On Sat, Aug 21, 2010 at 10:50 PM, Robert Hansen <email@example.com> wrote: > Kirby wrote ... > > - ---------------------------- > Immediately, I think of computerized numbers, which disappear when you pull the plug, i.e. they require energy to "stay alive" in the computations. > - ---------------------------- > > The "numbers" disappear? The abstraction ceases to be (i.e. the association of a particular charge distribution in the RAM ends) but the numbers are safe and sound, somewhere in the mathematical ether. Except for the physical construction and characteristics of the machine, a computer and its software is a great example of abstraction. >
Hey thanks for the nicely formatted dialog excerpts. I shall continue interleaving, as I consider this a productive thread.
Yes, the physical numbers go away. Some may believe in a mathematical ether, a kind of gas, where "real numbers" go to dream of themselves at night ("oh no, what if I'm really imaginary!"), but that superstition is not necessary to work in a math lab.
A consistent feature of my curriculum writing is the energetic cost of computations, in one place expressed in terms of hamburgers per capita per time interval (so like E/t or i.e. energy per time or "power", joules per second E = hf, f = 1/t, h = mvd i.e. momentum for a distance).
How many eighth graders does it take to compute such and such number of arithmetic operations? Depends in part on what they had for breakfast.
To this end, I work in:
(a) cooking and home economics for fractions (recipes) and (b) TV editing skills, like Julia Child (part of everyday communications these days), and (c) action figure role model teachers such as Roz Savage...
...whom I've had the good fortune to meet on two occasions), a woman who rowed the Atlantic solo, wrote a book about it, then took on the Pacific.
Packing a row boat for the Pacific is not unlike "Packing for Mars" (new book by Mary Roach) in that you have to be brutally honest with yourself about what you're going to need, physically, to stay alive for that long in the middle of nowhere.
What gets me about some mathematicians from the paper and pencil era is they still think our IEEE-specified floating point numbers are "real number wannabes", as if these physical numbers, implemented in silicon, were "trying" to be something they like to keep in their heads.
No, on our digital math track, we teach of these various number types (with a time-line), go through N < Z < Q < R < C as you've seen me do countless times (perhaps with a subset symbol) but when it comes the machine number types, such as int, float, decimal, bool, complex and so forth, we have to treat these as what they are: machine-implemented physical numbers with their own properties and characteristics.
They're *analogs* of what the paper and pencil people have, but if you pull the plug and try to re-implement this electronic civilization on paper or in chalk (clay tablets whatever), it won't work, won't be the same. People will see the difference, I guarantee.
> > - ---------------------------- > Have you heard of the Greenpeace plan to grant a PhD to all dolphins, honorary degrees through cooperating universities? > - ---------------------------- > > Yes, and other equally bizarre stories. >
"Bizarre" is what ya need sometimes, for documentary footage.
Better than "horrific" in my book, which is more the TV news style, scares people witless yet often doesn't teach anything useful, so is not worth the expense (yet silly advertisers sully their brands anyway, because they believe all that crap about "eyeballs" -- as if numbers were all that mattered, not mood, and not state of mind (psychometrics matters, even if you say it's just alchemy -- "quality, not quantity" is still worth remembering)).
> > - ---------------------------- > I think AI is 98% bunk and 2% clever marketing. > - ---------------------------- > > Yes, when you look at it from inception to this point in time, I would have to more or less agree. But we are at the stage where something of a Bohr model is emerging. Notions were much more naive in the past, just glimpses like science fiction. Part of what has changed recently is experience with very massive collections of data and very large clusters of machines and this causing us to search past what we know of abstraction. >
"Bunk up 'til now, but now, at last..." -- a sucker is born every minute, and no, Barnum never said that AFAIK. But an AI guy probably did.
> > - ---------------------------- > In other words, not every "education reformer" is interested in reforming human nature or revealing some new clever theory of some "inner child". Some just want to stay up to date, in a world that's anything but static (reform is therefore ongoing, is not about finally "getting there"). > - ---------------------------- > > Ok, well that is another type of reformer then but if I were you I would pick another name for that and I think any marketing department would wholeheartedly agree. The "reform" term is unfortunately soiled with decades of failure with all those other goals. Also, why do you pit your curriculum against math? And Litven's text is math with a CS component while you seem to promoting CS and trying to force us to see it as math. I find some of your characterizations of SQL and other such subjects to be beyond exaggeration. > >
I don't go around tarnishing myself with the "reformer" brush, others do that for me, like airbrush it in, adding pimples I don't have. However, I'm really into keeping it current, for the sake of both the ecosystem and the economy (what's the difference again?).
