**and communities of color. This

**legitimacy is then used to disenfranchise people****of people and communities of color."**

*erases the historical contributions*Is this for real? I'm reading a document (PDF) that purports to be the Seattle Public School's K-12 Math Ethnic Studies Framework. I'm seeing — at The American Conservative — "Woke Math In Seattle" by Rod Dreher, so I presume it is real.

I'm mostly worried about wasting kids' time with repetitious ethnic studies ideology, time that could be spent learning useful substance, like math. But maybe there are lots of kids who just won't learn math or have a horrible attitude about math because they see it as hostile territory, the domain of

*other*people. But what's the way to get over a negative orientation toward math? It's hard to believe that intensifying feelings of oppression and victimhood will stimulate positivity!

Are we capitalizing "smart" in Seattle now? Who gets to say what words are capitalized?Where does Power and Oppression show up in our math experiences?

● Who holds power in a mathematical classroom?

● Is there a place for power and authority in the math classroom?

● Who gets to say if an answer is right?

● What is the process for verifying the truth?

● Who is Smart? Who is not Smart?

● Can you recognize and name oppressive mathematical practices in your experience?

● Why/how does data-driven processes prevent liberation?

What is the process for assigning conceptions of bigness and smallness to letters and would you recognize it if it were oppressive?

Do you know the President of the United States "Uses Random Uppercase Letters" (NYT)?

He said he uppercases certain words for “emphasis” — not because they should, in fact, be capitalized.... Mr. Trump’s distinctive philosophy of capitalization has brought us Witch Hunt and Fake News, a big-B Border and Crime with a capital C....The Framers!

Experts say overcapitalization can be traced to the 17th and 18th centuries, when it was common to uppercase many significant words. In line with the times, the founding fathers used this style in the United States Constitution, said Kory Stamper, a lexicographer and the author of “Word by Word: The Secret Life of Dictionaries.”

Over the past several years, Ms. Stamper said, she has noticed that some people with conservative viewpoints have increasingly used frequent capitalization. “There is definitely a heavy tie to wanting to mimic the founding fathers, and they seem to have latched on to capitalization as the way to do it,” she said....Oh, really? What do the Ethnic Studies gurus have to say about That? "Rules"... "reason"... that might be oppressive and erasing. David Foster Wallace! Talk about a dead white male! But the New York Times is unlikely to see an ethnic studies dimension when the subject is Donald Trump is an Idiot.

Is it kosher to capitalize for emphasis? It depends, said Bryan A. Garner, a grammarian who is the author of “Garner’s Modern English Usage.”

Some acclaimed writers, such as David Foster Wallace, have used capitalization for emphasis in a way that many consider literary, he said. But, he said, the rules are there for a reason — and you have to know them in order to break them.

## 135 comments:

Who gets to say what words are capitalized?That’s the English, excuse me, Language Arts curriculum.

Progressivism dies in darkness.

I looked at the academic departments at Loyola Marymount University. I wanted to see what the Screenwriting major looked like. I was shocked at the number of “studies” departments. Not just Women and African American, but odd ones like Irish Studies. What a waste! But Screenwriting look good.

Q: Who gets to say whether this is all bullshit?

A: Not anyone is this class.

IIRC, from my high school German, all or many nouns are capped. Perbaps Trump's tendency is epigenetic.

Wow. We are truly living in the end times.

I guess all that talk about encouraging women and minorities to train for STEM jobs was just BS then. They can just keep becoming social workers and prison guards.

Yes it's real and it's been going on for some time now and it's not going to end until the bridges start collapsing. One of the things Jordan Peterson always pointed out is at the Western world was built on a competence hierarchy yet its destroyers claim it's built on a power hierarchy and so they seek only power destroying everything in their path and competence is thrown out the window. Actually, talking about competence or having competence is probably just white privilege at this point and whoever has it facing a Maoist struggle session from the Diversified. Things are going to start going bad at some point and white people are going to be the scapegoat. It's going to be open season on whitey.

Speaking of maff - I'm noticing (half caffeinated) that the MSM are ignoring Trump's huge rally in MN. The place was packed. The MSM are focusing on the anger and rage outside.

There are plenty of folks who are mathematicians who have helped create "woke" mathematics. There's a school of thought within mathematics that proofs only reflect the opinion or consensus of mathematicians, and that proofs have no objective truth value. They just reflect the power structure...

But I've never engaged any of them enough to know how far they take this. I'd be interested to talk about a famous and fundamental result, the proof of the infinitude of primes. It works like this:

Take all the prime numbers you know about, and multiply them by each other. Then add one.

The resulting number does not have any of your primes as a factor. So it either is prime itself, or it has prime factors not on your list. Either way, you know that there is at least one more prime number that you did not know.

And of course you can do this forever. So you can never have all the prime numbers, because you have a recipe for finding at least one more no matter how many you know about.

Is this idea really just a tool of the power structure? For literally thousands of years this idea has been examined, discussed, applied and extended. Which power structure was it intended to support? Athens? 18th century France? How is it so flexible and adaptable?

Leave it to the authoritarian left to make MATH bad.

The future belongs to manufactured progressive whiners and eternal victims. May your robot be with you.

So if I'm using a public school math curriculum to promote my silly religious world view -- I dunno, "How can we better understand God's perfect design for the world through mathematics," maybe -- it's completely unacceptable, but children in Seattle are compelled by law to sit through your silly religious world views about "power" and "oppression." Got it.

Maybe if we started emphasizing the contributions of Indian and Arab mathematicians, people would understand that there is no such thing as Western math.

Math, a 5000 year old system for examining the world around us, enhanced by the use of an 8th century treatise on the Hindu-Islamic base 10 numeric system with place holding zeros, is "too European".

And I seem to recall that pedestrian bridge collapse in Florida was the product of an engineering firm that had won awards for all the wimmin they were hiring.

Sidebar I can't help but say: my daughter is an aeronautical engineering student; her major is about 40% females and she says the majority of them are morons and/or are only there for the guys. Yay for the future!

I was exposed to three different math curricula in 6th grade. That didn't do me any good at all, and decades later I'm still pretty much useless in anything beyond very simple algebra.

This seems like an epic way to create a generation that will have my math problems for life.

As Whitney said - there's competence and there's power. It used to be competence took the lead, but the people pushing this idea are really only in it for the power, and damn the results. The kids will be screwed, but some academic's gonna get a good award for their "I Love Me" wall, and some mentions in papers and footnotes, and that's what's REALLY important, right?

