up in the movement, and made wan, and their cares will fade, and this pining and jealousy shall make them sorrowful and despaired.
Verses 71 - 74
The ambition of this learning shall tempt them to rise above their station, and whirl the "wretch" from high, and it will be bitter scorn, and like a sacrifice. The victim of their rage: the current status quo.
Verses 75 - 77
Falsehoods shall be tried, and hard unkindness of the learned behaviors an altered eye. It mocks the tear that's forced to flow. As in, their falsehoods shall be purified by academia, and this will make a hard unkindness in their eye, and it will mock the tears that are forced to flow from their ideology, and their learning. As in, they will be sharpened to think differently, and will lose the joy and innocence they once shared, shown in the beginning of the poem.
Verses 78 - 80
And when remorseful for the blood that they defiled, the moody madness shall laugh wild amidst their woes. By acting on their ideas, and the blood they will shed, it will make them mad, and woeful, though confident in their position, because it's what was taught.
Verses 81 - 84
So, the family of "Death" is more hideous than their queen--the ideas of Democracy are more hideous than their "Queen", than the royal order.
Verses 85 - 87
So this rage created by the enlightenment racks the joints, and puts fire in the veins. It makes every sinew strain, and it sends rage deep into the vitals.
Verses 88 - 90
And because poverty fills the band, and it numbs the soul with icy hands--that is hand quick to shed blood--and also slow consuming age causes this jadedness to occur, too.
Verses 91 - 93
Here, it's just saying all men suffer, and what we try to do to fix it, only makes things worse. So, be tender for another's pain.
Verses 94 - 96
Why should they know their fate? Why should they know their own poverty? Why should they be made aware of their lack of liberty?
Verses 97 - 100
Because happiness swiftly disappears when you're made aware of the world's engines, and thought destroys your paradise. Too much thought destroys the innocence of the previous stanzas. So, ignorance is bliss, and it is "a folly to be wise." Why? Because it ruins your bliss.
Thoughts:
I think this is the way of a mass movement, and how it starts. It starts in the intellectual spheres, and begins to move and matriculate. And Thomas is saying, "Why are they doing this? Why are they losing their innocence for this thing? Better to play on the fields, and study the beauty of the architecture of the buildings, and swim in the Thames, than get involved in the world's woes."
Gray, Thomas. Ode on a Distant Prospect of Eton College. Poetry Foundation. Web. 1.23.26 https://www.poetryfoundation.org/poems/44301/ode-on-a-distant-prospect-of-eton-college
How different number systems, relate to the same thing.
That’s a good question, and is the very foundation of math.
So, I’ll give it to you by relating it to Sine and Cosine. On a right triangle, if the hypotenuse is 1, the other two legs will equal something. And if you make a circle—hang on I’m going somewhere—with the hypotenuse, the legs will be equal to sine and cosine, based on the angle made by the hypotenuse and the cosine leg. So every single degree has a measurement for those numbers—which there’s no algebraic way to deduce, except through maybe pythagorean theorem or analytic geometry, but you also just have to measure it; which may also be what they mean by you can’t do a proof through algebra, except by trial and error
So, that number, which for sine of 60 degrees, the number is √3/2. So, in Roman Numerals or Binary, there will be a way to represent that. But the thing itself, is what the number actually represents.
So, in all things, a number represents a physical object. If Gravity, it’s Gravitational Force; if Mass or Weight; if Quanta; if atomic force or charge in a Chemistry Equation. So, those will represent the same value, based on the context of the equation.
Now a formula, is the next thing to learn. A formula is a shape, that relates to the numbers we measure, and it derives measurements for unknowns through logic, by figuring from what is known, to the unknown. As that’s what a formula is meant to do. A formula is the logic of a shape, so in Trig Functions, the formula is the shape itself, and the sine or cosine or tangent are the numbers we use, to derive information about unknowns. Such as to find area, or other side lengths. Which is highly useful. Because that’s what math is doing, is using known information, and logic, to come to conclusions about unknowns, because the logic of the shapes agree. And through ratios of the object’s similarity, we can augment this, or decrease it, to find new numbers.
B. K. Neifert 