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lipshits-continuous · 9 months ago

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Topological Spaces 1: Introduction and Metric Spaces

Welcome to the first of several posts about general topology! The goal of these posts is to give an overview and introduction to key concepts in topology. I will try to give intuitions about definitions and results so that even if you're not as aquainted with formal mathematics you can still get something from this. Whilst there aren't any prerequisties per say (for the reason above), for those who are interested in the moral formal aspects it will be helpful to be familiar with real analysis. Some familiarity with linear algebra is also helpful in this post though probably won't play a role going forward.

Topology is such a broad subject that assigning one goal is quite hard. One early goal is to generalise the notion of continuity and other familiar notions, which we shall do. Topology certainly doesn't stop there. One large goal is to find properties which are invariant under homeomorphism (bijective continuous maps whose inverse is also continuous). We shall see some examples of this as we go further!

The goal of this post is to give context to the definitions of topological spaces and continuity via the study of metric spaces. The definition of a topological space can seem quite dry and like it's been plucked out of thin air when just presented without motivation. In this sense, metric spaces are the bridge between familiar concepts in real analysis and the more general setting of topology.

1.1: Metric Spaces:

As the name might suggest, metric spaces are sets with an appropriate notion of distance between points in the set. For the real numbers, we have an intuitive sense of distance between two numbers: the absolute value of their difference. From this, we can immediately get three desirable properties we'd want a notion of distance to have:

Positivity: |x-y|≥0

|x-y|=0 if and only if x=y

Symmetry: |x-y|=|y-x|.

These are desirable because this says, in order, that distance is always positive, two points are the same only when the distance between then is 0, and the distance beween x and y is the same as the distance between y and x.

The last property is not as immediately obvious from the definition but is still a fairly intuitive property that we'd expect a notion of distance to have: the triangle inequality. Formally, for any x,y, and z real number we have |x-y|≤|x-z|+|z-y|. This just says that the distance between two points is always shorter than the distance achieved by adding an intermediate point. The name comes from visiualising this with lengths of a triangle! The proof that this holds for the absolute value can be found here.

You might ask whether there are any more properties we'd like but it turns out that this is enough to generalise a lot of concepts in real analysis in an appropriate way. That is, we still maintain a lot of nice results without requiring too many rules. So let us finally see the definition!

Definition 1.1:

Note: It's common to combine the first two axioms together but for the sake of clarity, I have separated them.

Examples 1.2:

The details of why each of these is a metric can be found in this post.

A result of the second example is that metric spaces are also an appropriate generalisation of normed vector spaces. The fact they are a generalisation is seen from the fact that the discrete metric cannot be seen as the result of a norm and isn't restricted to vector spaces.

1.2: Continuity:

Intuitively, continuous functions are ones that don't have gaps or sudden jumps. In the case of functions from the real numbers to itself, we can view this as "we can draw its graph without lifting the pencil". This can be restated as "points that are close to each other remain close to each other after the function is applied". But how does one formalise "closeness"? With distances of course!

Definition 1.3:

Remark: Continuity departs on the metrics. A function that is continuous in one metric isn't necessarily continuous in another.

Examples 1.4:

Now I'd like to prove a fairly common result to further demonstrate continuity.

Proposition 1.5:

1.3: Open Sets in Metric Spaces

Now we shall see the first aspects of topology creeping in. One way to think about open sets which don't have any points "at the edge". This is immediately clear in the definition we will give below but when we generalise the notion of an open set, we will seemingly lose this. However, we will see that this intuition will still hold!

Definition 1.6:

Example 1.7:

We will now define the notion of an open set using these open balls.

Definition 1.8:

This does indeed formalise "no points at the edge" since for open sets, all points close enough to x are always in U.

Remark: Openness depends on the metric. For example, {0} is open in the real numbers with the discrete metric but not with the absolute value metric.

Now, "open ball" would be a silly name for it if they weren't indeed open in the sense of definition 1.8 but luckily they are!

Proposition 1.9:

Example 1.10:

Open intervals of real numbers are indeed open with respect to the absolute value. If we have the open interval I=(a,b) for finite a<b, we may view I as an open ball by setting x=(b+a)/2 and r=|b-a|/2. Then I=B(x;r).

Now we shall prove a very important result about open sets that lets you build new open sets out of old opens but will also be the foundation upon which we generalise the notion of open sets!

Lemma 1.11:

Proof:

Remark: Finiteness is important for 3. If we consider the real numbers with the absolute value metric then (-1/n,1/n) is open for all (non-zero) natural numbers. However their intersection over all n is {0} which is not open in this metric.

Typically, courses would usually talk about closed sets now. However, since the discussion doesn't vary much between metric spaces and topological spaces, we will hold off for now.

1.4: Continuity in terms of open sets

This is a very important step in our journey in generalising continuity. This section with along with the next section will suggest that open sets are actually the structures we'd like to study!

Lemma 1.12:

Before we prove this, I'd like to just comment on why this still alligns with our intution about continuity. The right hand side is saying that points end up close together in Y must've been close together in X.

Remark: It is important to note that U open in X does not necessarily imply f(U) is open in Y when f if continuous. For example, take f(x)=x² in ℝ with its usual notion of continuity, then (-1,1) is open but f((-1,1))=[0,1) which is not open. Maps for which open sets are mapped to open sets are called open maps.

We will see examples of how to use the property on the right hand side in the next post!

1.5: Equivalent Metrics

The goal of this section is to see that sometimes different metrics will give rise to the same open sets!

Definition 1.13:

Example 1.14:

I will omit the details of the proof for brievity. Not that the 2 on the right hand side comes from the fact we're in ℝ² and isn't related to the 2 in the metric.

Remark: Not all metrics are equivalent. The discrete metric and d₂ are not equivalent metrics.

Proposition 1.15:

Corollary 1.16:

This ultimately means that some metrics generate the same open sets. Then Lemma 1.12 tells us that equivalent metrics give the same continuous funcitons since we can view continuity in terms of open sets. This suggests that what really matters here is which sets are open. This is what we shall exploit to generalise continuity even further! But that shall have to wait til the next post!

#maths posting #mathblr #maths #mathematics #topology #lipshits posts #long post #undescribed

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study-with-aura · 3 months ago

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Wednesday, August 28, 2024

It has been really busy around here since my parents are back to their campuses regularly again. That, and it has been so quiet! There's nothing wrong with the quiet of course, but it reminds me that Julien isn't at home anymore, which makes me sad. It is okay though. He is having a great time back at his university, and that makes me happy to know!

My updates may start to get sporadic again, as I am already starting to experience slight difficulties with staying motivated in studying. One would think, since I had an amazing summer break (despite the small studying I still did), that I would be good and ready to keep going until the next break. However, my summer was still packed with activity and maybe not a true break at all even though all of it was enjoyable and fun! The work this year is also more demanding. If you haven't noticed, there is a lot more revising going on with my notes and more writing and reading material in general. It will prepare me for more advanced studies of course, but I need to get back into the groove of it, so to speak, and I will.

Tasks Completed:

Algebra 2 - Learned about graphing linear inequalities + practice + practiced with the graphing calculator

American Literature - Copied vocabulary terms + read about Benjamin Franklin as a writer + read excerpts from The Autobiography of Benjamin Franklin + answered discussion questions + read about Benjamin Franklin's Poor Richard's Almanac in the article "The Prominent and Prodigiously Popular Poor Richard" + read over Benjamin Franklin's aphorisms and the virtues associated with them + wrote down three aphorisms from the list that I liked including what they meant + read over the article "Reflective Writing: A Basic Introduction" + read chapters 20-21 of The Scarlet Letter by Nathaniel Hawthorne

Spanish 3 - Read over an activity in Spanish to determine how much I could read and understand (I understood most of it) + reviewed gender and plural in Spanish

Bible 2 - Read 2 Samuel 22

Early American History - Watched a short video about the first Thanksgiving + read chapter 9 of Plymouth Plantation by William Bradford

Earth Science with Lab - Watched a video about hydroplate theory and Earth's radioactivity

Music Appreciation - Read about and listened to Musical Signatures associated with Gustav Mahler + read about and listened to the "Refuge and Renewal," "Triumph and Tragedy," and "Awe and Affirmation" tabs about Gustav Mahler + copied major necessary terms from the H section of the music dictionary

Khan Academy - Completed US History Unit 2: Lesson 3 (part 1)

Duolingo - Studied for approximately 30 minutes (Spanish + French + Chinese) + completed daily quests

Piano - Practiced for two hours in one hour split sessions

Reading - Read pages 211-277 of We Are All So Good at Smiling by Amber McBride and finished the book

Chores - None today

Activities of the Day:

Personal Bible Study (Matthew 5)

Ballet

Variations

Journal/Mindfulness

#study blog #study inspiration #study motivation #studyblr #studyblr community #study community #study-with-aura

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disorderofsevenstars · 9 months ago

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Gender and Divinity

At one end of the gender spectrum lies the Feminine, associated with Black and darkness, the Earth and mundane matters, collectivity, interconnection, receptivity, cyclicality, synthesis, and heterogeneity. At the other end lies the Masculine, associated with White and illumination, the Heavens and spiritual matters, individuality, separation, exclusivity, linearity, analysis, and homogeneity. These two extremes, Yin and Yang, interact to create a multitude of permutations which lie somewhere in between the purely Feminine and the purely Masculine. Everything that exists as part of what we usually call "reality" is located somewhere in this intermediate space. The extremes themselves are conceptual, and do not exist in material reality, as they are characterized by a purity which cannot be found in Nature.