Oh, Whitney - as far as bridges falling? Does this count?

https://miami.cbslocal.com/2018/03/15/bridge-collapses-florida-international-university/

Much touted for the 'diversity' of the design team, apparently they missed a few courses in material design and strengths under load...

It's important to remember that when the Left hears "merit", "competency", "credentials", what they understand that "someone powerful reached down, patted you on the head, gave you an A, and passed you to the next level". They believe that a physics PhD is awarded to people that other physics PhDs approve of and see as worthy to become one of them, NOT because anything in the dissertation is objectively true or has any sort of objective merit or because physics is of any use whatever in understanding the real world, it just reflects the power structure of physics.

Is it surprising that these ideas are entrenched in academia? Is it surprising that they believe that disparate impact is itself evidence of discrimination? Is it surprising that they believe schools have magic bricks that make students graduate and makes them educated?

How about this for power and oppression. Conquering armies steal a mathematical breakthrough made by indigenous people. They present it to the world as their own discovery and even name it after themselves. Outrageous? Or just the history of "arabic" numbers?

The struggle of "who gets to pick the right answer" is between those who can build a bridge and those who have a bridge to sell.

● Who holds power in a mathematical classroom?People who can do math

● Is there a place for power and authority in the math classroom?Yes, the power of the ability to do math, and the authority of the proof

● Who gets to say if an answer is right?People who know how to do math

● What is the process for verifying the truth?Proofs

● Who is Smart? Who is not Smart?People who can do math. People who can't do math

● Can you recognize and name oppressive mathematical practices in your experience?Reality is pretty oppressive when you can't do math

● Why/how does data-driven processes prevent liberation?Data drive process don't prevent liberation, the liberate you from subjectivity.

When a 1 identifies as a 4. From z to b, and a or C, selectively. Labels and judgment. Stop the hate.

Arithmetic supremacist? Semantic supremacist? Numbers and letters are rabid diversitists, pure indices and descriptors, respectively. 0s amd 1s, in particular, are cis-numbers correspond to male and female sex, masculine and feminine gender. A logical progression from the Chamber's reduction of a baby is a fetus is a colorful clump of cells, profitable parts, and carbon-based threat to green lawns and blue skies. Oh, and sentence diagrams are incontrovertible evidence of a grammar chauvinist. That said, welcome to the Twilight fringe.

It sounds like the Seattle Public Schools and the New York Times have finally broken. Their not-Smart power analysis and goofy ethnology are creating programs that can only be considered insane.

I can't wait for the empirical test of this nonsense.

Don't send your children to public schools. Know the curriculum of any private school to which you send them. Be careful of any college.

Creationism is less damaging than this nonsense.

Education is a sewer. We may move closer to the Grandkids to help the parents deprogram them from crap being pushed. That's what we had to do when our kids were in school.

As usual, Barbie was right.

Somebody tell them you can’t measure inequity without maths. That’ll slow them down a bit...

Progressivism dies in darkness.The natural state of liberalism (i.e. divergence) is dysfunction. That said, the products of progressive policy were recently uncovered, again, and again, and again, through improper carbon-based fetal sequestration, perhaps a whistleblower from the grave.

Q: Who is Smart?

A: Maxwell Smart, Agent 86.

Arithmetic! Algebra! Geometry! Grand trinity! Luminous triangle! He who has not known you is a dolt! - Lautreamont

Q: Who is Smart?

A: Maxwell Smart, Agent 86.

Funny how "western" mathematics, which works (almost magically) virtually everywhere in the universe, doesnt seem to work in Seattle.

Maybe that explains why Seattle itself doesn't work.

BTW, I'm setting up a trust fund to send my new granddaughter to a private school that will actually give her an education. I guess they call that privilege.

Are you sure that's not from the Babylon Bee?

This sounds like the defense offered by those who are unwilling or unable by those who are unwilling or unable to teach them.

Bring back "Math is hard" Barbie and add "Math is hard" Ken, Steven, and Christie.

Noam Chomsky designs the math curriculum. What could go wrong?

https://www.nationalreview.com/2017/10/math-racist-university-illinois-professor/

Can you recognize and name oppressive mathematical practices in your experience?Yes, happens to me every April 15th...

The educators seem to understand the concept of "lowest common denominator":

"The latest initiative started five years ago, when the School Board set 2018 as the deadline for significantly reducing the gaps in achievement among ethnic groups [the "gaps" increased], which a Stanford researcher recently pegged as some of the largest in the nation.

The district has since taken steps forward[sic], creating new racial equity teams at 41 schools and a committee that focused specifically on black boys, who traditionally[sic] score lower, on average, than other groups."

***

The eye-popping gap between white and Asian students in Seattle is shockingly small. I blame a lack of racism.

Yes it's real and it's been going on for some time now and it's not going to end until the bridges start collapsing.@whitney, what do you mean “start collapsing”? Go look up Florida International University. That bridge, designed by a woman-owner firm, collapsed under the weight of

just one person.You will learn to believe "2 + 2 = 5" and you will rejoice!

“Garner’s Modern English Usage.”

I know it's the guy's name but I still find it funny.

AA says: "I'm mostly worried about wasting kids' time with repetitious ethnic studies ideology, time that could be spent learning useful substance, like math."

I think about this all the time. African Americans comprise only about 13% of the U.S. population the last time I checked. So their representation in virtually every professional field or important industry is necessarily going to be very limited. However, if that's a problem, it's a problem made much, much worse by the fact that so many of the best and brightest black students go into these "studies" disciplines. The same applies to young women, of course, or any group whose champions lament that such group is not adequately represented in STEM, corporate boardrooms, the military high command, or whatever.

"too European".Almost all the math dreamed up by non-Europeans is covered in elementary school.

Math is the truth. Anyone can try as hard as they want to bend, mold, or taunt it - but in the end, math is the truth.

Beevis to Butthead (in math class): "I hate numbers- there's too many of them ! "

When the history of the collapse of America is written, I believe it will be traced back to the radical left's overtaking the education complex. I never understood why conservative, moderates and uninvolved allowed the progressives to control education.

My guess is most people think "they mean well."

Words fail. The people behind this insane woke education nonsense need to fired on the spot. It's child abuse.

● Who holds power in a mathematical classroom?

The people who actually understand mathematical processes and want to learn more. They have the power. You want some power...shut up and learn.

● Is there a place for power and authority in the math classroom?

Yes. Shut up and listen to the teacher and other students who are getting it.

● Who gets to say if an answer is right?

Duh! Math is math. The process is what proves the correct answer. If you have to even ask this question then you are not "Smart" with a capital S

● What is the process for verifying the truth?

You mean the correct math answer. Shut up and listen to the teacher and learn you giant dim bulb lump

● Who is Smart? Who is not Smart?

