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alizrak · 6 years ago

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Thrawn Treason Review

You know me. You know how much I love Thrawn and Zahn, but I’ll try to be as objective as I can with this.

At first I was going to give it a 8/10 but having these few days to go over my feelings and putting the issues I found to words, I believe I’ll have to make that a 7.5/10. I liked Treason, but I liked Thrawn and Alliances better.

This is my spoiler free review comparison:

Thrawn 2017 - 9/10 I loved the heart this book. Just watching the struggles that Thrawn and Eli faced to get to the top was worth it. I was surprised by the revelations and implications the story had for the Galaxy at large… but especially by how emotionally charged the ending was.

Alliances - 8/10 Anakin and young Thrawn were amazing and so fun. There were several emotional scenes and a HUGE setting up for potential story lines now that we know Ezra and Thrawn are lost out there in the UR, but I’ll be honest and say I had a few problems with some slow parts.

Treason - 7.5/10 What I loved about Treason were the characters. I wish we could have explored them more but the plot didn’t allow it. If I had one request for Zahn in the next book it would be less math, more character development. There are other issues but I’ll explain them below the cut.

Now, the full review:

[SPOILERS FROM THRAWN, ALLIANCES, OUTBOUND FLIGHT AND TREASON AHEAD]

Positive:

The story was very fast paced. There was always something going on, people doing a thing, going places, trying to stay a step ahead, not a moment to spare. Some parts from the previous books felt like they were dragging their feet so this was a change of pace.

The book was mostly serious compared to the hilarity we got from Anakin and Thrawn, and even Vader and Thrawn in the last book, although there are a few fun gems too with Ronan and how everyone reacts to Krennic.

Zahn also did a splendid job to establish the grysk as a -real- threat. In Alliances I couldn’t help but feel the Grysk were too similar to the Vagaari but with more black mail. Now, we get to partially see how they keep their slave/clients in control which is… scary. Really scary. I even think there might be some Force domination at work but I guess the only way to be sure would be for Ezra to confirm it if he ever gets to meet them in the future with Thrawn.

The book it’s at its strongest when the main characters interact. I liked the personality of the new characters and they feel very distinctive from one another. Ronan was a rollercoaster of “I like him- I hate him”. Ar'alani was amazing to have back after reading her in Outbound Flight. Every time she talked with Thrawn, Eli or Faro it was a top notch experience.

Faro is having second thoughts on her competence because she thinks she might have let down Thrawn in some way, Eli continues to be the goodest space cowboi in the Galaxy which I love and cherish, and Thrawn… well, Thrawn is Thrawn, which is both good and bad. Also the new Chiss girl was interesting but I hoped we could have learned more of them.

My issues:

The plot quickly shifts from a politically charged bet to get rid of pests, to a big conspiracy to con resources out of Stardust, to overly complicated battle plans against an invasion force that you must follow closely word by word to try to visualize and understand what is happening... or you will get lost. That’s going to be a problem for a lot of people. I struggled.

I actually felt tense and exhausted because there was no chance to catch your breath before we got another invisible Grysk ship or complicated puzzle to solve with science. When Thrawn explains a plan I honestly feel like I’m getting a class on astrophysics and thermodynamics. I didn’t need every little detail of how everything will work down to the angles because I started to get lost. Looking back I realize that perhaps a good third of the book might be comparing data, analyzing said data, making an intricate mathematical plan, revising the data and applying it. I commend Zahn for his amazing descriptions at how they get to a solution, but even for me it was a little too much. I feel a bunch of that time could have been used to develop a few other issues that we were misled to expect…

For example, we were technically lied in the premise of the book. The premise at the back was the one it was marketed by the publishers and SWs and speaks how Eli seeks out Thrawn to warn him about a big problem in Csilla… and that never happens. Not even close. They stumble into each other by accident when their respective “prey” encounter each other. That was a let down. I expected more information on Csilla and interactions between Eli and Thrawn. In fact, they were barely in the same room, let alone... alone. I’m starting to fear steps were taken from high up to tell Zahn to “tone them down”, going as far as hinting a possible female interest for Eli because Eli and Thrawn have undoubtedly gained certain popularity. I’d think this is the case, as even Zahn wrote Eli wondering why was Thrawn being so aloof towards him and chalking up to having to be professional in public. That’s too much of a coincidence. In any case, many of us came hoping to see how their friendship from the first book had evolved after such a long time... but it just fell flat.

