Tag Archives: Mathematics

Basic Math, by Robert Gore

Mathematical grounds for optimism concerning the coronavirus, but not governments.

This is a companion article to “The Last Gasp.”

One of the things this coronavirus outbreak has revealed is widespread mathematical illiteracy. Early on, the number of cases was said to be growing exponentially, which was true, but only for a short while. As an equation, exponential growth is of the form f(x)=ax (x is an exponent, I cannot type a superscript), where a and x are both greater than one. With exponential growth, assuming days are the time period, the daily change is greater each day, but the percentage change remains constant. The sequence 2, 4, 8, 16, 32 … is exponential, f(x)=a2 (the exponent is 2) where a at time 0 (I cannot type a subscript) = 1. The change between numbers grows, but the percentage change remains 100 percent. As a graph, exponential growth is a curve bending upwards. Viruses typically show exponential growth early on, but that cannot continue or eventually the virus would take over the entire planet and then the entire universe.

When the percentage change starts decreasing, there is no longer exponential growth. What has happened with the coronavirus is that the curves have tended to shift from exponential progressions to linear. Linear progressions are straight lines, described by the equation f(x)=ax, where x is a multiplier. 2, 4, 6, 8, 10 is an arithmetic sequence, where a at time 0 = 1 and x = 2. With linear progressions, the daily absolute change remains constant, and the daily percentage change shrinks. Most countries’ coronavirus graphs have already shifted from exponential to linear. The US’s is no longer exponential, but it’s not yet linear.

The next stage is when the daily absolute changes start decreasing. The progression is no longer linear, it bends down. This is what happened in China, even if one incorporates a fudge factor for allegedly fake statistics, and South Korea, which nobody suggests has fudged statistics. South Korea’s graph and widely acclaimed success in stopping the coranavirus are due to its widespread testing early on and its isolation only of people who had tested positive. That should serve as a model for the rest of the world, not lockdowns for the healthy and infected alike. Such lockdowns keep everyone inside, where they are often breathing recirculated air and exposing themselves to the coronavirus from people who are infected but have not tested so and consequently, have not been isolated. Lockdowns also keep people from sunshine, fresh air, and exercise, all of which boost the immune system. I’m grateful to Bill Sardi for the insight on the lockdowns.

The good news is that over the last few days, many countries linear graphs have started to bend down, even where the restrictions are most draconian. Italy’s daily confirmed cases have started to decline. This may only be statistical noise, but it is happening in many different countries with different medical protocols and statistical procedures, which suggests it’s not. The global graph is linear, but as more countries’ daily change numbers decline, the global daily change number will also start to decline and the graph will begin to bend down.

When, not if, the US joins the declining group will depend on how widely effective tests are performed, how many jurisdictions enact lockdowns, and how stringently those lockdowns are enforced. If testing increases from current numbers, it may show more confirmed cases. However, the daily increase in confirmed cases will attenuate as total actual cases do. Lockdowns will increase actual cases, and the more they are enforced, the more they will increase them. Regardless of testing and lockdowns, the US’s actual cases will first go linear (on current, admittedly imperfect numbers we’re already close) and then the curve will bend downward. The curve is certainly not exponential.

Which means that many of the projections both globally and for the US, based as they are on exponential growth that no longer exists, will be off the mark by orders of magnitude. As this becomes clearer, the dictatorial types will panic and try to enact still more dictatorial measures. The time to oppose them is now, with everything you’ve got. Please circulate this article and yesterday’s article, The Last Gasp, from either SLL or TBP as widely as possible. Sunlight, the wonder drug, is the best cure for ignorance.

Source: John Hopkins University Covid-19 website

Feelings Now Acceptable As Answers To Math Problems, from The Babylon Bee

WASHINGTON, D.C.—An update issued Tuesday to the 2017–2018 Common Core educational standards now allows students to answer mathematics problems by responding with whatever their feelings are telling them at the time.

One example problem given to illustrate the updated standards asked students to figure out when a 6:00 a.m. train leaving Boston at thirty miles per hour and a 7:00 a.m. Milwaukee train headed the opposite direction at forty miles per hour will intersect. A list of possible solutions to the sample problem published in the Common Core standards obtained by reporters indicated that “Ugh,” “I’m offended,” “Triggered,” “Trains scare me,” “Boston scares me,” “Milwaukee scares me,” and “Kill yourself,” would all be scored as correct.

“Any emotion, feeling, statement, or catchphrase is an acceptable answer to most of the problems in the new mathematics standards,” a Common Core representative told reporters. “As long as students are being sincere, genuine, authentic, and true to themselves at the time they are answering the question, that’s all we can ask as educators.”

“Who are we to tell anyone that their own mathematical truth is wrong?” the rep added.

According to the rep, the Common Core standards will be updated next year to include feelings as acceptable responses to any and all questions pertaining to biology, chemistry, grammar, and history, while sources claim that English literature teachers have already been accepting emotions as responses for years.

U.S. Kids Keep Getting Dumber; Ranked 31st Of 35 Developed Nations In Math, New Study Reveals, by Tyler Durden

It would be one thing if the US spent a lot of money on education and we were well-education, but we’re not, and as the title notes, our kids keep getting dumber. This is why SLL said in “Making America Competitive Again” that education has to be 100 percent privatized. From Tyler Durden at zerohedge.com:

The U.S. Department of Education has just released it’s latest ranking of international education systems (Program for International Student Assessment – “PISA”) and performance of U.S. students just continues to deteriorate on both absolute and relative terms.