Smart people listen and learn the mathematical processes and also use Math in real life. Not Smart?? You are by asking these stupid questions that have no relationship the topic at hand which is MATH.

● Can you recognize and name oppressive mathematical practices in your experience?

No. Because math doesn't oppress. It is a scientific function. People oppress. Like you are doing now by taking time away from actual learning.

● Why/how does data-driven processes prevent liberation?

OMG. This is too stupid. I think I'll use some physics make some calculations and precisely lob cannon balls onto your office and stop this stupidity.

So in Seattle it’s possible that 2 + 2 really does equal 5. Apparently 1984 arrived 35 years

Cuz knowing arithmetic is so racist. Com'n, man.

Do people do these things anymore,

- count the change received

- balance checkbooks

- be able to estimate a percentage quickly, like for a tip

- do an estimate of the range of what the items in the grocery cart should total

Things are going to start going bad at some point and white people are going to be the scapegoat. It's going to be open season on whitey.Maybe the white people communities will have the only bridges that don't fall and the only houses with heat in winter. Why do they think all these "refugees" want to come here? The only kids that go to public schools will soon be the ones that have no furure.

Pants @ 7:50: Just so. And we used to be shocked at the Mao-praising Chinese schoolchildren and their little red books.

Just another rotten fruit from the stinking tree of progressive thought. I suppose it was inevitable once education began to focus on the self-esteem of pupils instead of their competence. Math is hard, as Barbie wisely observed. Harder for folks with shorter attention spans, lack of capacity for delayed gratification, and lower cognitive ability by traditional measures. So. Let's just wish reality away with another feel good program for the right ethnicities.

Well Michelle Obama certainly didn't need math to Bring Back Our Girls.

She just frowned and poof!, Our Girls appeared safe and secure from all harm, as the fella says.

So you take your math and you shove it.

That explains it: the damned Chinese and Indians must be using Eastern Math (which is probably even more patriarchal).

Good God, they seriously don’t believe this is racist as hell? Just one more excuse to push poorly-prepared and poorly-supported POCs and poor kids through the shitty school system as painlessly and unproductively as possible. Just one more example of the vicious exploitive contempt in which Progressives hold POCs.

Not Asians, natch. Well, not middle-class STEM Asians, natch.

● Why/how does data-driven processes prevent liberation?Reality itself is anti-liberation and thus racist. Neat.

A lot of people have pointed out the bridge collapsing in Florida and yes I did think about that. Here's another fun one. The Navy ship Fitzgerald disaster was because there were two women on watch that night that were having a bitch fight and they weren't speaking to each other.

I thought a lot of "Western" math was propounded by the Arabs, back when they were still capable. We use their numerals, including the zero they invented, and don't forget that Algebra is an Arabic word.

It's gonna be easy for some people to clean up in the developing idiocracy. The woke are creating a class society with the woke crowd on the bottom unable to support themselves and the sensible traditionally centered on top with real knowledge, skills, and capacity. Like today, the makers can always pose as woke, but you can't fake competence for long, and getting paid for nothing but wokeness will collapse of it's own dead weight. Don't blame us. Your coming oppression was a choice out of stupidity, lies, and sloth.

How about using "knowledge necessary to prosper as an adult in the United States" as an endpoint, and requiring that the school systems provide a set of paths to that. Anything that isn't a requirement for one of those paths can be an elective.

“There are some ideas so absurd that only an intellectual could believe them.” -- George Orwell.

The only cure for this posturing is mockery.

BTW, the foundations of mathematics have been explored (and their boundaries identified) by such as John von Neumann and Kurt Goedel.

This bimbo should go away and digest their work before piping up on this topic again.

Tcrosse

Zero was a Hindu invention.

This antimath movement is bound to appeal to all the math-averse reporters and lawyers!

A three-fer!

On the bright side: the kids who can't learn simple arithmetic won't be able to make heads or tails out of the new curriculum either.

@DBQ, I'm glad to see you here since I guess it means you have Power.

This Math topic conjures up the soft bigotry of low expectations to me. It's like 'the left' wants to give non-whites another thing to blame if they can't make it in math. Maybe it math were taught as an Arabic invention, Seattle would be more for it?

I thought a lot of "Western" math was propounded by the ArabsNope."Arabic numbers" came from India.

We're doomed.

"I'm mostly worried about wasting kids' time with repetitious ethnic studies ideology, time that could be spent learning useful substance, like math."

Schools have always been largely a waste of time.

Math is a handful of premises (some of which are considered self evident) combined with what we call "logic".

Those that attempt to label mathematics using political terms are profoundly ignorant and misguided. They see mathematics as a "white" thing. They have stumbled across the truth that mathematical knowledge is a form of power that is inaccessible to them. They don't think that is fair.

I DON’T CARE.

I do not drive across a bridge thinking about math history.

I just want the bridge not to fall when I’m on it.

The Egyptians built the pyramids. They weren’t stupid.

First, normalize lowered expectations, then cite the dysfunction as proof of rabid diversity. It's a wicked cycle of straw clowns posing as straw men for profit and democratic leverage.

I had not noticed PDJT's use or misuse of capitalization. I gather this is mainly in Tweets, which he supposedly types himself, right? Anything more formal is probably typed/edited by an assistant who would correct capitalizations.

It doesn't bother me much since I suffer from the same problem especially in things like comments where I may not go back and edit. When I do edit, I generally catch them.

I have always found the capitalization in the Constitution odd. For example:

We the

People of the United States, inOrder to form a more perfectUnion, establishJustice, insure domesticTranquility, provide for the common defence, promote the generalWelfare, and secure theBlessings ofLiberty to ourselves and ourPosterity, do ordain and establish this Constitution for the United States of America.And so on through the entire document. Bolding added.

I have never understood it since it seems almost random. If it is for emphasis, why is Blessings capitalized but not defence?

I've read other writings from that period, some by the same folks that wrote the Constitution and never noticed anything funky about capitalization. (It may have been edited by the time I read it)

So anyway, PDJT is trolling by purposely mis-capitalizing and when caught will say "I believe in the Constitution and the founding fathers. If random capitalization was good enough for them, it is good enough for me."

Sort of like the covfefe flap.

Unfortunately, Twitter is a gramatical and spelling cesspit and nobody notices his troll. Hence I would call it a failed troll.

John Henry

Article I (Article 1 - Legislative)

Section 1

All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives.

Section 2

1: The House of Representatives shall be composed of Members chosen every second Year by the People of the several States, and the Electors in each State shall have the Qualifications requisite for Electors of the most numerous Branch of the State Legislature.