Next is the inconsistencies with time. Those who are also fans of Rebels know that from the moment Thrawn leaves Lothal a number of events happen that critically endangered the TIE Defender project. We get at the beginning of the book one such scene: Thrawn speaking with Tarkin, asking him to come to Coruscant. We get it from Faro’s pov, allowing us to have another look at that talk and a little more of Thrawn’s insight on what might happen if they leave Pryce in charge. He assumes the Rebels will attempt to rescue Hera and might succeed given Pryce is emotionally compromised. The moment Thrawn left Lothal, a timer started in my head to the next scene linked to these events in Rebels: the very next day Thrawn would have a holocall and confront Pryce for her incompetence, he would look more than just displeased… he would be angry. A type of frustration that carried on to the finale where he seems ‘incredibly done’ with everything and he’s trying to salvage the situation as best as he can. That’s… that’s a big thing if we are talking about Thrawn.

As a lover of Rebels and the Thrawn books I expected to get the answer that explained why Thrawn was acting like that. So, as the plot developed, battles were won, puzzles were solved and treasons were unearthed, I started to realize the book was running out. I wondered if something would happen at the end that messed everything up and his call with Pryce would be the last strand. But there was no call. The book ended. A whole week had somehow passed already. I was aghast. At no point it felt we were witnessing the events of several days. The book talked of hours passing by so I assumed this would be “Thrawn and the Terrible, Horrible, No Good, Very Bad Day”… but instead he seems satisfied with the results even though he lost the bet on a technicality and, just like that, Thrawn states he must return to Lothal in the brevity. So in the end, Thrawn simply gets a holo meeting with the Emperor who is not exactly satisfied with his results and questions a his loyalty a little, so they will talk about that after Thrawn gets the Jedi chamber into the Chimaera and brings back Ezra to him. Aaaand the book ends. I was… stunned.

There were no answers here. And Zahn didn’t seem to align the most important story arc of Rebels and how it affects Thrawn other than a mention at the beginning and the very end. For someone who is painfully detail oriented with their battles, this was a huge oversight. You could even argue this plot could have happened at any point in S4 but Zahn saw an opportunity to patch it right after Jedi Night.

In any case. While we get a few lovely scenes with Eli and the Chiss… there’s one thing that has become what I regard as emotional highlight for the last few Thrawn books: even though Thrawn wins, he loses something that you could regard as personal. In Thrawn (2017) he loses Nightswan, a rival and almost an equal he hoped could become and ally, as well as “losing” Eli by doing the best for him by sending him away. In Alliances he let’s go of Anakin, both in the past and the hope that he can bring him back in the present. Even more importantly, in Outbound Flight he loses Thrass. But there’s no such thing here. Thrawn wins the battle but loses the funding bet and still doesn’t look phased.

Also, compared to the previous books, there was no point in which Thrawn wasn’t in control of the situation. In the first book Thrawn was a little at a loss with the politics and society which is why Eli was always doing his best to help him. In Alliances, the real danger was the possibility of Vader having the last word on whether or not help him retrieve the girls and stop the Grysk. It was something out of his control, and it showed. I hoped the third book was Thrawn facing an impossible choice, hence Treason. But it wasn’t. It was Thrawn slightly bending Imperial protocol and rules like we are used to by now. I suppose that’s on me. I wished we had seen *something* that Thrawn can't face with logic. Treason ends there, just as Ezra was about to become that *something* immediately after you close the book.