What I find amazing is that I have to defend "polyhedra" as relevant on a list calling itself math-teacher. That's a shocking state of affairs, not to mention bizarre.
So then you store those polyhedra as vertexes A-Z (26 of them for starters) connected in circuits called "faces" (another table). This is better then just using "edges" (another table, related to vertexes), because now you know what the faces are, for coloring purposes, adding alpha channel opaqueness (or subtracting it). OFF format is like this. Check antiprism.com for good examples (open source, high school ready).
Yes, we're using a ray tracer and VRML (x3d?), maybe having Python do string substitution to spit out the code, typical math lab stuff, what any digital math student might be doing, then printing to a T-shirt and showing off around town (picture Asian girls, boys too, in PDX with rhombic triacontahedra entwined with snakes, looks like a gang symbol (like some have a skull in the middle, kinda gothic) but also Escher).
Where I talk with Gary Litvin about his approach is on math-thinking-l (another list, mostly quiet). Whether to call it digital math or not. Whether we might get polyhedra swept in using the "graph theory" loophole.
I think that's working by the way (using that loophole), flies easily, as mathematicians connect topology, graph theory, and polyhedra all the time, in all kinds of dimensions (a lot like cyberspace, this hyperspace of theirs).
> - ---------------------------- > When you have 40 students in each class, some with parents at home, others in a boarding situation, parents back in Japan, you won't be able to take this individualized approach except maybe in helping with the exercises. > - ---------------------------- > > I fully understand that, and without tracking you are really screwed. We have an elementary school here that does something very different. Two teachers teach one class of 36 first graders and as the class moves through the lessons the first teacher presents things in a traditional manner while the second teacher is able to spend additional time with the students needing more help. I can't attest to it's effectiveness but it sounds interesting and I have a friend with a son in that class so I intend to keep abreast of how it goes. >
I'm a big fan of pair teaching, along with peer teaching. Gets 'em ready for pair programming in future.
I know what you said about engineers retreating to their respective cubicles and doing their own work (URL? -- a recent post here), but remember the eXtreme Programming crowd isn't into that. Your peer is literally right there looking over your shoulder, perhaps kibitzing on every piece of code you write, or just taking notes.
Later in the day, you might be in that same position with respect to another coder, though not necessarily the same one.
Not every company practices this, not having managed like that before, but some 30-somethings are starting to take it more for granted, though I grant you also that solo time slips in, i.e. it's not a 24/7 proposition and sometimes you just wanna code without some hot babe from Krakow breathing down your neck (actually happened to me in Vilnius, not unpleasant, but this was just a workshop, woulda been hard to spend whole days doing that, at least at first -- she was a Java pro, worked for Google, was just learning Python, originally from some other country I forget which).
> > - ---------------------------- > I used to attend the Florida school system and was amazed by all the racism and sexism going on. My international school circuit was more enlightened, and Portland felt more like home when I finally returned here in the 1980s... > - ---------------------------- > > You remind me a lot of a cousin of mine that lives in the north. When I was (much) younger and going to high school (70's) she was visiting from Indiana and made a similar statement, driven by a complete lack of any real experience I suppose. Being naive and innocent and of the age where High School is your entire world, I asked her how is it different there, what are blacks like in high school. She replied that there was only a few in the school and none in any of her classes. > > You see Kirby, I know what the demographics of Oregon and Florida are... > > http://en.wikipedia.org/wiki/Oregon#Demographics > http://en.wikipedia.org/wiki/Florida#Demographics > > I have also seen the demographics of the schools you have mentioned and can compare them to the schools I attended or the schools in my area. The reason you feel better in Portland is that you can enjoy your imaginary and abstract notions of race relations because you don't actually have to test them. And I do not doubt your glee experienced when you were able to return to your imagination after your foray in Florida, but I'll stick with the actual results (albeit not perfect) here in Florida rather than imaginary notions such as yours and my cousin's. >
You left out the part where, after leaving Portland in the 1960s, my family was employed by the government of Libya to draw up 50 year plans, followed by stints in Egypt, Bhutan, Lesotho, Bangladesh and the Philippines, though not necessarily in that order. I got to Florida somewhere in the middle of all that, my head still spinning, then left after one semester. Southeast High. Not far from a Tropicana plant. Bradenton, FL. Autobio on-line.