I was just reading about Winston's father, Randolph Churchill, who served briefly as Chancellor of the Exchequer. Randolph complained about the drudgery of the office and about how hard it was to understand the significance of all those decimal dots and keep all those numbers straight. Math is hard, especially when you have tertiary syphilis or, more probably, a brain tumor. That, nonetheless, did not prevent someone with the proper breeding and connections from managing the budget. The British Empire at its zenith had a remarkable number of stupid people in responsible positions who performed their duties with aplomb and self assurance.

The son of a Duke could look beyond these little decimal points and see the big picture.....I've read that Artificial Intelligence has the edge over human intelligence not simply because AI is not subject to emotions and morality but because AI does not use logic in analyzing problems. The governing principle of the cosmos is random selection. Happenstance not math is the highest truth. We need to look beyond 2+2=4 to these higher truths. Boohoo. Some bridge fell down. What does that matter in the larger order of things.

Sounds like they're finally beginning to realize that there are things you can teach the white kids that you can't teach the black kids. Huh.

Who gets to say if an answer is right?Yeah, like my answers were wrong just because they were in base 7 instead of base 10. Elitist base tenners, trying to oppress me!

Question for any grammarians here:

All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives.Should "Congress", "Senate" and "House of Representatives" be capitalized here?

I could go either way but it occurs to me that while "the Senate" should be capitalized because it implies a specific senate, "a senate" should not be.

(Too much time on my hands today trying to avoid getting started writing)

John Henry

I was taught in high school that until we got the concept of zero from the Arabs, western mathematical advancement was at a dead end. Lot’s of non western mathematicians have made significant contributions to math.

This is particularly distressing to me because I grew up in a very poor area, eating government powdered eggs and powdered milk and canned chicken(yum!) and didn’t know anybody in my personal life who had ever gone to college, and the only way I managed to escape it was that I had the ability to do math. Why cut off that route out for other people?

"What is the process for verifying the truth?”

That’s a great topic, it kind of obviates the rest.

Do they also go to the playground and apply these constructs to kids playing basketball? Why is this guy six foot four? Why does this guy have the uncanny ability to sink three pointers? Why can this guy dunk a basketball when these other guys can’t?

Let’s go down to the music department. Why does this girl play the violin like a rusty saw, and this girl play it so beautifully? Why can this boy play the trumpet like a jazz musician, and this guy can barely play a C major scale?

Summon the Handicapper General! I thought that

Harrison Bergeronwas supposed to be satire!@DBQ, I'm glad to see you here since I guess it means you have Power.Yes. Understanding math gives you the Power!! Power to not be ripped off of bamboozled.

Example: Went to Costco the other day and because we spend a lot there at a time (usually over $300 to $400), we get pulled aside (flagged) at the check out stand to be pitched into upgrading to an Executive status. For a "mere" $120 a year membership we can get all sorts of

benefits that we will never use. Instead of the $60 we pay now.PLUS...2% back on our purchases and just THINK that would pay us back for the membership. We asked...how much have we spent so far this membership year? (since June) Because we really don't keep track and it was a bit over $1500.

Doing some quick MATH in my head, I said..."So about $30 back so far. We would have to spend $6000 dollars a year just to break even. I don't see the benefit to me. No thanks."

The sales person looked at me like I just grew 2 heads. Math is Haaaard!!!

Not a big deal or a lot of money going for $60 to $120. Or a 100% increase in my fees. BUT a really sweet deal for Costco because they get a 100% increase in fee income and very very few people will actually reach the threshold of spending to get their money back. And they will buy more to try to reach the goal. Win win for Costco.

Math can save you from being bamboozled.

As I re-read

Atlas Shrugged, I'm finding even more application to today's scene than to that of the 60's when I first read it. Enforced mediocracy in the guise of public good and the conceit of academia.@MadMan, "soft bigotry of low expectations" indeed! In the 21st century people who can't handle logic and reason from 2+2 to 4 are going to be poor, and poor people will vote for whoever can promise them free Obamaphones and whatnot. It's a scam.

Maf bees HAR!

It's real.

https://www.k12.wa.us/sites/default/files/public/socialstudies/pubdocs/Math%20SDS%20ES%20Framework.pdf

This is entirely consistent. Mathematics is a way to understand the objectively real world. The woke hate that world and, as such, hate mathematics.

Feelings! Nothing more than feelings. But how can you hold onto feelings in the face of...numbers. Numbers make you go numb, that's why they're called numbers.

“It's important to remember that when the Left hears "merit", "competency", "credentials", what they understand that "someone powerful reached down, patted you on the head, gave you an A, and passed you to the next level". They believe that a physics PhD is awarded to people that other physics PhDs approve of and see as worthy to become one of them, NOT because anything in the dissertation is objectively true or has any sort of objective merit or because physics is of any use whatever in understanding the real world, it just reflects the power structure of physics.”

Let me state up front my biases - at least 3rd of at least 4 generations of math or engineering degrees (grandfather a chemical engineer and artillery officer, his sister a MA in math from Columbia in 1925, my kid with BS in physics and math, PhD in engineering). Of the five in my generation, two had math degrees, and two were in engineering. So, we grow up doing and thinking regular math. I had my kid doing derivatives in middle school. Etc.

That said, graduate schools are far from being immune from politics. It’s fairly well known that pro AGW gets most federal funding, and most STEM PhDs are funded by research. This means that far more pro AGW dissertations are done and accepted than anti AGW dissertations. Then in another instance, friend was a 4th year ABD grad student, his advisor was run out of the school, and no one stepped in to pick him up. His choice was to follow his advisor, along with wife and two kids, or drop it. He dropped it. Finally, another friend is working in physics for his 4th doctorate. His advisor doesn’t understand his topic well enough to mentor him, and is talking about dropping him, and, again, no matter he is stepping in from his dept to take over. If his theory is true, it would disrupt a part of physics, and he is finding it hard to find a new advisor. We are desperately trying to find him some physicists smart enough to either tell him what he is wrong, or explain to others why his theory is plausible. He really is that smart, and it has to be remembered that the average IQ for PhDs is very close to that of most other doctorates (MD, JD, DDS, etc), about one standard deviation above the population mean. That means that a distinct majority of PhDs don’t qualify as geniuses. Average PhD is as mediocre as the average lawyer, and we know there are plenty of those.