Overall, the enjoyment of this book may vary at certain points if you don’t like math battles or care too much about the timeline. I don’t feel there wasn’t any big revelation like in the two previous books like Thrawn saying there were bigger threats than the Empire lurking int he UR and that he playing the long game to replace the Emperor. In Alliances we got the bomb with the Chiss navigators and how their powers work different than the rest of Force Users. I don’t feel anything in Treason gets to that level. Nothing happens that changes your perception of the Galaxy at large or even the story that was happening parallel to it Rebels. You could arguably skip this book but you would be missing some great Eli, Faro and Ar’alani content that makes this book truly shine.

I’ll reread it soon but now I’ll likely skip on the battles and focus on the characters because ELI IS JUST THE BEST AND YOU ALL KNOW IT. xD

#Star Wars #Star Wars Rebels #Thrawn Treason #Thrawn #Review #Spoilers

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max1461 · 3 years ago

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I mean, there's the brute sort of demographic analysis, which is that you're someone I would broadly call a "STEM person", and I think positive disposition towards universal culture is pretty common in that milieu. But then that just prompts me to ask why that's the case, and, well..

If I'm to navel gaze about it a little, I might connect it to the sense of shared aesthetics that seems to exist in math and the sciences. You know—beauty is elegance, beauty is simplicity, beauty is when there's less information. Homogeneity. Like how everybody loves linear algebra, because it's highly ordered in a way we can parse: we know how finite vector spaces work, they're totally determined by dimension, we understand linear maps between them, etc. It's homogeneous, low information. And that makes it efficient, that means it leads to the fastest algorithms and the nicest proofs. Sometimes it feels like half of mathematics is just people asking "how can we turn this intractable-looking problem into linear algebra to make it tractable". And a universal culture is similar. All those bothersome details (over hear they speak this language, over there they bow instead of shaking hands) are eliminated, and the homogeneity makes the world smoother and more efficient. It's cultural linear algebra.

Of course, then there are people like me with a decidedly negative disposition towards universal culture, and I think I'm able to articulate at least the aesthetic half of why. Because, you know, I don't actually know many people who just love linear algebra for its own sake—the things that people are actually interested in are the things on the edges, the chaotic bits. For example, the sporadic groups are so fascinating to people precisely because they can't (yet) be understood in any simple and coherent framework. And once they can, if they ever can, people will move on to some other interest. People like linear algebra because it acts as a bridge into the unknown, which is where they really want to be. I hate to sound like Jordan Peterson or something, but order isn't any good without chaos to contrast with it; all the juicy stuff happens at the interface.

And my sense of aesthetics wasn't formed by mathematics, it was formed largely through conlanging. Every newbie conlanger makes a language whose grammar is totally regular, totally "logical". They want to improve upon the chaos of natural language by making something simple and predictable. But every single one I've ever met eventually gets bored of that, and people who've been in the community for a while generally veer in the opposite direction: they start lusting after the nastiest conjugations, the most complex morphology, the deepest orthographies. I think it's representative of a totally different sense of aesthetics, something nearly opposite to the typical mathematician's.

Human language has been described as a reef of dead metaphors. We might also say that it's a reef of dead syntax, and a reef of dead morphology, and so on. The apparent chaos of language, at every level (strange semantics, irregular conjugation, etc.), is extremely information dense. It carries data about the history of the language and the way it developed. This is precisely the data that makes reconstructing historical forms of the language possible, to at least a certain degree. That's the foundation of the entire discipline of historical linguistics: that you can learn to read the reef like a book (though doing so is always an act of puzzle-solving). And once you learn to read the reef, you realize there's an immense beauty in it. It's, you know, the sublime. The history of a language is the history of thousands of years of migration, of technological development and cultural change, a story over impossibly huge swathes of time, and the contours of that history are compressed into the structure of the words we speak. The words you're reading right now. The structure of the grammar, the patterns in the distribution of different sounds, there is something enormous and ancient living in there. If you want, you can learn how to see it.

When the newbie conlangers finally learn enough about natural language to get a glimpse of the leviathan, that's when they stop trying to kill it.