Anyway, funny how your mind jumps straight to white-black relations, whereas out here in Oregon it's more about lingering memories of Haida, which Hudson Bay Company used to fight for control over assets (established Oregon City as the territory capital), started busing in big Samoan types, Hawaiians, by boat, cuz they were getting their butts kicked.
Then came the flooding of Celilo Falls (1957) followed shortly by a certain ignominious chapter in USA history that resulted in its defeat (197?), and a flooding of many brands of Asian refugee into the region, adding a layer to the native Latino migration patterns (some over 10K years old, though now interrupted -- we hope temporarily -- by these pesky Anglo-Euro types who think they own the place (everyone else is "illegal") when they don't and never will (not in the domineering sense to which they somehow feel entitled).
"We share, we don't surrender" is the mindset out here. Lotsa casinos. Casino Math (chance and probability, statistics) is one of my four Digital Math modules for a reason.
Then as I was mentioning, we have a cosmopolitan population of engineers and health care workers, big Iranian subculture, a fair number of Palestinians, lots of software types. They want a good education for their kids and are dismayed by how backward the schools seem to be, still much like they were in the 1950s except in the 1950s that was excusable whereas by now it's inexcusable tardiness.
The corruption goes right to the top, not politically but academically. Analytic philosophy has let everyone down, allowed the AI dweebs to run the show, keep crashing on Wall Street with their stupid models. Too many bankers and lawyers, not enough engineers, all because philosophy went to seed, stopped policing the other disciplines. Math was unable to hold the line, as corruption crept in. Ethics got flushed down the toilet and you have a mindset not unlike pre-1900s Germany's, which Nietzsche commented upon:
One pays heavily for coming to power: power makes stupid. The Germans - -- once they were called the people of thinkers: do they think at all today? The Germans are now bored with the spirit, the Germans now mistrust the spirit; politics swallows up all serious concern for really spiritual matters. Deutschland, Deutschland uber alles -- I fear that was the end of German philosophy.
Walter Kaufmann, The Portable Nietzsche, Penguin Books reprint, 1977, page 506.
Note that he wrote that in 1888, well before it all went to hell with the 3rd Reich and Aryan Nation crapola. The USA after Eisenhower went into a similar decline, dreaming itself a "superpower" (uber alles) while slaughtering its own youth in a rush to insolvency. Good thing we stopped at the brink eh? Or are you one of them "nuke Iran" uber-dudes?
> - ---------------------------- > One secret to getting good at basketball is having a private hoop somewhere and just shooting over and over until the cows come home. Skateboarding, learning an instrument (e.g. keyboard) -- takes a lot of investment of solo time, which means a belief in and vision of yourself. > - ---------------------------- > > I agree. (Very) many students are nothing but consumers. I have often wondered about that and some say that our society promotes consumerism and I see their point but when you look back it seems that a large proportion of individuals were always of this mindset and society just reflects this. And I must note that civilization and the quality of life we are accustomed to relies on an economy of consumerism. You might even say that consumerism is the essence of an economy. The one required element. Fortunately, some of us spend all that time in our bedroom pouring over math or music or at the park playing hours of basketball and represent the other side of the human condition. >
What "quality of life" are we talking about exactly?
I see a lot of disgraceful, shameful squandering of stuff, amidst a lot of unhappiness and spoiled rottenness. Nothing the rest of the world wants, mostly just hideous over-produced television with people saying a lot of silly stuff, clearly airheads.
Al Jazeera is better than CNN these days, have you noticed? The shallowness of the "TV news" around here tells me this "civilization" is over-ripe. VOA is still pretty good, though BBC is better. Funny spoof of BBC here:
Fortunately, given the huge diversity in this population, adaptations are likely to keep pace, at least in pockets. Not every zip code is a carbon copy of every other.
Oregon has Spirit Mountain Casino (Grande Ronde Federation) which has been putting some funds back into the community, helping to fund OMSI for example (our native science museum). That's where we're hosting the Einstein exhibit. Did you know he'd been asked to be president of Israel? They also showed parts of his FBI file, as the the McCarthyites were crazy about him.