Sleeping, dreaming, and Death-as-a-state (in contrast with Death-as-a-process) fall within the domain of the Feminine, as do gravity and magnetism, Zero and the even numbers, the elements of Water and Earth, the Moon, and the Cosmic Void or World Egg. Femininity denotes a state of rest, stability, and equilibrium. It promotes slowness and longevity, regeneration and even immortality, characteristic of oceanic or cold environments and the organisms that live there, shielded from the mutagenic properties of solar radiation. The influence of the Feminine on human societies manifests through tribalism, collectivism, and egalitarianism, giving rise to social structures such as animist and polytheistic religions, cults, clans, matrilineal descent systems, polygamy and polyamory, democracy, communism, hedonism, mysticism, subcultures and countercultures. It is driven by the Dionysian impulse to shed the Ego, losing the Self within something larger, like a drop of rain falling into the ocean. The Moon is a mirror; it does not generate its own light.

Femininity is the original and final state of all things. It is prominent in small children and the elderly, more so in non-human animals (especially large and slow-moving animals, those animals which are more primordial or lower on the food chain, as well as small animals with collectivistic tendencies such as ants), even more so in plants, and still more so in rocks, soil, and water. In animals, it is highly oriented toward the senses of touch, taste, and smell. During the course of our evolution, we developed eyes, learned to hunt, learned to walk on land, learned to stand upright, became taller, acquired language and logic, mastered the use of tools and fire, and lost our fur; some of us also lost our melanin. The development of an embryo into an infant, into a child, into an adult, involves a loss of plasticity; bones harden and fuse, the percentage of water in the body decreases, and neural pathways become more rigid. All of these traits indicate a process of Masculinization.

The Masculine is the domain of awareness, alertness, problem-solving, and conflict. It governs changes, transitions, and boundaries. Masculinity is a property of electricity, odd numbers, prime numbers, the elements of Fire and Air, the Sun, and the Axis Mundi. It is dynamic and always in motion, striving to reach the Feminine rest-state, like an arrow flying towards a target, or a key inserted into a lock. The influence of the Masculine on human societies manifests through individualism and inequality, giving rise to colonialism, capitalism, competition, war, monotheism, monogamy, patriarchy, the nation-state, asceticism, and scientific thought. Driven by the Apollonian impulse towards separation and clarity, it prioritizes facts over feelings.

Unable to coexist and seeing plurality as a threat, Masculinity seeks to dominate the Other and propagate the Self, often through violent means; Western culture, Christianity, and Islam are examples of this. Monotheism and patriarchy have a mutual affinity, and in many cases, one promotes the other. The god of a monotheistic religion is usually male. The Sun is the central axis around which all bodies in the Solar System revolve. This tendency of the Masculine to see itself as superior lies behind the association of Light with Good, and Darkness with Evil. Humans, considered as a whole, lean towards Masculinity, and serve as a Masculine counterpart to the natural environment of Earth.

The supreme divinity is like a polygon with an infinite number of sides: simultaneously circular and linear. Fate arises from the interconnection of individual wills, a product of emergent complexity, many individual entities inadvertently working together in a larger system. "GOD" can be described as genderless, or a perfect balance of all possible genders. It has the Feminine quality of Being, and the Masculine quality of Unity. It is an all-pervasive energy field of pure universal consciousness, which can be channeled into various manifestations that possess genders and other specific attributes, like white light being split by a prism into its spectral components. These facets of divinity are conceptualized in every pantheon of deities, in the 12 signs of the Zodiac, in the 22 Major Arcana or 22 letters of the Hebrew Alphabet, in Kabbalah as the 10 Sefirot, in Christianity as the Holy Trinity, in the Tzolk'in as the 20 Naguales, and in Chinese cosmology as the Ba Gua (Eight Trigrams) and 64 Hexagrams of the I Ching.

[3/16/2024]

#occult #philosophy #gender

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religion-is-a-mental-illness · 1 year ago

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By: Julia Steinberg

Published: Jul 27, 2023

“California is America, only sooner” was an optimistic phrase once used to describe my home state. The Golden State promised a spirit of freedom, innovation, and experimentation that would spread across the nation. And at the heart of the state’s flourishing was a four-letter word: math.

Math made California prosper.

It’s most obvious in top universities like Stanford, Caltech, Berkeley, and UCLA. Those schools funneled great minds into California STEM enterprises like Silicon Valley, NASA’s Jet Propulsion Laboratory, and aeronautical engineering. Both the Central Valley and Hollywood—America’s main providers of food and fodder, respectively—rely upon engineering to mechanize production and optimize output.

All of this has made California’s GDP $3.6 trillion—making it the fifth largest economy in the world as of last year.

But now “California is America, only sooner” is a warning, and not just because of the exodus of people and jobs and the decay of our major cities, but because of the state’s abandonment of math—which is to say its abandonment of excellence and, in a way, reality itself.

Perhaps you’ve read the headlines about kooky San Francisco discarding algebra in the name of anti-racism. Now imagine that worldview adopted by the entire state.

On July 12, that’s what happened when California’s Board of Education, composed of eleven teachers, bureaucrats, professors—and a student—decided to approve the California Mathematics Framework.

Technically, the CMF is just a series of recommendations. As a practical matter, it’s the new reality. School districts and textbook manufacturers are already adapting to the new standards.

Here are some of them:

Most students won’t learn algebra until high school. In the past, when that was expected of middle schoolers, the CMF tells us, “success for many students was undermined.”

This means calculus will mostly be verboten, because students can’t take calculus “unless they have taken a high school algebra course or Mathematics I in middle school.”

“Detracking” (ending advanced courses) will be the law of the land until high school; students will be urged to “take the same rich mathematics courses in kindergarten through eighth grade.”

Lessons will foreground “equity” at the expense of teaching math basics like addition and subtraction. “Under the framework, the range of student backgrounds, learning differences, and perspectives, taken collectively, are seen as an instructional asset that can be used to launch and support all students in a deep and shared exploration of the same context and open task,” the CMF continues. It adds that “learning is not just a matter of gaining new knowledge—it is also about growth and identity development.”

Letter grades will be discouraged in favor of “standards-based assessments.” (It’s unclear what those are.)

Never mind that before California lowered its standards, the United States already ranked far behind the best-performing countries in math—places like Singapore, China, Estonia, and Slovenia. All those countries teach high school students calculus and, in some cases, more advanced linear algebra. (If we’re really in the midst of a cold war with China, we sure aren’t acting like it.)

The California Board of Education thinks the CMF is exactly what’s needed. That’s because the board has a fundamentally different approach to education—and it’s important that all Californians, indeed, all Americans, understand that.

The board’s overriding concern is not education or mathematical excellence, but minimizing racial inequity. Since a disproportionate number of white and Asian kids perform at the high end of the mathematics spectrum, and a disproportionate number of black and Latino children are at the bottom end, the board was left with two options: pull the bottom performers up, or push the top performers down. They did the easier thing.

In case anyone is wondering whether this works, whether it actually achieves greater racial equity, we need only look to San Francisco, which adopted CMF proposals like detracking before the CMF formally did.