Also, there is a good argument to be made that we are still teaching Sputnik era mathematics, trying to close a science gap with the Soviets. Which was probably not going to happen, since Russians tend to be some of the best mathematicians in the world. Luckily for us, they were not nearly as good in engineering (true story - at one job, our company had a half dozen design labs around the world. The patent disclosures from our Russian labs were essentially esoteric equations and the like. I had to tell them that that wasn’t patentable, except maybe in Russia, and to come back when they could find and explain a use for the equation). In any case, that fear caused a reorientation of math curriculum towards preparing everyone for college math, science, and engineering. Apparently “white” math in middle and high school is still often taught with an AGA “sandwich” - Algebra, Geometry, then more Algebra. My partner, to this day, thinks her math curriculum in middle and high schools was silly. She still, despite now being eligible for Medicare, sees no use for either subject. Learned them to get As, then promptly forgot them, as neither subject had any use in her life. And, for much of the country, that remains true. It is mostly those of us who end up in STEM who use it, and needed that training as a fundamental tool. It has been suggested that maybe K-12 math, or maybe at least 6-12 math for the masses be oriented more towards understanding the mountains of data that we now encounter in daily life. Arithmetic is good. So is balancing a checkbook. But neither needs Algebra or Geometry (or, Calculus, etc). Despite coming from a family that excels in this sort of math, I am at least willing to look at changing how math is taught in school for the masses.

Big Mike said...

...Apparently 1984 arrived 35 years...Or 34 years. Or 37 years. Or 139 years. I mean really, who's to say?

"the domain of other people"

Considering that few blacks have made any contributions to mathematics, that sentiment would be correct.

I actually sympathize with the woke attack a little bit: much math ed is a kind of repetitive intelligence test, using a subject that for the majority of students has little meaning beyond basic algebra and geometry.

And a question for our (retired) conlaw professor:

Is there any legal significance to the capitalization in the Constitution? Is there any legal point that might hang on whether a particular word is capitalized or not

John Henry

Blogger whitney said...

The Navy ship Fitzgerald disaster was because there were two women on watch that night that were having a bitch fight and they weren't speaking to each other.And Karen Hultgren was murdered by the Navy brass when they made her a Naval Aviator, put her in a plane she was not really qualified to fly, and required her to make a carrier landing that she was not really qualified to do. Or at least attempt a landing she was not qualified to do. She died trying.

Affirmative action murdered her.

John Henry

Speaking of post-modernism, remember that great old Stones album, "After Math"?

With those math songs "It's Not Easy (doing math on your own)", "Stupid Girl (can't do math)".

Jaime Escalante is rolling over in his grave.

Who gets to define what an oppressive practice is? I propose letting Rush Limbaugh make all those decisions. Prove to me that you are more qualified than is he for this job. What are going to use -- academic credentials? (Academic credentials awarded to you by the white supremacist patriarchy, I mean.)

About our numberals (including zero) and the Arabs: The Arabic cultures were pretty good caretakers through the middle ages of things they picked up from cultures that came before them. They helped preserve the learning of the Greeks (after also contributing to forcing that learning underground by, for instance, sacking the great Library at Alexandria). The Greeks had a terrible number system -- didn't use place value. So the Arabs adapted the reasoning of the Greeks to the much better numeral system they had picked up in India. The official name of our system is "Hindu-Arabic".

By the way, you don't really *need* a zero if you're not using place value. Zero is simply the symbol you put in a column to indicate there is nothing there. Without it, 302 and 32 would be difficult to distinguish. (That was actually a problem the Babylonians had faced -- they had a place value base 60 system with no zero!)

"... wasting kids' time with repetitious ethnic studies ideology..."

Sure, wasted time is the problem. Of course K-12 is a LOT of time.

But maybe there are lots of kids who just won't learn math or have a horrible attitude about math because they see it as hostile territory, the domain of other people

Then they are racist pigs, and the proper response is to tell them to drop the racism and grow up.

Stop rewarding ignorance and evil

Blogger Susan said...

The struggle of "who gets to pick the right answer" is between those who can build a bridge and those who have a bridge to sell.

I'm going to steal that

Those questions seem pretty easy to me . . . are these trick questions?

● Who holds power in a mathematical classroom?People who can do math

● Is there a place for power and authority in the math classroom?Yes, because it is impossible to study when students are being disruptive.

● Who gets to say if an answer is right?Whoever can prove it.

● What is the process for verifying the truth?I always liked proofs by contradiction, but induction works too I guess.

● Who is Smart? Who is not Smart?People who can do algebra are Smart. People who can't aren't people.

● Can you recognize and name oppressive mathematical practices in your experience?I am morally opposed to use of the Jacobian. Or maybe Jacobins? Same difference.

● Why/how does data-driven processes prevent liberation?Data helps disprove theories when they are wrong.

she says the majority of them are morons and/or are only there for the guysSupport for the moron theory: If you're looking for men college isn't a target rich environment. You'd better have a lot to offer to the few men that are there.

Jaime Escalante is rolling over in his grave.He must have been a WHITE Hispanic.

@Balfegor, here's some proof by induction for you.

Is this for real?How, after all these years of exposure to Post-Modernism can Prof Althouse wonder if this is "for real"?

I posted this some time ago in this forum, and it deserves a re-post now:

The modern "mendacious" Left that we struggle with here each day (the media, academia, activists, etc) are Post-Modern Lefties. Epistemologically, they do not believe, especially as concerns social phenomena, that there exists any such thing as "objective" truth. There are only competing subjective viewpoints, viewpoints mediated by language & subjective experience. These subjective viewpoints linguistically develop & cluster into "discourses". Whoever propogates the discourse that crowds out the others wins, and that discourse is called "True".

For the rest of us who are conservative, libertarian, or classical liberals, we tend to come out of the philosophical traditions of Natural Law or out of the Enlightenment, and we tend to believe that language is simply an instrument that we use to communicate about an objective reality "out there" to which we all have epistemological access. We see situations, even social situations, as having foundational facts, beyond dispute after examination. The PoMos don't.

Mathematics is simply one more white, hetero-normative discourse for the PoMos. It has no more relation to "Reality" than any other discourse does, which is to say, possibly none.

You guys really need to read up on Post-modernism as a philosophy/ideology. 'Cause, once you know what to look for, you see that its tendrils are everywhere.

@Skylark:

I was taught in high school that until we got the concept of zero from the Arabs, western mathematical advancement was at a dead end.You were lied to.

I thought a lot of “Western” math was propounded by the Arabs, back when they were still capable. We use their numerals, including the zero they invented, and don't forget that Algebra is an Arabic word.There's some truth to that, in spirit at least, but the statement also includes much that's not so.