> > - ---------------------------- > There's not just one IQ or EQ. Over-simplified models lead to pigeon-holing in ways that fail to optimize, squander "human resources". > - ---------------------------- > > Well, it is also a fact that we will all die and we seem to get over that easy enough, but then we don't have much of a choice do we. You say that there is more than one IQ, I am saying that people can't even accept the notion of IQ period. Until they come to grips with this any model they create will be corrupt. >
I think you're saying they're in denial about their being a Bell Curve.
Actually there be *lots* of bell curves and you can't beat "being average" on some of them, which is actually OK. I'm quite happy being average in so many dimensions, helps anchor the persona when I go several deviations out in directions I've pioneered.
My Martian Math is pretty "out there" but as a classroom teacher I come across as a pretty ordinary joe a lot of the time, no one they can't work with. No antennae coming out of my head, like Ray Walston's.
You have this way of holding yourself out as a role model of some guy who knows math, is able to reason, and who knows how this pertains to getting certain kinds of jobs. I respect that, consider you a recruiter for a particular way of life.
You represent an ethnicity, one that uses mathematics and doesn't want to cut corners when it comes to raising a next generation of "replacements" (or "clones"). You seek to continue your lineage. No problemo. That's what schooling is here to help with.
However, I'd be averse to any one subculture taking over center ring in this circus and just doing all elephants, all the time. Monoculture is unhealthy, national standards suspect.
You gotta share the road. When the clowns come on, with their juggling of polyhedra, I don't think you should throw food or say "that's philosophy not math" as people paid to see this stuff too, not just your particular brand of abracadabra, and certainly not just calculus, which many would consider boring and inapplicable to the careers they most crave (some calculus is OK, but lets not be pigs about it -- shouldn't be the only "royal road").
> > - ---------------------------- > If your students are always struggling with the idea they might be failures, all washed up, no where to go, because they don't know what reasoning "feels like", then maybe you live in the wrong state where the NCLB schools don't even have hi-def TV in the geometry classrooms, unlike in Korea. > - ---------------------------- > > The last three high schools built over the last 10 years have wide screen projectors in every classroom and many also have smart boards. And the older high schools have been mostly retrofitted. Multimedia has always had a sweet spot in school here, from the days of overheads and 16mm film, through the days of VCRs and TVs on wobbly stands to the present day of the ceiling mounted projector. Multimedia will not make much of a difference NOT because it is insignificant but because it has been part of the curriculum for the last 50 years. You can't have A, B and C and then say let's improve it by adding A because A is already there. >
Another way of saying it is that we have a lot of infrastructure, but don't always take full advantage.
Consider regular civilian television for example. When 'Sesame Street' first came on, and over the years following, it made a lot of waves, helped parents get through the day with their young ones.
Yet nothing about the technology of TV had changed that much. It was the programming, the quality of the curriculum material, both in terms of content and production values. The Muppets had arrived!
I had high hopes for this format when at McGraw-Hill in the 1980s, sent my ideas to Childrens Television Workshop (CTW). Big Bird doesn't teach about complex numbers, but the repetitive use of video clips from a database, short ones, lots of spiraling, is right on....
The Videogrammatron (my proposed name for it) never materialized but then we got Youtube, similar services, so many prayers answered -- now if only it weren't verboten to watch it in classrooms...
Likewise, it's not the mere fact of a hi-def screen in the room that makes the difference, but whether it shows any Martian Math or not (as an example), displays any computer language e.g Python + VPython (per my Martian Math site).
As you very well know, teachers might get in hot water pretty fast if they start showing the "wrong" documentaries (such as you might find at Laughing Horse Books and Video collective), as students will tell their parents and parents will phone the principal, demand reprimands. So teachers toe the line. 'Team America: World Police' is probably the most you'd get away with, in sleepy backwater Florida.
Math, being mandatory, has to be the safest in some ways. That's probably why they took out all the time-lines, white-washed the whole place, made it spic 'n span, just like the Stepford Wives would like (very "pleasant", very "sanitized", very "corporate" (hospital gray)).
Literature has always been more colorful and problematic, as some books are inflammatory, bring up forbidden subjects and spark frank discussions some teachers would rather not deal with. A short list of approved "controversial books" is drawn up, such as 'Catcher in the Rye' or 'The Jungle' by Upton Sinclair.