“I want to be very clear on one fact that is based in our data: our current approach to math in SFUSD is not working,” San Francisco Unified School District Superintendent Matt Wayne said. “That is a tragedy, because we want to do right by our students. And we’re not meeting our goals around math. And particularly our students, especially black and brown students, are not benefiting from the current way we do math in the district.”

I emailed Jo Boaler, a Stanford education professor, one of the CMF’s authors, and a co-founder of youcubed, a center at Stanford that has pioneered ideas about equity and math education that figure prominently in the plan. I wanted to know what I was missing. What Matt Wayne was missing.

Boaler replied that she didn’t have much to say about the CMF and that she was a “small cog in the system that produced the framework.”

When I pressed her to see if she could offer any thoughts about the ideas behind the CMF—ideas she’s well versed in—she suggested I speak with “lead writer” Brian Lindaman, a math education professor at Chico State. Lindaman did not reply to my email.

Eventually, I did manage to speak with Kyndall Brown, the executive director of UCLA’s California Mathematics Project, which is charged with implementing the CMF.

I started by saying the CMF is clearly focused on racial inequity—noting, for example, that Chapter 2 is all about equity and that it’s shot through with mentions of racial “disparities” and “gaps” when it comes to “student outcomes.”

Brown, who, like other CMF supporters, believes those disparities are largely, if not entirely, the fault of racially or culturally insensitive teaching methods, replied simply: “Do you know how racist that sounds?”

When I asked him what, exactly, was racist about that, he replied: “What mathematicians of color did you learn about as a student? What female mathematicians did you learn about?” (He appeared to be alluding to medieval Arab contributions to the fields of algebra and number theory—which are fascinating and important when studying the history of ideas, but not obviously germane when teaching ninth graders about quadratic equations.)

The thing is, the CMF will exacerbate racial inequities. I went to a private school in Los Angeles filled with white and Asian students, and I know exactly how those kids—and definitely their parents—would react if they were told they could no longer take advanced math. They would enroll in rigorous programs outside school, like the Russian School of Mathematics, that would push them way beyond wherever their peers are. By the time college applications came along, the racial gap would be more like a yawning chasm.

I turned to Alan Schoenfeld, a Berkeley education professor who advised members of the Board of Education on the CMF, to see what he thought about this, and he said the same thing opponents of affirmative action have—that lower-performing students might perform better and develop greater confidence if they’re in a less rigorous environment. “Now some of them are going to turn out to enjoy mathematics, and they’re going to pursue mathematical careers,” Schoenfeld told me.

Ian Rowe, a CMF critic best known for founding several independent schools in the Bronx, said of the plan’s supporters: “They’ve embraced this ideology of oppressor-oppressed framework, where it’s assumed that black kids are these marginalized, oppressed human beings, and white kids are somehow the privileged oppressors. You see this all across the country, where expectations are being lowered in the name of equity by teachers and principals to somehow level the playing field.”

Let’s be clear: the CMF is racism pretending to be progressive, and all the fancy ed speak—about “frameworks” and “detracking” and “identity development”—can’t obscure as much. Indeed, the ideological gap is basically nonexistent between CMF supporters and reactionaries who once thought black and Latino kids were cognitively or culturally incapable of advanced mathematics.

We should be blaring this from the rooftops and on our social media feeds, over and over—lest we lose the California Dream, a.k.a. the American Dream, which once made this place so special.

Kids can't fail math if you don't teach it to them.

"Luxury beliefs are ideas and opinions that confer status on the upper class, while often inflicting costs on the lower classes." -- Rob Henderson

#Julia Steinberg #neoracism #woke racism #math #woke math #mathematics #corruption of education #luxury beliefs #time to homeschool #homeschool your kids #antiracism as religion #antiracism #equity #bigotry of low expectations #low expectations #religion is a mental illness

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la-pheacienne · 11 months ago

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So this is something I have always found interesting. While doing research on my PhD I read a greek paper about gender equality in Greece that said that basically, women's position in society was much, much more prominent during the byzantine empire (our "middle age" - not exactly but whatever) than it was during the first period of greek urbanization (early 20th century). Which is wild to me. But then the professor explained it by saying that during byzantine empire we had an agricultural economy so women had an active role in the means of production, they actively participated (in some instances even dominated) in the agricultural activities of their household, which were the main revenue for the family, aka, women worked and this work was, in fact, recognized as such. They had actual control and power over their household and over their (small) agricultural communities. I am not even talking about the privileged women that had actual political power. Also, raising children was pretty much NOT one woman's work. It wasn't a man's work of course, but women were not isolated in this. There were multiple women raising one woman's child, grandmothers, sisters, cousins, sisters-in-law, mothers-in-law, neighbours etc, while the woman was out, working in the fields, literally.

So. What happened with urbanization was that women were cut off their communities and got isolated in the big cities. They lost their support system, the tight social network of an agricultural community and most importantly, they lost their role in the means of production. They then became housewives, whereas before they were active participants in the agricultural economy. It is in that context that the gender inequality, in the sense of real societal imbalance between men and women, reached its peak, which later on led to the greek feminist movement as an echo of foreign feminist movements, and then the two wars completely changed the rules of the game and the rest is known.

I don't think this only applies to greek history btw, and we should always have in mind that actually no, women weren't mere broodmares in the middle ages and progress is not always linear. It has ups and downs.

all RIGHT:

Why You're Writing Medieval (and Medieval-Coded) Women Wrong: A RANT

(Or, For the Love of God, People, Stop Pretending Victorian Style Gender Roles Applied to All of History)

This is a problem I see alllll over the place - I'll be reading a medieval-coded book and the women will be told they aren't allowed to fight or learn or work, that they are only supposed to get married, keep house and have babies, &c &c.

If I point this out ppl will be like "yes but there was misogyny back then! women were treated terribly!" and OK. Stop right there.

By & large, what we as a culture think of as misogyny & patriarchy is the expression prevalent in Victorian times - not medieval. (And NO, this is not me blaming Victorians for their theme park version of "medieval history". This is me blaming 21st century people for being ignorant & refusing to do their homework).

Yes, there was misogyny in medieval times, but 1) in many ways it was actually markedly less severe than Victorian misogyny, tyvm - and 2) it was of a quite different type. (Disclaimer: I am speaking specifically of Frankish, Western European medieval women rather than those in other parts of the world. This applies to a lesser extent in Byzantium and I am still learning about women in the medieval Islamic world.)

So, here are the 2 vital things to remember about women when writing medieval or medieval-coded societies

FIRST. Where in Victorian times the primary axes of prejudice were gender and race - so that a male labourer had more rights than a female of the higher classes, and a middle class white man would be treated with more respect than an African or Indian dignitary - In medieval times, the primary axis of prejudice was, overwhelmingly, class. Thus, Frankish crusader knights arguably felt more solidarity with their Muslim opponents of knightly status, than they did their own peasants. Faith and age were also medieval axes of prejudice - children and young people were exploited ruthlessly, sent into war or marriage at 15 (boys) or 12 (girls). Gender was less important.

What this meant was that a medieval woman could expect - indeed demand - to be treated more or less the same way the men of her class were. Where no ancient legal obstacle existed, such as Salic law, a king's daughter could and did expect to rule, even after marriage.

Women of the knightly class could & did arm & fight - something that required a MASSIVE outlay of money, which was obviously at their discretion & disposal. See: Sichelgaita, Isabel de Conches, the unnamed women fighting in armour as knights during the Third Crusade, as recorded by Muslim chroniclers.

Tolkien's Eowyn is a great example of this medieval attitude to class trumping race: complaining that she's being told not to fight, she stresses her class: "I am of the house of Eorl & not a serving woman". She claims her rights, not as a woman, but as a member of the warrior class and the ruling family. Similarly in Renaissance Venice a doge protested the practice which saw 80% of noble women locked into convents for life: if these had been men they would have been "born to command & govern the world". Their class ought to have exempted them from discrimination on the basis of sex.

So, tip #1 for writing medieval women: remember that their class always outweighed their gender. They might be subordinate to the men within their own class, but not to those below.

SECOND. Whereas Victorians saw women's highest calling as marriage & children - the "angel in the house" ennobling & improving their men on a spiritual but rarely practical level - Medievals by contrast prized virginity/celibacy above marriage, seeing it as a way for women to transcend their sex. Often as nuns, saints, mystics; sometimes as warriors, queens, & ladies; always as businesswomen & merchants, women could & did forge their own paths in life

When Elizabeth I claimed to have "the heart & stomach of a king" & adopted the persona of the virgin queen, this was the norm she appealed to. Women could do things; they just had to prove they were Not Like Other Girls. By Elizabeth's time things were already changing: it was the Reformation that switched the ideal to marriage, & the Enlightenment that divorced femininity from reason, aggression & public life.