The term “algebra,” for instance, is indeed a word invented by “the Arabs” — mathematical writer al-Khwarizmi (c. 780–c. 850), who wrote in Arabic (whose very name is the origin of the English word “algorithm”) — but his term “algebra” (or

al-jabras he wrote it) prior to that verbal innovation apparently wasn't an Arabic word.More significantly, algebra (the mathematical topic, not the word) itself greatly predates Islamic civilization: there was considerable progress toward what we now call algebra during Babylonian times [!], for instance (during the early 2nd millennium BC) — while the “Father of Algebra” so-called (in modern mathematical historical parlance) was a Greek — Diophantes, who lived and flourished in Alexandria during the 3rd century AD (i.e., classical Roman times), still nearly half a millennium before Mohammed.

As for the system of numeration often termed “Arabic numerals,” which we today are perhaps likelier to call “decimals” or “base 10” (ten) notation, those so-called “Arabic” numerals were invented not by “the Arabs” but by Hindus — the system was basically popularized by mathematician Brahmagupta, who lived and worked (c. 598–c. 668) in what's now southwestern India.

Almost two centuries later Brahmagupta's book was read by that same Al-Khwarizmi in Baghdad — who subsequently re-popularized the base-10 system all over the Islamic (and Western) world. Note that Al-Khwarizmi did not claim the decimal system — its Hindu origin was assumed — but over time the little detail that it actually originated in India got mostly overlooked, and the base-10 numerals became known across Europe simply as Al-Khwarizmi's (eventually the “algorismi” then “algorism” then “algorithm”) system of computation.

Note that this “base 10” system as it was transmitted from the Hindus through the Arabs, and indeed as it initially arrived in the attention of the West (before the turn of the 2nd millennium AD), consisted of

ninesymbols only — there wasno(column placeholding)zero. Where did the zero come from? All we know is that sometime later (after the year 1000 AD from the viewpoint of the West), someone unknown added a zero symbol to the “decimal” system. It could have been an Arab mathematician, it could have been a Greek, nobody knows.It's pertinent in this regard that

thousands of yearsbefore the base-10 “decimal” system first appeared on the scene (during the late 1st millennium AD), already extant was the originally Babylonian, base-60 “sexagesimal” numbering system: which was extensively employed for millennia (from long before Ptolemy to after Copernicus) by scientists and mathematicians throughout the West and also Islam whenever they needed to perform complex computations.Note that a (placeholding) zero symbol got added to the

sexagesimalsystem more than1,000 yearsbefore Mohammed. It also so happens that the decimal (“Arabic numerals”) zero after it got added to that system bears a suspiciously close (nearly identical) graphical resemblance to the far older sexagesimal zero.The upshot is that, with few exceptions (al-Kashi in the 15th century AD, for instance), “the Arabs” had little to do with

improvingthe decimal system beyond simply transmitting the base-10 numerals they received (+ 0) on to the West.{Continued on the next page: page 2}

{Continued from previous page; page 2}

Getting back to the topic of algebra, what al-Khwarizmi's contribution in history

waswas as an effective popularizer ofelementaryalgebra. For that considerable service it's arguable perhaps that he deserves the epithet “father of algebra,” in lieu of the earlier Greek Diophantes.Mathematical historian Carl B. Boyer evaluates al-Khwarizmi's contribution to algebra in his intriguing

History of Mathematics: [quoting…]In two respects the work of al-Khwarizmi represented a retrogression from that of Diophantus. First, it is on a far more elementary level than that found in the Diophantine problems and, second, the algebra of al-Khwarizmi is thoroughly rhetorical, with none of the syncopation found in Diophantes'

Arithmeticaor in Brahmagupta's work. Even numbers were written out in words rather than symbols! […]Nevertheless, al-Khwarizmi's

Al-jabrcomes closer to the elementary algebra of today than the works of either Diophantus or Brahmagupta, for the book is not concerned with difficult problems in indeterminate analysis but with a straightforward and elementary exposition of the solution of equations, especially of the second degree.The Arabs in general loved a good clear argument from premise to conclusion, as well as systematic organization — respects in which neither Diophantus nor the Hindus excelled. The Hindus were strong in association and analogy, in intuition and an aesthetic and imaginative flair, whereas the Arabs were more practical-minded and down-to-earth in their approach to mathematics.

[/unQuote]

Historian Boyer goes on to assess the overall contribution of Arabic civilization to the science of mathematics thusly: [quoting…]

Arabic mathematics can with some propriety be divided into four parts: (1) an arithmetic presumably derived from India and based on the principle of position [i.e., decimal notation]; (2) an algebra which, although from Greek, Hindu, and Babylonian sources, nevertheless in Muslim hands assumed a characteristically new and systematic form; (3) a trigonometry the substance of which came chiefly from Greece but to which the Arabs applied the Hindu form and added new functions and formulas; and (4) a geometry which came from Greece but to which the Arabs contributed generalizations here and there. […]

In connection with (4), there was a significant contribution about a century after Alhazen by a man who in the East is known as a scientist but whom the West recalls as one of the greatest Persian poets. Omar Khayyam (ca. 1050–1123), the “tent-maker,” wrote an

Algebrathat went beyond that of al-Khwarizmi to include equations of the third degree. […]It is sometimes held that the Arabs had done little more than to put Greek science into “cold storage” until Europe was ready to accept it. But the account in this chapter has shown that at least in the case of mathematics the tradition handed over to the Latin world in the twelfth and thirteenth centuries was richer than that with which the unlettered Arabic conquerors had come into contact in the seventh century.

[/unQuote]

____

(Carl B. Boyer,

A History of Mathematics, Second Edition, John Wiley & Sons, 1989, pp. 228, 240-241, 245)____

Ah, but my Computations, People say, Have squared the Year to human Compass, eh? If so, by striking from the Calendar Unborn To-morrow, and dead Yesterday.

Omar Khayyam (

Rubaiyatin the FitzGerald version)By the way, you don't really *need* a zero if you're not using place value. Zero is simply the symbol you put in a column to indicate there is nothing there. Without it, 302 and 32 would be difficult to distinguish. (That was actually a problem the Babylonians had faced — they had a place value base 60 system with no zero!)Mostly true, but incorrect as far as the Babylonians' sexagesimal system is concerned: a placeholding zero symbol was added to that system during about the 4th century BC (that is: more than a millennium before Mohammed and the beginning of Arabic civilization).