But what about 'Fast Food Nation' and/or 'Supersize Me'? I used to tout those in this archive years ago when they first appeared, connected to my perennial themes about cooking and calories -- but then I've always been a maverick on this list, talking about healthful living when everyone else wants to play "mafia wars".
Math, of all disciplines, doesn't have to deal with the sordid business of history -- or at least that's the illusion that gets sold, the snake oil our mostly Anglophone analytic philosophers have proved too weak to counter. They refuse to understand Wittgenstein and they won't admit that tetrahedral mensuration falls within their bailiwick. Anything to smoke a pipe and sound like Karl Popper I guess, kinda steam punk and retro.
Does your school district block Youtube? At the AAPT conference, a teacher in the audience asked about that, and was told by a panelist to basically start a revolution as social networking tools are part and parcel of tomorrow's schools (even today's in some zip codes).
Teachers -- librarians especially -- are in revolt against any district policies to censor access to the Internet to the extent that this hampers their academic freedom and the freedom of their students. They're role modeling, fighting Big Brother, who is often just a moralizing idiot who can't stop thinking about kids looking at porn (drives him wild).
The USA ranks about 30th in terms of providing Internet access to its people. Getting it all tied up in privatized cable networks, forgetting about optical fiber, and turning it into a one-way delivery mechanism (to consumers) for sports, news, and entertainment, has merely retarded the Lower48 even further, to the point where I wouldn't blame Hawaii or Alaska for jumping ship -- who wants to lose all that freedom to corporate-minded dweebs?
What? Off shore service providers for Hawaiian public schools, not bound by district policies? Maybe for a few experimental charters with special permission from the State Department? You won't recruit those elite international blends if you let the unimaginative and mediocre manage your facilities. Future diplomats need schooling too, for their more gypsy-like lifestyle.
Students today need to learn peer-to-peer teaching, A/V editing, along with multi-ethnic cooking (a form of cross-cultural collaboration, like at Intel).
Making these world class schools all be "private" is unethical though, as in undemocratic. We need them to be public and open to "we the people", not just for privileged sons and daughters of CEOs.
You see, I'm reconciled to what everyone has been telling me: the shiny new math track I envision will not be allowed in flailing, under-funded, under-appreciated, everyday high schools within the Lower48. They're just too backwater and people never change. NOT! (more below).
It's verboten to talk about overhaul as that means acknowledging how broken things are, whereas the job of an administrator is to be reassuring, calming. Who wants parents in a panic because Johnny can't program? Lull them back to sleep with the familiar lullabies: "you won't need to have skills, cooking and gardening is for the birds, always eat fast food, and just learn how to shop until you drop..." (a "quality of life" nightmare a lot of people subscribe to even in their waking hours! -- TV has been effective in neutering the population, dumbing it way down).
> > - ---------------------------- > There's a popular spelling teacher on Youtube, among 15 year old boys especially, whom you might have learned "antidisestablishmentarian" from (a word I used recently in one of my blog posts). > - ---------------------------- > > Lol, yeah she's hot. I swear to god that in one of her videos she isn't wearing panties, or the gamma on my monitor is off. Of course, I only noticed that because I was critiquing her curriculum.:) >
She's pithy, gets a lot across in under five minutes. There's a premium placed on the Lightning Talk as an art form these days, with the 'Ignite' events in Colorado, Oregon, maybe some other states.
In some of my recent classes, I've gotten that going, with students taking turns. It's a lot like show and tell, or having a student come to the board. Add a few cameras and you've got the raw material for making TV (an important communications skill, as I've mentioned). In Baltimore, both of my students were space telescope scientists, very good at math.
> > - ---------------------------- > Some kids withhold their participation because the school seems corrupt, is abusive, isn't really about teaching useful skills. It's about social control and sending the message they're failures, that they just "don't get it". > - ---------------------------- > > Wow, they must be really really intelligent. I remember a couple of kids that you might be describing, but only a scant couple. The bulk of that crowd must have hid it very well. Or it could be that, like your imaginary race utopia, such a crowd doesn't even exist. I know, let's ask Occam.:) >
Varies by zip code.