For more on this topic, read Katherine Hager's article "Endowed With Manly Courage: Medieval Perceptions of Women in Combat" on women who transcended gender to occupy a liminal space as warrior/virgin/saint.

So, tip #2: remember that for medieval women, wife and mother wasn't the ideal, virgin saint was the ideal. By proving yourself "not like other girls" you could gain significant autonomy & freedom.

Finally a bonus tip: if writing about medieval women, be sure to read writing on women's issues from the time so as to understand the terms in which these women spoke about & defended their ambitions. Start with Christine de Pisan.

I learned all this doing the reading for WATCHERS OF OUTREMER, my series of historical fantasy novels set in the medieval crusader states, which were dominated by strong medieval women! Book 5, THE HOUSE OF MOURNING (forthcoming 2023) will focus, to a greater extent than any other novel I've ever yet read or written, on the experience of women during the crusades - as warriors, captives, and political leaders. I can't wait to share it with you all!

#sorry for the long ramble it is kind of irrelevant to the OP but also somewhat relevant #patriarchy #also when I compare my two grandmas I see that the professor was right #my grandma in the village was much much more powerful than my grandma in the city #my grandma in the village basically controlled everything #the one in the city was stuck in the housewife role and had zero help and support

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elmadrasahplatform · 11 days ago

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Important information about the SAT Math exam in the UAE

The SAT Math exam in the UAE is a major gateway for Emirati students wishing to enroll in prestigious universities and colleges in the world. This standardized test measures the student's understanding of basic mathematical concepts and his ability to apply them to solve various problems.

What is the SAT Math exam in the UAE?

The SAT exam is a standardized test widely used for admission to universities and colleges in the United States and other countries, including the UAE. The mathematics section of this exam measures your ability to understand and solve mathematical concepts, and apply them to various problems.

The importance of the SAT Math exam in the UAE

University admission: The SAT is a prerequisite for admission to many prestigious universities and colleges in the UAE and the world.

Scholarships: Excellent SAT results can help you obtain scholarships and financial awards.

Level assessment: The SAT helps you evaluate your mathematical abilities and compare them to the abilities of other students.

What does the SAT Math exam cover?

The SAT Math exam in the UAE covers a wide range of mathematical topics, including:

Algebra: Equations and inequalities, functions, linear systems, and more.

Geometry: Geometric shapes, measurement, geometric transformations, and more.

Statistics and probability: Data, statistical inference, probability, and more.

How to prepare for the SAT Math exam in the UAE?

Study the syllabus: Review the syllabus for the mathematics subjects you studied in school.

Solve practice problems: Practice solving as many practice problems and mock tests as possible.

Focus on weaknesses: Identify your weaknesses in mathematics and work on strengthening them.

Enroll in a preparatory course: You can enroll in an SAT preparatory course to help you better understand the concepts and prepare for the test.

Important tips for your success in the SAT Math exam

Time management: Allocate enough time for each question and make sure to answer all the questions.

Read the questions carefully: Understand the question well before starting to solve.

Use the calculator: Use the calculator correctly and effectively.

Check your answers: Make sure to review your answers before submitting the exam.

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madrasahel1 · 3 months ago

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Understanding the EMSAT Math Syllabus: A Comprehensive Guide

The EMSAT Math syllabus is a crucial component for students preparing for the Emirates Standardized Test (EMSAT). This standardized test is designed to assess students' proficiency in various academic areas, and Mathematics is a significant part of the assessment. In this article, we will delve into the EMSAT Math syllabus, exploring its key components, the skills it aims to evaluate, and how Elmadrasah.com plays a pivotal role in helping students succeed in this examination.

Overview of the EMSAT Math Syllabus

The EMSAT Math syllabus is meticulously crafted to ensure that students possess the necessary mathematical skills and knowledge to excel in higher education and professional fields. The syllabus covers a broad spectrum of mathematical concepts, ranging from basic arithmetic to advanced topics. Understanding the EMSAT Math syllabus is essential for students aiming to perform well in the exam.

Key Components of the EMSAT Math Syllabus

Number and Algebra: This section includes fundamental concepts such as arithmetic operations, fractions, decimals, percentages, and algebraic expressions. Students are expected to demonstrate their ability to solve equations, understand inequalities, and manipulate algebraic expressions.

Geometry: Geometry topics in the EMSAT Math syllabus involve understanding shapes, sizes, and the properties of space. Students must be proficient in concepts such as angles, triangles, circles, and polygons. The ability to calculate area, volume, and surface area is also essential.

Statistics and Probability: This component focuses on the ability to interpret data, understand probability, and analyze statistical information. Students are required to work with various types of data representations, such as graphs and charts, and apply statistical measures to real-life scenarios.

Functions: Understanding different types of functions, including linear, quadratic, and exponential functions, is a key aspect of the EMSAT Math syllabus. Students should be able to interpret function graphs, solve function-related problems, and apply function concepts to various contexts.

Problem Solving and Reasoning: The EMSAT Math syllabus emphasizes critical thinking and problem-solving skills. Students are expected to approach mathematical problems methodically, use logical reasoning, and apply appropriate mathematical techniques to arrive at solutions.

The Role of Elmadrasah.com in EMSAT Math Preparation

Elmadrasah.com has established itself as a leading platform for educational resources and training. For students preparing for the EMSAT Math exam, Elmadrasah.com offers a range of services designed to enhance their understanding of the EMSAT Math syllabus and improve their performance. Here’s how Elmadrasah.com contributes to EMSAT Math preparation:

Comprehensive Study Materials: Elmadrasah.com provides detailed study materials aligned with the EMSAT Math syllabus. These resources include textbooks, practice problems, and interactive content that cover all key areas of the syllabus.

Online Courses and Tutorials: The platform offers online courses and tutorials specifically designed to address the EMSAT Math syllabus. These courses are taught by experienced educators who break down complex concepts into manageable lessons, making it easier for students to grasp challenging topics.

Practice Tests and Mock Exams: To help students assess their readiness for the EMSAT Math exam, Elmadrasah.com provides practice tests and mock exams. These practice assessments are designed to simulate the actual test environment, allowing students to familiarize themselves with the exam format and identify areas where they need improvement.

Personalized Tutoring: Elmadrasah.com offers personalized tutoring sessions for students who require additional support. Tutors work closely with students to address their specific needs, providing targeted instruction and feedback to enhance their understanding of the EMSAT Math syllabus.

Interactive Learning Tools: The platform features interactive learning tools that engage students and make learning more effective. These tools include video lessons, quizzes, and educational games that reinforce key concepts from the EMSAT Math syllabus.

Expert Guidance and Support: Elmadrasah.com’s team of experts provides guidance and support throughout the preparation process. From answering questions to offering study tips, the support team helps students stay on track and build confidence in their mathematical abilities.

Progress Tracking and Feedback: To ensure that students are making progress, Elmadrasah.com offers tools for tracking performance and providing feedback. Students can monitor their progress, review their strengths and weaknesses, and adjust their study strategies accordingly.

Resourceful Blog and Articles: Elmadrasah.com maintains a blog with articles and resources related to EMSAT Math preparation. These articles offer valuable insights, study tips, and updates on changes to the EMSAT Math syllabus.

Community and Forums: The platform hosts forums and community groups where students can connect with peers, share experiences, and seek advice. Engaging with a community of learners can provide additional motivation and support.

Flexible Learning Options: Recognizing that students have diverse learning needs, Elmadrasah.com offers flexible learning options. Whether students prefer self-paced learning or structured courses, the platform provides resources and support to accommodate different preferences.

Conclusion

The EMSAT Math syllabus encompasses a wide range of mathematical concepts and skills that are crucial for academic and professional success. Understanding the syllabus and preparing effectively are key to achieving a high score in the exam. Elmadrasah.com plays a significant role in supporting students through comprehensive study materials, interactive learning tools, and expert guidance. By leveraging the resources and services offered by Elmadrasah.com, students can enhance their preparation, build confidence, and increase their chances of excelling in the EMSAT Math exam.