One might note, too, that even during the millennium and a half

precedingthat creative 4th century BC event — across all of which earlier centuries sexagesimals possessednozero — even then they still seldom needed one (which is probably why it took so long to add the zero): because base-60 columns inherently turn up containing a zero only 1/6th as often as do base-10 columns — plus, since it's base-60, you need far fewer columns!We see this principle demonstrated, for instance, in the computation of 2π that late medieval Arabic mathematician al-Kashi performed whereby in 1436 AD he computed 2π to the same (huge) degree of precision using both decimals and sexagesimals. Notice that the sexagesimal version (which is to 16 places in decimal!) in sexagesimal requires

zerozero symbols:2π = 6.2831853071795865 (decimal)

2π = 6;16,59,28,34,51,46,15,50 (sexagesimal*)

(*A semicolon marks the sexagesimal point; comma separated decimals indicate separate digits of the base-60 sexagesimal fraction.)

This was really the first moment in history when decimals began to equal the computational capabilities which sexagesimals had possessed for millennia. Only after that (really, after western mathematicians accomplished the same thing as al-Kashi) did decimals begin to displace sexagesimals for use in scientific computation.

My daughter's math teacher is from India. I tell my daughter to make sure she does all her homework, because the Indians invented zero, and the teacher isn't shy about handing them out. But now I realize that the Indians are just oppressing my blond haired, blue eyed girl.

People who can't [do algebra] aren't people.True!

The Volokh Conspiracy

Sterilization of the “intellectually disabled”

Data helps disprove theories when they are wrong.If the data are sound.

It's important to remember that when the Left hears "merit", "competency", "credentials", what they understand that "someone powerful reached down, patted you on the head, gave you an A, and passed you to the next level".Stupid people don't accept the idea of merit because they aren't smart enough to understand what smart people understand. Thus they think people held out as smarter are just better at claiming to be smart.

Dunning Kruger

There are two different kinds of zero that need to be considered here. First, is the empty-column placeholding symbol kind of zero useful really only in a positional numbering system such as decimals, or sexagesimals, or vigesimals (Maya numbering) — which is what we've been talking about up-thread. This concept was not invented by Indians/Hindus, but rather by Babylonians (as I note up-thread, around the 4th century BC). The newfangled decimal zero (at least from its close graphical similarity) appears to have simply copied the sexagesimal zero.

However, there's also the concept of the

numberzero — that is, the integer 1 less than 1. That concept of zero has an independent existence and (contrary to our unimaginative imaginings) not necessarily obvious connection with the positional-system placeholding zero. Certainly the connection appears to not to have occurred to Brahmagupta (mentioned up-thread), who invented the idea of the number zero, described the modifications to arithmetic needed to get it to work (also inventing negative numbers and their arithmetic) — all without going on to create aplaceholdingzero for the new decimal (“Arabic numerals” not) system that he also knew about and even popularized!@Rick:

Thus they think people held out as smarter are just better at claiming to be smart.I'd put it as, they think "smart" is

definedby the award of a stamp saying "smart". They think that the stamp--the degree, credential, whatever--has nothing whatever to say about what a person knows or can do other than that someone conferred upon them a stamp. The stamp is not "for" anything but the approval of the stamp-awarder.To most of us commenting here, if someone who knows no physics is given an physics degree, that is wrong. The stamp was awarded in error or unjustly. If someone who knows physics fulfills the requirements and is denied an physics degree, that is wrong. The stamp was withheld in error or unjustly.

To the left, if an oppressed minority is denied the stamp for any reason, that is an injustice, it is a mechanism of oppression. Physicists are not letting someone in their club because they don't want to share.

In other words, they think exactly as the Scarecrow did when Oz gave him a diploma or the Woodman when Oz gave him a heart. The Scarecrow thought the award of the diploma

made him able to thinkand the Woodman though the heartmade him feel. But the Scarecrow of course had been thinking and the Woodman had always had feelings.I would hazard a guess that this is not in the curricula of the private schools where the people approving this send their children/grandchildren. On the other hand, considering the gibberish of which new consists, the kids may not be worse off.

Doing some quick MATH in my head, I said..."So about $30 back so far. We would have to spend $6000 dollars a year just to break even. I don't see the benefit to me. No thanks."

Except, since you are already paying $60, you would only be paying an additional $60, so you would only need to get $60 back to break even, which means you would only need to spend $3000 at 2%. But if you've only spent $1500 by October, you probably aren't going to spend even $3000 this year, unless you do a lot of Christmas shopping at CostCo.

"● Who gets to say if an answer is right?"Oh mein Gott.

Seattle's ethnic studies task force wants to integrate identity politics into all subjects. http://bit.ly/2pnu4vP

I suspect math teachers will spend an extra two minutes telling kids that the 0 and algebra have a non-European origin. Perhaps they'll have more examples of how to use math to solve problems more "real world" than calculating the progress of that poor guy rowing against the current. (I spent my school years wondering why he didn't row with the current.)

We can tell students that it's OK for black people to do math because math isn't "white." (Where I live, in California, white kids think math is Asian.) But I think it's more useful to explain that learning to do math is not contingent on racial or ethnic origin. Anyone, even Barbie, can learn math if they're willing to work at it.

My husband's grandfather was a barrel maker from Calabria, the descendant of poor, uneducated peasants. His children didn't go to college, but most of their children and grandchildren (male and female) are engineers, and most of the rest are in other math-centric fields. They were taught math in school.

No matter who invented Math, and we have established that it was not White People, to rationalize being bad at it due to institutional racism smacks of Sour Grapes.

@GRW3:

I would hazard a guess that this is not in the curricula of the private schools where the people approving this send their children/grandchildren.You'd be wrong. You don't think there's woke math at Sidwell Friends where the Obamas sent their kids and the Clintons sent Chelsea?

Who credentials and trains the private school teachers? The universities that generate and propagate these ideas that people like Clintons and Obamas believe.

You CAN find private schools that teach things traditionally of course, in some places, at some price points. But the folks who believe this, they WANT the woke curriculum for their kids. They DEMAND it.

Balfegor is oppressing me! Make him stop!

I've forgotten what the jacobian is, though I swear I did know at one time. A square matrix was involved. Beyond that it is a bit foggy.

But if he's opposed to the jacobian, then so am I. Whatever it is.

Joanne Jacobs: Your husband should not sell his ancestors short. Certainly, if you don't put enough staves into the barrel, it will leak. Math can help prevent this.

“What is the process for verifying the truth?”

The field of mathematics has a procedure, called a

proof, whereby the truth of a statement may be verified.When I was studying math I always liked proof by induction ... but that’s just me.

"The modern "mendacious" Left that we struggle with here each day (the media, academia, activists, etc) are Post-Modern Lefties. Epistemologically, they do not believe, especially as concerns social phenomena, that there exists any such thing as "objective" truth."