Once you get a few student and/or community organizers in the picture, heightening consciousness, the demographics change. In Portland, a lot of the activism has centered around our charter schools movement, as some of the most socially conscious teachers wanted to have a new kind of high school.
That happened, a few years ago. More peer teaching, less "divide and conquer" techniques among the teachers. This idea of always competing with your peers -- that's gotta go. One of the first things that goes in military trainings as well. You need team players.
You do compete sometimes though. I'm not saying that all solo "me first" stuff is bad or wrong. I'm not an anti-individualist.
Years ago, I worked with Asian and Latin American youth around Portland on just such consciousness raising programs. We were not "anti teacher" in any way, but did teach critical thinking, especially w/r to the media.
The kids got to do TV production work, got their own show on cable TV (Voz Juvenile it was called, broadcast in Spanish). United Voices is still in operation, even though I'm not in my old position with the program (search afsc.org for more info).
Hip hop culture was at the core in some ways and we had some black participation, as well as white, but these were in the minority.
A lot of our program grads are now looking at this freedom of movement issue (so-called "immigration"), questioning a system that lets corporate persons move about freely, without passports, seeking "cheap labor" while penning humans into these barbed wire prison camps called "nations" (once proud, now lackeys and puppets for the most part, not believable).
A lot of art colonies are inventing themselves as "virtual nations" this days, almost in parody. Heard of Uz? How about NSK? http://www.nskstate.com/ Still trying to join NATO? I have no idea (so many threads).
> > - ---------------------------- > I think your notion that "reasoning is a feeling" is rather quirky...You never mention the "left brain" versus "right brain" stuff, which even if somewhat metaphorical at times, is rich in supplying an opposition. What your theory lacks is a strong plot line, as what's > the opposite of "reasoning" in your mythos? > - ---------------------------- > > I did give the other side, it's called conditioned behavior, otherwise known as rote. But it isn't the "opposite" because we all practice it for most of our day. One theory is that "reasoning" as we know it showed up later in the gene pool and hasn't been fully distributed yet, although I am not sure if "yet" has any meaning in the modern world. And even if it were fully distributed there would still be a distribution curve. And of course, everything is not about "reasoning". Music, art, literature. They all have their "feelings" to. >
What I've argued is music contains its own form of reasoning, as do art and literature.
I would consider "logic" as in inheritor of these reasoning forms, as a relative late-comer to the theater of human thinking, although "mathematical reasoning" in a broader sense, is a lot older and was/is often bound up with the practice of some priesthood, usually characterized by some trademark form of architecture, e.g. Giza Pyramids, Taj Mahal, Montreal 67 biodome. Note: by "priesthood" I don't mean "only men" (our Silicon Forest is home to many genders).
> I am not saying that there are not gains to be had, I just think if you are not realistic then you will very much corrupt your effort and not only fail but make things worse. For example, the current fad is Algebra for all, yet even optimistic assessments of the current algebra reality is that only 15% get it enough to even label them as getting it. When the "algebra for all" movement meets this unsightly truth you can bet money on the fact that rather than moving 3 million students to the algebra finish line, they will realize that it is very much easier to move the algebra finish line to the 3 million students. >
I'm willing to write off the Lower48 as past hope, but then there's the rest of the world to think about. Actually, not true, I lied. I want the Lower48 to stage a comeback.
There's no reason for such a lot of tragic unhappiness here. There's so much great infrastructure, going to waste, getting squandered. It's what's between the ears that makes no sense, and that might be addressed.
We'd need to restore philosophy though, which includes ethics. That's something for universities to look at. What's up with those high tuitions and no real philosophy to speak of?
Obviously these are rather cosmic and big picture vistas I'm exploring and it'd difficult to see how some former math teacher from Jersey City is gonna make a difference to university philosophy departments, in faraway places like Stanford for example. Do I have no sense of my own limitations? Of course I do. I'm talking about zeitgeisty stuff, mega-trends. I don't necessarily have to lift a finger to have some students switch to a digital math track in an international school setting. That's already been happening.
Plus as long as the Silicon Forest is paying me to teach Martian Math at Reed College, I don't have to worry about Portland's getting a grip. What about Florida though?
You may think it's none of my business, but doesn't EPCOT stand for something? Unless Florida is a source of positive futurism, as well as oranges, I think it's selling itself short. But with then with shuttle program winding down... What's the vision? You say Apple iPads? But that's not indigenous.