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frenchschoolofaustin · 6 months ago

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Dr. Hind Louali: The Artistic Expression Influenced by French Language and Culture

Exploring French Language and Cultural Influence in Artistic Expression with Dr. Hind Louali

According to Dr. Hind Louali, founder of French School of Austin - Ecole Jean-Jacques Rousseau, the French language and culture are esteemed in the world of art and exert a profound influence on artists across various mediums. This article explores how the nuances of French artistic traditions have shaped global creative landscapes, from literature and painting to film and fashion.

French culture, renowned for its deep historical roots and emphasis on intellectual rigor and aesthetic refinement, has long been a beacon for artists seeking inspiration. The French language itself, with its precise vocabulary and inherent musicality, offers a rich palette for poetic and literary expression. This linguistic elegance has captivated writers and poets around the world, prompting them to either adopt the French language in their work or imbue their native languages with its stylistic qualities.

In literature, the French tradition has been particularly influential. The works of French authors such as Marcel Proust, Victor Hugo, and Simone de Beauvoir have transcended national boundaries, their themes of human emotion, social struggle, and existential inquiry resonating universally. Proust's intricate descriptions and introspective style in "In Search of Lost Time" have inspired countless writers to explore the depths of memory and time in their narratives. Meanwhile, Hugo's passionate advocacy for social justice in novels like "Les Misérables" has ignited artistic endeavors that aim to illuminate and critique societal inequalities.

The influence of French culture extends robustly into the visual arts. Dr. Hind Louali, founder of French School of Austin - Ecole Jean-Jacques Rousseau mentions that French painters' revolutionary techniques have often set new directions for artistic expression. For instance, Impressionism, born in France, changed the course of painting with its emphasis on light and movement. Artists like Claude Monet and Edgar Degas captured moments with vividness that influenced painters far beyond France's borders, encouraging a more spontaneous, personal approach to art.

Moreover, the Surrealist movement, spearheaded by French writer André Breton, opened new avenues for artists to explore the unconscious mind. This movement's impact is evident in the works of global artists who adopt surrealism's dream-like and fantastical elements, demonstrating the movement's enduring appeal.

Cinema, too, has felt the touch of French artistic sensibility. The French New Wave, a cinematic movement of the late 1950s and 1960s, introduced innovative storytelling techniques and visual styles that rejected traditional cinematic norms. Directors like Jean-Luc Godard and François Truffaut broke conventional narratives to focus more on character and auteur-driven perspectives, which have significantly influenced global filmmaking. Their techniques, from jump cuts to non-linear storytelling, continue to be foundational in both independent and mainstream cinema.

Fashion is another field in which French influence is unmistakable. Paris, often considered the fashion capital of the world, has been the launching pad for numerous groundbreaking designers such as Coco Chanel and Christian Dior. Their designs went beyond mere clothing, reflecting broader cultural themes and pioneering trends that dictated fashion worldwide. The elegance and innovation seen in French fashion have inspired designers globally, making an indelible mark on the industry.

Additionally, the French dedication to the culinary arts has also permeated global culture, encouraging a worldwide appreciation for gastronomy as a form of artistic expression. The meticulous preparation and presentation techniques championed by French chefs have elevated cooking to an art form, inspiring chefs around the world to treat their cuisine as a canvas for creativity.

Dr. Hind Louali, founder of French School of Austin - Ecole Jean-Jacques Rousseau, says that the French language and culture have been pivotal in shaping artistic expression across the globe. Whether through the poetic potential of the language, the groundbreaking techniques of its painters, the disruptive narratives of its filmmakers, or the trend-setting visions of its fashion designers, France has consistently fostered and exported a unique aesthetic and intellectual style. This cultural export has not only enriched global art forms but has also encouraged a continuous exchange of ideas and innovations, cementing French artistic traditions as central to the ongoing dialogue of global creativity.

#frenchschoolofaustin #education

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ekalman · 8 months ago

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Peer-graded Assignment: Getting Your Research Project Started

Good afternoon, dear reader,

For my Data Visualization course assessment I have chosen working on the dataset provided by GapMinder organization.

After looking at the code book and variables available I decided that I am particularly interested in income rate dependences. Simple questions to answer include the following:

Is higher oil per person associated with higher income per person? If not, how it can be explained?

Is longer life expectancy associated with higher income per person?

How the rates of general/female employment connected to the income rate per person in various countries?

For now I would like to concentrate more on the first question, but I suspect that there will be no linear correlation between oil and income per person. I checked the published articles and there was one that attracted my attention - Does oil drive income inequality? New panel evidence - ScienceDirect. It made me think to include policy score variable into my analysis as well, since average income cannot be a reliable variable if population inequality deepens. I'll need to create countries categorization based on policy score and it will be possible to additionally see the dependency between higher oil per person rate and worse policy scores.

As result, I'd like to determine if average income per person is dependent on oil per person rate taking policy score into consideration. Currently my assumption is that the average income grows with higher oil consumption, but the lower policy score is, the higher income inequality will be.

I prepared a partial code book for my further studies; it is attached below:

Best regards,

Evgenia

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study-with-aura · 3 months ago

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Monday, September 2, 2024

Today is a holiday, so I did not have ballet tonight. Instead, I decided to take a break and rest my body by gaming on a day I would not normally game. Because it's a holiday, I think it's okay. No one has school today, but seeing as I'm homeschooled, I usually don't take holidays except the usual breaks in the fall (Thanksgiving), winter (Christmas), and spring (Spring Break). It keeps me on track.

I cannot believe that it is already September. My family is doing the September studies course the person who writes my curriculum offers like we have the past few years. It gives us something to discuss as a family and focus on near the start of the school year. Even my brother joins us through video call, which is nice.

Have a great week everyone! I will try to be more active with posting than I was the last two weeks. My goal is two times a week, but I do enjoy posting daily too, if I am able to.

Tasks Completed:

Algebra 2 - Completed worksheet on applications of linear inequalities in two variables

American Literature - Copied vocabulary terms + read about transcendentalism + read about Nathaniel Hawthorne + read an article about "Young Goodman Brown" discussing the literary conventions and contexts + read "Young Goodman Brown" by Nathaniel Hawthorne + wrote a response to literature and emailed it to mom for grading (30/30) + worked on outline of reflective essay

Spanish 3 - Reviewed grammar page on adjectives and compound nouns + completed exercise + reviewed vocabulary

Bible 2 - Read 1 Kings 1:1-37

Early American History - Read an excerpt about where the Plymouth Colony settled and why + finished reading Plymouth Plantation Book 2 Chapter 1

Earth Science with Lab - Read about ocean trenches + read about the origin of trenches + completed short answer question explaining ocean trenches formation using Hydroplate Theory

Music Appreciation - Read about Gustav Mahler + listened to music excerpts on the pages + copied major necessary terms from the K section of the music dictionary

Khan Academy - Completed US History Unit 1 Test

Duolingo - Studied for approximately 30 minutes (Spanish + French + Chinese) + completed daily quests

Piano - Practiced for three hours in one hour split sessions

Reading - Read pages 126-160 of Missing Clarissa by Ripley Jones

Chores - Cleaned my bathroom + cleaned windows in my bedroom and in the study + took trash and recycling out

Activities of the Day:

September Study (John 14:1-2)

Personal Bible Study (Ephesians 4)

Gaming

Journal/Mindfulness

#study blog #study inspiration #study motivation #studyblr #studyblr community #study community #study-with-aura

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mathsminds · 8 months ago

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Feature of Math

Mathematics

Content of Mathematics

Course Overview:

This course aims to provide a comprehensive understanding of fundamental mathematical concepts and techniques. Through a combination of theory, problem-solving exercises, and practical applications, students will develop critical thinking skills and mathematical proficiency necessary for success in higher-level mathematics and related fields.

Module 1: Number Systems

Understanding the properties of real numbers

Integers, rational numbers, irrational numbers, and their properties

Introduction to complex numbers and their operations

Exploring number patterns and sequences

Module 2: Algebraic Expressions and Equations

Simplifying algebraic expressions

Solving linear and quadratic equations

Factoring polynomials and solving polynomial equations

Graphing linear and quadratic functions

Module 3: Functions and Relations

Understanding the concept of a function

Identifying types of functions: linear, quadratic, exponential, logarithmic, etc.