I think you give them way too much credit. They don't believe anything so ethereal as all that, they are just lying scum who will advance any claim that might help them get their way. But they can do arithmentic perfectly well when there is money involved.

Joanne says:

(I spent my school years wondering why he didn't row with the current.)

My theory is that he probably wasn't headed downstream. ;-) Having rowed--and paddled--upstream more than a few times I can sympathize.

Data helps disprove theories when they are wrong.

-If the data are sound.

- And the analysis is right.

Narr

The science is settled: there's no connection between occupation or social status of ancestors and mathematical--or any other--ability, talent, or skill.

Me

Doing some quick MATH in my head, I said..."So about $30 back so far. We would have to spend $6000 dollars a year just to break even. I don't see the benefit to me. No thanks."Jupiter: Except, since you are already paying $60, you would only be paying an additional $60, so you would only need to get $60 back to break even, which means you would only need to spend $3000 at 2%. But if you've only spent $1500 by October, you probably aren't going to spend even $3000 this year, unless you do a lot of Christmas shopping at CostCo.

True, however, I was responding to the idea that if I increased my fees by 100%, in order to get all the money back by the end if the "MEMBERSHIP YEAR" which began in June of 2019 and ends in May 2020 I would have to spend a total of $6000 to recoup $120 by next May.

June, July, August, Sept....that is 3 months of a Membership year; in which we had already spent a little over $1500....not including the $380 we just spent.

I would then next year (June to May) also need to spend $6000 for a measly 2% return to get my investment back. Not a good deal, especially when the rest of the fabulous benefits are something that I won't use or not likely to want. Not a totally bad deal but why sink and extra $60 bucks that I am not going to get back.

If they were offering me 2% on my existing fee of $60...maybe a deal and easily will easily break even at the end of the MEMBERSHIP year.

But that isn't their aim. They just want to increase their fee income by 100% and also get suckers (I mean customers) to step up their spending. NTTIAWWWT :-)

Math really is hard.

Re: Phidippus:

Now you're making me wish I had named something actually oppressive, like quaternions, instead of going for the pun . . .

@Jupiter,

I think you give them way too much credit. They don't believe anything so ethereal as all that, they are just lying scum who will advance any claim that might help them get their way. But they can do arithmentic perfectly well when there is money involved.Even liars justify their lies to themselves somehow. Post-Modernism can be very useful that way.

Ideologies exist not only the minds of the true believers who can articulate their premises, but also as the foundational assumptions that guide the day to day life of ordinary people. Post-modernism has been around for a long time, and it's had time to move outside of academia into the broader life-world.

Without a knowledge of Post-Modernism, it is impossible to understand the ideology that drives the modern Western Left. The Right tends to think it's some form of Marxism, but it's way past Marxism, and many of its assumptions are actually contrary to orthodox Marxism.

"Having rowed--and paddled--upstream more than a few times I can sympathize."My trips always seem to have me paddling upstream. Both ways.

“ ‘Power and oppression, as defined by ethnic studies....’ ”

He who defines power assumes power.

I wasn't talented at math but I dragged myself through a year of calculus, then graduate statistics and computer modeling. I came to appreciate what mathematicians meant when they described pieces of mathematical reasoning as "elegant."

One of them said, "Math is the only branch of science that hasn't visited its own funeral."

In these slippery times, I wish we could acknowledge the value of a discipline in which Truth can be found.

Wait until the woke crowd hear about imaginary numbers.

The Seattle school system document that Ann Althouse links to is just saturated with hate and racism. The children of Seattle are being taught to hate and despise and blame white people for all the things wrong in their life.

It's every bit in the same spirit as the hatred the German Nazis directed towards the Jews.

Maybe I need a better name, maybe I need a different word to describe it, but still I'm not lying or spreading falsehoods when I say that Seattle employs one heck of a lot of people who are the equivalent of Nazis and that in this respect the Seattle school system is malignant and evil.

Moving on from that and please don't pretend that what is going in Seattle is meant to do good, my belief is that the primary value of teaching math is that people discover a new way to think, and that this different way of thinking is about far more than just doing math. I don't think everyone gets it, and it is entirely possible to pass math courses without ever learning to think mathematically, but some percentage do get it, and once they get it, it will ripple out and open up and change all of their thinking.

Finally let's not lie about our past. The greater proportion of what we call math was invented by Caucasians, or at least as far as we know. That's an important qualification.

We know that that mathematical thinking happened in early India, but the manuscripts that survive are quite limited.

The foundations of math, arithmetic, are old and deep and I think every culture that has had a written language has also had some kind of arithmetic. As with written language, we know that arithmetic was independently invented at least twice, in the Americas and in what we today call the Middle East. But it's possible that it was independently invented in China, and the only reason for doubting that is that there was a chain of people connecting the two areas. And it is also possible that it was independently invented many times.

Likewise we know or believe that an early form of algebra was invented in some part of what we today call India (or maybe it was Pakistan) and we know that Muslim scholars in the Middle East added to it.

But if you look at all the ideas that we describe as algebra today, 99% of it came from Caucasians. Or at least that would have been true if this were the 1950s. But things change fast, and math is not a stagnant field and new discoveries are being made all the time. And there are mathematicians all over the world now and that means that the new discoveries are going to come pretty much from everywhere.

@Balfegor:

quaternions“Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell.” William Thomson, Baron Kelvin, 1892

“This was really the first moment in history when decimals began to equal the computational capabilities which sexagesimals had possessed for millennia. Only after that (really, after western mathematicians accomplished the same thing as al-Kashi) did decimals begin to displace sexagesimals for use in scientific computation.”

Why base 10? Why not base 2? Or base 60? Mathematically, they are all identical. I spent too many years working with computers at a low level to ever want to use base 2. Way too many digits to deal with. We naturally use base 8 (octal) or base 16 (hexidecimal) instead. Why not base 60 instead? My guess is that it is too hard to learn the symbols, and almost impossible to learn the addition, subtraction, multiplication, etc tables. I suspect that if we hadn’t picked base 10, because we have 10 fingers to count on, base 8 would have been the choice. Almost as much information per digit, and math tables are only 2/3 the size of base 10 systems, while base 16 tables would be roughly 2 1/2 times as big.

I'll out myself as a non-mathematician and ask Bruce Hayden and others-- did I miss any discussion of base 12, or is that implicit in one of the others?

Narr

(I was great in geometry, though!)

● Who gets to say if an answer is right?Can we Agree, that SOMEONE got the answer WRONG?

New Orleans Hard Rock hotel under construction collapses

● What is the process for verifying the truth?that your building lasts long enough to be completed?

Maybe the contractors will blame Racism?

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