Perhaps it’s time to have a real conversation about the complete failure of “Common Core” and the idiocy of allowing teachers’ unions to hold our children hostage while hiding behind ridiculous contracts that grant tenure after 6 months and make it impossible to fire underperformers. Just a thought for the incoming Trump administration.

The Washington Post’s Valerie Strauss summed up the problems nicely:

There are many reasons children aren’t learning anything during the long hours they spend in government schools. Sometimes, their teachers don’t show up to work because they’re out on the teachers union picket line demanding taxpayers pick up the tab for their plastic surgery. Other times, students are forced to sit in classes led by totally unqualified teachers who will never leave because they’re protected by tenure.

For every disgraceful teacher, though, there are tons of good ones who are doing their best. The problem often isn’t teachers’ incompetence, it’s that they’re forced to instruct kids using rubbish. Look at the Common Core State Standards, which were adopted initially by 46 states because their federal education funding depended on it. The math is backwards, confusing, and, as the National Review so suitably dubbed it, “dumb.” The reading standards fill students’ minds with filth in the form of raunchy books and with yawn-inducing “informational texts.”

Our schools no longer teach reading, writing, and arithmetic. Rather than be taught how to think and problem-solve, children are thought what to think and how to feel. All these money-making and money-spending schemes tend to sound nice, of course, but they inevitably fall flat.

To continue reading: U.S. Kids Keep Getting Dumber; Ranked 31st Of 35 Developed Nations In Math

The War On Abstract Thought, by Robert Gore

Two systems of abstraction allow humanity to think: language and mathematics. Both are systems of symbols, hierarchical, and governed by rules. There is a direct relationship between proficiency with these abstract systems and proficiency of thought, but both proficiencies start with fundamentals. The mind that appreciates the beauty of Shakespeare’s language first had to grasp “See Spot run.” The mind that understands the implications of E=M(CxC) once learned 9×9=81.

Yesterday, SLL posted James Howard Kunstler’s modest proposal to improve the situation in Baltimore and other urban disaster areas: “[T]each young black kids how to speak English correctly.” It is an excellent proposal, but it is only the tip of the iceberg. Conceptually, teaching either language or mathematics is fairly straightforward. As hierarchical systems, learning starts with the basic building blocks—letters and numbers. Once those are mastered, language education moves up to syllables, words, sentences, and so on; mathematics education proceeds from addition and subtraction to multiplication and division, theorems and proofs, algebra, geometry, and so on.

Just as nobody in economics ever got a PhD with a thesis about supply and demand, nobody in education got one explicating or extolling “old school” hierarchical, step-by-step learning. In both fields, academic honors are won with incoherent prose, complicated statistics, Greek-letter-equations, and abstruse theories. The fairly simple concepts both fields can honestly lay claim to have been discarded or dressed up to make them appear much more substantial than they actually are.

Education theses gather dust; the damage they’ve inflicted is evident in the lamentable state of language and mathematical proficiency among the majority of students, documented year after year by much-maligned standardized tests. While SLL claims no expertise in the arcane field “Education” has become, it appears that the crippling of students’ minds has had two broad components: dispense with step by step learning and jump among steps, on the theory that as the later steps are learned, the earlier steps will somehow be mastered, and dispense with hierarchies, on the theory that everything is interrelated, so by teaching everything at the same time, the student learns everything.

Evidently, “rote memorization” of foundational concepts has become the scourge of the educational establishment. First and second graders no longer repeat arithmetic and multiplication tables until they are drilled into their heads for life. Rather they are “exposed” to them, along with many other concepts, repeatedly through many grades, which leaves middle schoolers counting on their fingers as they try to perform the addition, subtraction, multiplication, and division necessary for fractions, decimals, the Pythagorean theorem, and algebraic proofs. Similarly, words are not built syllabically through phonics; the parts of speech and rules of grammar are “discovered” rather than drilled, and standard methodologies about sentence, paragraph, and compositional structures are abandoned, scorned as inhibiting free expression. Consequently, students never learn how to give a coherent speech or presentation, or write a lucid report or essay. Most of them, however, are amazingly proficient at texting.

Learning language and mathematics basics takes time and is hard work, often involving rote memorization, but you can’t build a house before you lay the foundation. Life would indeed be simpler if we only communicated with grunts and gestures, and if our mathematics was limited to what could be done on our fingers and toes, but that takes us back to the stone age. It is the ability to formulate ever rising hierarchies of abstract concepts that has propelled the human race. Some have said the war on abstraction is being waged to dumb down humanity, making it easier for an elite group to rule. If that is the plan, it has gaping holes, as all such plans do. The weapons to threaten us, the technology to monitor us, the mass communications to propagandize us, and the economy that supposedly would provide our bare subsistence and the rulers’ aristocratic splendor all require high-level abstraction and consequently, high-level thought. The war on abstract thought will have no winners.

TRY BUILDING A FACTORY, OR FIGURING OUT WHEN A POLITICIAN IS LYING, WITHOUT ABSTRACT THOUGHT

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