Analyzing graphs of functions and their transformations

Solving systems of linear equations and inequalities

Module 4: Geometry

Exploring geometric shapes and properties

Understanding angles, lines, and polygons

Calculating area, perimeter, and volume of geometric figures

Introduction to trigonometry: sine, cosine, tangent, and their applications

Module 5: Probability and Statistics

Understanding basic concepts of probability

Calculating probabilities of events and outcomes

Introduction to descriptive statistics: mean, median, mode, and range

Analyzing data sets and making statistical inferences

Module 6: Calculus

Introduction to limits and continuity

Understanding derivatives and their applications

Calculating rates of change and optimization problems

Introduction to integrals and their applications in finding area and volume

Module 7: Discrete Mathematics

Exploring combinatorics and counting principles

Introduction to sets, relations, and functions

Understanding logic and proof technique

Exploring graph theory and its applications

Module 8: Mathematical Modeling

Understanding the process of mathematical modeling

Formulating mathematical models for real-world problems

Analyzing and interpreting mathematical models

Evaluating the effectiveness and limitations of mathematical models

Module 9: Applications of Mathematics

Exploring interdisciplinary applications of mathematics in science, engineering, finance, and other fields

Case studies and real-world examples demonstrating the relevance of mathematical concepts

Ethical considerations and implications of mathematical applications

Module 10: Review and Final Assessment

Reviewing key concepts and techniques covered in the course

Solving comprehensive problem sets and practice exam

Final assessment covering all topics and skills learned throughout the course.

#mathematics #basic math

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walusa · 2 years ago

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Finance Major Is Crucial To Your Corporation. Learn Why!

bankrugby.com - Graduates of a Master in Accounting and Finance can normally discover careers with the government, in enterprise or in consulting. For instance, degree-seekers can examine healthcare finance and actual estate funding evaluation. Along with the Calculus I and Introduction to Probability and Statistics courses that their friends in different business packages take, these students will possible study Calculus II and III, Linear Algebra with Differential Equations, Applied Linear Regression, Fourier Analysis and Partial Differential Equations and Computers and Numerical Algorithms. The sphere attracts quality links from laptop science, statistics and applied mathematics. Taking a Masters diploma in Quantitative Finance prepares students for the broad market of high quality finance management that is dynamic. Some of these goals are not any poverty, zero starvation, good health and wellbeing, quality education, gender equality, clear water and sanitation, inexpensive and clear vitality, first rate work and financial progress, industry, innovation and infrastructure, reduced inequalities, sustainable cities and communities, strengthening international partnerships for the aim, among others. In relation to gender parity, finance is likely one of the final frontiers.

The Department of Finance, Insurance and Real Estate (FIR) on the University of Memphis is certainly one of six departments throughout the Fogelman College of Business & Economics which is the only business school in the Memphis space absolutely accredited by the prestigious AACSB. 1 college enterprise incubator on this planet, Rice University’s Finance M.B.A. It’s enriched by several challenge-based studying and networking opportunities such because the Rice Marketing strategy Competition, the world’s largest and richest scholar begin-up competitors. There’s a manner to combine business with pleasure at Rice University! Since our founding in 1935, Morgan Stanley has consistently delivered first-class business in a primary-class way. Getting a quote for finance task writing is a superb technique to keep away from the stress of completing a challenge your self. The course is grounded on the Project Management Institute’s Project Management Body of data (PMBOK®) rules. Pelletier additionally notes that 88 percent of Vermont adults imagine that guaranteed entry to a personal finance course for all Vermont high school students is urgently wanted. If you’re in search of a means for your college students to take a private finance course, try Edmentum’s course catalog.

It makes college students extra marketable all over the world. However, an internet MBA consists of extra normal enterprise programs, while a grasp's in finance focuses on sensible finance expertise. Indiana University’s Kelley School of Business offers a full-time Master of Science in Finance that combines a student��s nonbusiness education with cutting-edge industry expertise. Master of Finance, the science program of managing funds, builds on the principles of danger, time and cash and the way these interplay with each other. Columbia’s Master of Science in Financial Economics is a STEM-based program which takes two years to complete. Students within the monetary markets program observe mak-ing real strategic funding choices for the Bulldog Fund LLC (a inventory portfolio price over one million dollars) in the state-of-the-artwork Wells Fargo Financial Markets Lab. The Department of Finance gives a web-based Bachelor of Business Administration (BBA) degree in Finance with a focus in Business Finance with the primary objective to offer the essential concepts, principles and analytical tools essential for business selections in the fields of finance.

From the junior-yr Integrated Core Experience, probably the most rigorous business curriculums in the nation, college students take on their focus in their senior yr. A Master in Quantitative Finance degree will help college students in constructing dependable expertise whereas developing the finance theory. This system is designed to assist college students purchase the most effective expertise in trading, structuring, investing and evaluation or credit risks as well as developing markets. Department of Labor and the BLS to help you perceive the possible ranges of income throughout the finance sector. A private finance funds is data made up of your income and expenses and the extra correct this info is, the more seemingly you might be be able to fulfill your goals and notice your desires. Of all enrollees, 94% are awarded some form of monetary aid, so students ought to meet with a monetary help officer to debate whether they qualify for any funding alternatives. The sphere of examine comes with effective training of students in fixed earnings and derivatives as well as administration and hedging of the resulting markets. Margaret Reid, a professor of Home Economics at the identical university, is recognized as one of many pioneers in the study of shopper habits and Household habits.

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Xiong has published greater than 15 papers in scientific journals, together with Physical Review Letters, a prestigious world journal in physics. It's a usually aggressive program that focuses on advanced accounting and monetary management research, together with international accounting. UT-Austin’s McCombs School of Business affords a 10-month MS Finance program selectively open to college students from all academic backgrounds with no earlier work expertise. Students gain exposure to a lecture series, social interplay alternatives with industry leaders, and a high-profile Investment Banking program on Wall Street known as iBank. From our origins as a small Wall Street partnership to becoming a global firm of greater than 60,000 workers in the present day, Morgan Stanley has been committed to clients and communities for eighty five years. You may be essentially the most charismatic and impressive salesperson Wall Street has ever seen. However, many finance graduates may face problem find a place for themselves in an appropriate job. The SUNY College of Technology at Canton has a web based BBA in Finance degree program that boasts a 100% job placement price for graduates willing to relocate.

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sexytiime · 3 years ago

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Shulamith Firestone on Marx & Engels

From the first chapter of The Dialectic of Sex: The case for Feminist Revolution:

“ Before we can act to change a situation, however, we must know how it has arisen and evolved, and through what institutions it now operates. Engels’s ‘[We must] examine the historic succession of events from which the antagonism has sprung in order to discover in the conditions thus created the means of ending the conflict.’ For feminist revolution we shall need an analysis of the dynamics of sex war as comprehensive as the Marx-Engels analysis of class antagonism was for the economic revolution. More comprehensive. For we are dealing with a larger problem, with an oppression that goes back beyond recorded history to the animal kingdom itself.

In creating such an analysis we can learn a lot from Marx and Engels: not their literal opinions about women – about the condition of women as an oppressed class they know next to nothing, recognizing it only where it overlaps with economics – but rather their analytic method.

Marx and Engels outdid their socialist forerunners in that they developed a method of analysis which was both dialectical and materialist. The first in centuries to view history dialectically, they saw the world as process, a natural flux of action and reaction, of opposites yet inseparable and interpenetrating. Because they were able to perceive history as movie rather than as snapshot, they attempted to avoid falling into the stagnant ‘metaphysical’ view that had trapped so many other great minds. (This sort of analysis itself may be a product of the sex division, as discussed in Chapter 9.) They combined this view of the dynamic interplay of historical forces with a materialist one, that is, they attempted for the first time to put historical and cultural change on a real basis, to trace the development of economic classes to organic causes. By understanding thoroughly the mechanics of history, they hoped to show men how to master it.

Socialist thinkers prior to Marx and Engels, such as Fourier, Owen, and Bebel, had been able to do no more than moralize about existing social inequalities, positing an ideal world where class privilege and exploitation should not exist – in the same way that early feminist thinkers posited a world where male privilege and exploitation ought not exist – by mere virtue of good will. In both cases, because the early thinkers did not really understand how the social injustice had evolved, maintained itself, or could be eliminated, their ideas existed in a cultural vacuum, utopian. Marx and Engels, on the other hand, attempted a scientific approach to history. They traced the class conflict to its real economic origins, projecting an economic solution based on objective economic preconditions already present: the seizure by the proletariat of the means of production would lead to a communism in which government had withered away, no longer needed to repress the lower class for the sake of the higher. In the classless society the interests of every individual would be synonymous with those of the larger society.

But the doctrine of historical materialism, much as it was a brilliant advance over previous historical analysis, was not the complete answer, as later events bore out. For though Marx and Engels grounded their history in reality, it was only a partial reality. Here is Engels’s strictly economic definition of historical materialism from Socialism: Utopian or Scientific :

“Historical materialism is that view of the course of history which seeks the ultimate cause and the great moving power of all historical events in the economic development of society, in the changes of the modes of production and exchange, in the consequent division of society into distinct classes, and in the struggles of these classes against one another.” (Italics mine)

Further, he claims:

“...that all past history with the exception of the primitive stages was the history of class struggles; that these warring classes of society are always the products of the modes of production and exchange - in a word, of the economic conditions of their time; that the economic structure of society always furnishes the real basis, starting from which we can alone work out the ultimate explanation of the whole superstructure of juridical and political institutions as well as of the religious, philosophical, and other ideas of a given historical period.” (Italics mine)

It would be a mistake to attempt to explain the oppression of women according to this strictly economic interpretation. The class analysis is a beautiful piece of work, but limited: although correct in a linear sense, it does not go deep enough. There is a whole sexual substratum of the historical dialectic that Engels at times dimly perceives, but because he can see sexuality only through an economic filter, reducing everything to that, he is unable to evaluate it in its own right.

Engels did observe that the original division of labour was between man and woman for the purposes of child-breeding; that within the family the husband was the owner, the wife the means of production, the children the labour; and that reproduction of the human species was an important economic system distinct from the means of production.

But Engels has been given too much credit for these scattered recognitions of the oppression of women as a class. In fact he acknowledged the sexual class system only where it overlapped and illuminated his economic construct. Engels didn’t do so well even in this respect. But Marx was worse: there is a growing recognition of Marx’s bias against women (a cultual bias shared by Freud as well as all men of culture), dangerous if one attempts to squeeze feminism into an orthodox Marxist framework - freezing what were only incidental insights of Marx and Engels about sex class into dogma. Instead, we must enlarge historical materialism to include the strictly Marxian, in the same way that the physics of relativity did not invalidate Newtonian physics so much as it drew a circle around it, limiting its application - but only through comparison - to a smaller sphere. For an economic diagnosis traced to ownership of the means of production, even of the means of reproduction, does not explain everything. There is a level of reality that does not stem directly from economics.

The assumption that, beneath economics, reality is psychosexual is often rejected as ahistorical by those who accept a dialectical materialist view of history because it seems to land us back where Marx began: groping through a fog of utopian hypotheses, philosophical systems that might be right, that might be wrong (there is no way to tell), systems that explain concrete historical developments by a priori categories of thought; historical materialism, however, attempted to explain ‘knowing’ by ‘being’ and not vice versa.

But there is still an untried third alternative: we can attempt to develop a materialist view of history based on sex itself.

The early feminist theorists were to a materialist view of sex what Fourier, Bebel, and Owen were to a materialist view of class. By and large, feminist theory has been as inadequate as were the early feminists attempts to correct sexism. This was to be expected. The problem is so immense that, at first try, only the surface could be skimmed, the most blatant inequalities described. Simone de Beauvoir was the only one who came close to - who perhaps has done - the definitve analysis. Her profound work The Second Sex - which appeared as recenlty as the early fifties to a world convinced that feminism was dead - for the first time attempted to ground feminism in its historical base. Of all feminist theorists De Beauvoir is the most comprehensive and far-reaching, relating feminism to the best ideas in our culture.

It may be this virtue is also her one failing: she is almost too sophisticated, too knowledgeable. Where this becomes a weakness - and this is still certainly debatable - is in her rigidly existentialist interpretation of feminism (one wonders how much Sartre had to do with this). This, in view of the fact that all cultural systems, including existentialism, are themselves determined by the sex dualism. She says:

“Man never thinks of himself without thinking of the Other; he views the world under the sign of duality which is not in the first place sexual in character. But by being different from man, who sets himself up as the Same, it is naturally to the category of the Other that woman is consigned; the Other includes woman.” (Italics mine.)

Perhaps she has overshot her mark: Why postulate a fundamental Hegelian concept of Otherness as the final explanation - and then carefully document the biological and historical circumstances that have pushed the class ‘women’ into such a category - when one has never seriously considered the much simpler and more likely possibility that this fundamental dualism sprang from the sexual division itself? To posit a priori categories of thought and existence - ‘Otherness’, ‘Transcendance’, ‘Immanence’ - into which history then falls may not be necessary. Marx and Engels had discovered that these philosophical categories themselves grew out of history.

Before assuming such categories, let us first try to develop an analysis in which biology itself - procreation - is at the origin of the dualism. The immediate assumption of the layman that the unequal division of the sexes is ‘natural’ may be well-founded. We need not immediately look beyond this. Unlike economic class, sex class sprang directly from a biological reality: men and women were created different, and not equal. Although, as De Beauvoir points out, this difference of itself did not necessitate the development of a class system - the domination of one group by another - the reproductive functions of these differences did. The biological family is an inherently unequal power distribution. The need for power leading to the development of classes arises from the psychosexual formation of each individual according to this basic imbalance, rather than, as Freud, Norman O. Brown, and others have, once again over-shooting their mark, postulated some irreducivle conflict of Life against Death, Eros vs. Thanatos.

The biological family - the basic reproductive unit of male/female/infant, in whatever form of social organization - is charactereized by these fundamental - if not immutable - facts:

(1) That women throughout history before the advent of birth control were at the continual mercy of their biology - menstruation, menopause, and ‘female ills’, constant painful childbirth, wetnursing and care of infants, all of which made them dependent on males (whether brother, father, husband, lover, or clan, government, community-at-large) for physical survival.

(2) That human infants take an even longer time to grow up than animals, and thus are helpless and, for some short period at least, dependent on adults for physical survival.

(3) That a basic mother/child interdependency has existed in some form in every society, past or present, and thus has shaped the psychology of every mature female and every infant.

(4) That the natural reproductive difference between the sexes led directly to the first division of labor at the origins of class, as well as furnishing the paradigm of caste (discrimination based on biological characteristics).

These biological contingencies of the human family cannot be covered over with anthropological sophistries. Anyone observing animals mating, reproducing, and caring for their young will have a hard time accepting the ‘cultural relativity’ line. For no matter how many tribes in Oceania you can find where the connection of the father to fertility is not known, no matter how many matrilineages, no matter how many cases of sex-role reversal, male housewifery, or even empathic labour pains, these facts prove only one thing: the amazing flexibility of human nature. But human nature is adaptable to something, it is, yes, determined by its environmental conditions. And the biological family that we have described has existed everywhere throughout time. Even in matriarchies where woman’s fertility is worshipped, and the father’s role is unkown or unimportant, if perhaps not on the genetic father, there is still some dependence of the female and the infant on the male. And though it is true that the nuclear family is only a recent development, one which, as I shall attempt to show, only intensifies the psychological penalties of the biological family, though it is true that throughout history there have been many variations on this biological family, the contingencies I have described existed in all of them, causing specific psychosexual distortions in the human personality.

But to grant that the sexual imbalance of power is biologically based is not to lose our case. We are no longer just animals. And the kingdom of nature does not reign absolute. As Simone de Beauvoir herself admits:

“The theory of historical materialism has brought to light some important truths. Humanity is not an animal species, it is a historical reality. Human society is an antiphysis - in a sense it is against nature; it does not passively submit to the presence of nature but rather takes over the control of nature on its own behalf. This arrogation is not an inward, subjective operation; it is accomplished objectively in practical action.

Thus the ‘natural’ is not necessarily a ‘human’ value. Humanity has begun to transcend Nature: we can no longer justify the maintenance of a discriminatory sex class system on grounds of its origins in nature. Indeed, for pragmatic reasons alone it is beginning to look as though we must get rid of it.

The problem becomes political, demanding more than a comprehensive historical analysis, when one realizes that, though man is increasingly capable of freeing himself from the biological conditions that created his tyranny over women and children, he has little reason to want to give this tyranny up. As Engels said, in the context of economic revolution:

“It is the law of division of labour that lies at the basis of the division into classes. [Note that this division itslef grew out of a fundamental biologival division.] But this does not prevent the ruling class, once having the upper hand, from consolidating its power at the expense of the working class, from turning its social leadership into an intensified exploitation of the masses.”

Though the sex class system may have originated in fundamental biological conditions, this does not guarantee once the biological basis of their oppression has been swept away that women and children will be freed. On the contrary, the new technology, especially fertility control, may be used against them to reinforce the entrenched system of exploitation.

So that just as to assure elimination of economic classes requires the revolt of the underclass (the proletariat) and, in a temporary dictatorship, their seizure of the means of production, so to assure the elimination of sexual classes requires the revolt of the underclass (women) and the seizure of control of reproduction: not only the full restoration to women of ownership of their own bodies, but also their (temporary) seizure of control of human fertility - the new population biology as well as all the social institutions of child-bearing and child-rearing. And just as the end goal of socialist revolution was not only the elimination of the economic class privilege but of the economic class distinction itself, so the end goal of feminist revolution must be, unlike that of the first feminist movement, not just the elimination of male privilege but of the sex distinction itself: genital differences between human beings would no longer matter culturally. (A reversion to an unobstructed pansexuality - Freud’s ‘polymorphous perversity’ - would probably supersede hetero/homo/bi-sexuality.) The reproduction of the species by one sex for the benefit of both would be replaced by (at least the option of) artificial reproduction: children would be born to both sexes equally, or independently of either, however one chooses to look at it; the dependence of the child on the mother (and vice versa) would give way to a greatly shortened dependence on a small group of others in general, and any remaining inferiority to adults in physical strenth would be compensated for culturally. The division of labour would be ended by the elimination of labour all together (through cybernetics). The tyranny of the biological family would be broken.

And with it the psychology of power. As Engels claimed for strictly socialist revolution: ‘The existence of not simply this or that ruling class but of any ruling class at all [will have] become an obsolete anachronism.’ That socialism has never come near achieving this predicated goal is not only the result of unfulfilled or misfired economic preconditions, but also because the Marxian analysis itself was insufficient: it did not dig deep enough to the psychosexual roots of class. Marx was on to something more profound than he knew when he observed that the family contained within itself in embryo all the antagonisms that later develop on a wide scale within the society organization, the bioloigcal family - the vinculum through which the psychology of power can always be smuggled - the tapeworm of exploitation will never be annihilated. We shall need a sexual revolution much larger than - inclusive of - a socialist one to truly eradicate all class systems.

I have attempted to take the class analysis one step further to its roots in the biological division of the sexes. We have not thrown out the insights of the socialists; on the contrary, radical feminism can enlarge their analysis, granting it an even deeper basis in objective conditions and thereby explaining many of its insolubles. As a first step in this direction, and as the groundwork for our own analysis we shall expand Engels’s definition of historical materialism. Here is the same definition quoted above now rephrased to include the biological division of the sexes for the purpose of reproduction, which lies at the origins of class:

“Historical materialism is that view of the course of history which seeks the ultimate cause and the great moving power of all historic events in the dialectic of sex: the division of society into two distinct biological classes for procreative reproduction, and the struggles of these classes with one another; in the changes in the modes of marriage, reproduction, and child care created by these struggles; in the connected development of other physically-differentiated classes [castes]; and in the first division of labour based on sex which developed into the [economic-cultural] class system.”

And here is the cultural superstructure, as well as the economic one, traced not just back to economic class, but all the way back to sex:

All past history [note that we can now eliminate ‘with the exception of primitive stages’] was the history of class struggle. These warring classes of society are always the product of the modes of organization of the biological family unit for reproduction of the species, as well as of the strictly economic modes of production and exchange of goods and services. The sexual-reproductive organization of society always furnishes the real basis, starting from which we can alone work out the ultimate explanation of the whole superstructure of economic, juridical and political institutions as well as of the religious, philosophical and other ideas of a given historical period.

And now Engels’s projection of the results of a materialist approach to history is more realistic:

The whole sphere of the conditions of life which environ man and have hitherto ruled him now comes under the dominion and control of man who for the first time becomes the real conscious Lord of Nature, master of his own social organization.

“

#shulamith firestone #radical feminism #radfemsafe #terfs please touch #terfs please interact #marxism #engels feminism #marxist feminism

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girlwithouthands · 3 years ago

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Travellers arriving in an unfamiliar city used to worry that they’d climb in a taxi and be driven to their destination by the most circuitous route possible, racking up an enormous bill. That’s pretty much what Big Oil and its allies in government and the financial world are doing with the climate crisis—in fact, at this point, it’s the heart of the problem.

Yes, there are a few bitter-enders who refuse to acknowledge that change must come. Earlier in the summer, the Saudi Minister of Energy, Abdulaziz bin Salman, reportedly told a Bank of America gathering that “every molecule of hydrocarbon” will be drained from his country’s oil fields. But most fossil-fuel profiteers have learned to talk the talk. Jamie Dimon, the C.E.O. of JPMorgan Chase, for instance, has lent more money to the fossil-fuel industry than anyone else—but he was wise enough to say, in April, that “climate change and inequality are two of the critical issues of our time.” The bank has pledged that, by 2030, it will invest a trillion dollars in “green initiatives that boost renewable energy and clean technologies.” Does that mean one of America’s largest financial institutions is moving away from fossil fuels? Of course not. Last year, Chase once again topped the charts as Big Oil’s biggest financial lifeline. Indeed, earlier this month, DeSmogBlog released transcripts from an “energy capital conference” held earlier in the year. There, Chase’s managing director, Greg Determann, was asked by one expert if the company was “still going to be lending to oil and gas companies.” “For a long time,” Determann said, without hesitation. “Mr. Dimon is quite focussed on the industry. It’s a huge business for us and that’s going to be the case for decades to come.”

The same logic that governs companies often governs countries, too. As the veteran energy analyst Ketan Joshi pointed out, the Australian Prime Minister, Scott Morrison, has set the de-rigeur target of “net zero by 2050,” but, in April, indicated that “the trajectory to any net-zero outcome is not linear, and anyone who thinks it is I think doesn’t get it.” Morrison traced a curve in the air with his hand after he spoke, Joshi noted, “suggesting emissions reductions occur very late in the 30 years between now and 2050.” “What we are seeing here is a mumbled acknowledgement of the macro problem, but an aggressive refusal to consider the micro components that comprise it,” Joshi wrote. “It is the core engine of climate inaction.”

This is absolutely correct. We call it “greenwashing,” but that’s too technical a term. We should call it what it is: people with a vested interest are learning how to slow-walk this crisis. They’ve done it with a thousand other crises, too, of course—one thinks of how, following the Supreme Court’s ruling in Brown v. Board of Education, segregationists managed to delay action for a decade or more, focussing on a single phrase in the decision: “with all deliberate speed.” But here they’re doing it in the face of an absolute deadline imposed by science. As the United Nations’ Intergovernmental Panel on Climate Change has made clear, we must cut emissions in half by 2030 or our chances of meeting the targets that we set in Paris just six years ago fall by the wayside. Slow-walking is sabotage—smiling, and deadly.

And, in the course of that slow-walking, Big Oil is figuring out how to game the system in every way possible: as Inside Climate News recently reported, energy companies and their lobbyists are filling the infrastructure bill with billions of dollars for carbon-sequestration projects—essentially, getting taxpayers to fund equipment to capture the climate-destroying gases that Big Oil’s products emit. That’s absurd: it would be much cheaper to simply shut down those power plants and build out solar and wind power instead. But, for the fossil-fuel industry, preservation of the business model is paramount—they want to burn the stuff they own, no matter the consequences. The Biden Administration is caught in a very hard place: the White House is sincerely trying to accelerate climate action, but to do so it has to get past industry allies in the Democratic Party (Joe Manchin, for instance, who fears that we’re “going to the EV” too fast), not to mention a business-friendly judiciary, which has, for instance, blocked Biden’s plans to stop new drilling leases on federal lands. That’s why, one guesses, you get leaders who know better, like the domestic-climate czar, Gina McCarthy, repeating old bromides about “all of the above” energy supply, or ignoring the increasingly bitter protests over follies like the Line 3 tar-sands pipeline, which runs through Minnesota.

The eventual outcome is not in doubt: eventually, the planet will run on renewable energy. But how long that transition takes will determine what kind of shape we leave the planet in. At the moment, the bankers and politicians in the driver’s seat are taking us for a very long, very dangerous, and very expensive ride. We didn’t ask for Hell when we climbed in the cab, but that may well be where we end up, unless we figure out how to grab the wheel.

#climate change #x #Bill McKibben #anthropocene tag

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