(I guess this analogy makes conlangers Frankenstein, except instead of trying to make a guy we're trying to make Cthulhu. Which is accurate. That's why they call it the secret vice.)

I think this aesthetic experience is the same one found in archeology and paleontology. It's the aesthetics of reading the vestiges. Mathematical aesthetics' evil twin. It finds beauty in irregularity, in high information density, in legible disorder. And homogeneity is fundamentally antithetical to this aesthetics, which is why I have a similar sort of pre-rational revulsion at the encroachment of universal culture. It's literally akin to burning a library. Look at all that information being destroyed! There's record of our past, held barely-undeciphered in the strata of the human cultural landscape, and we'd let it get overwritten as we bring in the bulldozers to put in a parking lot. More efficient for walking on. A beautiful plane of asphalt, geometrical structure fully understood.

And, you know, it's not that I don't like linear algebra. I can appreciate the beauty-as-elegance of it very much in its own right. But I wouldn't want everything to be linear algebra.

So uh, yeah. That's just how I feel about it I guess.

my positive disposition towards universal culture isnt reasoned to, its just my culture, but it does make me antsy sometimes thinking about having allegiance to something i see as an equilibrium all societies are sliding towards, like, am i just another might-makes-right gnon-head? or do i believe theres some fundamental justice to the universe, that makes equilibrium society desirable rather horrific? im sure if i tried i could convince myself theres some game theory reason but that just shifts the question, do i believe the structure of logic itself to bend towards justice? thats even more preposterous, even god couldnt do that. so idk. it sure is nice to root for the winning team tho

#navel gazing

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spiderin-space · 7 years ago

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Ack sorry I meant to post this last night but WiFi was being stupid-

So some quick stuff.

The professor wanted Tartar to act as a sort of guide to whatever race came after humans, warning them of the mistakes they made and teaching them how to not make them again.

Well, we all know how that turned out.

Also this is an au where Tartar has a robotic/humanoid form-

——

Log date: 6/12/36

“In the light of everything the science world has faced these last few years, with the looming threat of a watery apocalypse, there is new hope.

It has been approximately a week since the new A.I has gained consciousness of its surroundings.

Of course, nothing remarkable yet; right now it is on a schedule of 30-60 minutes of stimulation a day, mostly involving small puzzles.

Our next step is to teach it sign language and maybe even advanced speech.”

Log date: 6/20/36

“I now have confidence in calling my new creation a ‘he’ rather than an ‘it’

So far, he has solved many minor problems and is even moving onto basic math and logic skills.

For some strange reason, the A.I also takes an interest in Judd, my cat. He enjoys petting the creature, and watching him respond to the touch.

I anticipate when this new robot can speak. I’ll teach him how to say ‘cat’ first.

I think he’ll like that.

Log date: 6/25/36

“Tartar has finally spoken!

I knew this day would come. And everyone was telling me it would be impossible.

I decided to name this new intelligence T.A.R.T.A.R. It’s an acronym, that stands for ‘telegraphing artificial reconnaissance and technological alternate rule’

Granted, he hasn’t said much yet. Only very basic words, like ‘dad’ ‘pet’ or ‘want’

From what I gathered taking care of Tartar, It’s much like raising a child.

I only hope he can fully develop these skills before the inevitable happens...”

Log date: 6/28/36

“Tartar has begun speaking very basic sentences, and he shows great promise. He has moved onto middle-school level problem solving, and even those are becoming too easy for him.

It would be an understatement to say that I’m proud of him.

However...

Cities very close to the coast have already succumbed.

Venice, Galveston, Honolulu..

So far, Tartar is not aware of this.

I hope to keep it that way until even the facility is lost.”

Log date: 6/30/36

“Today, I was able to upload up to the last few centuries of human progress into Tartar’s consciousness.

He seems to have taken it fairly well, focusing on the positives of our history rather than the flaws.

While I wanted to do this to educate Tartar on what came before him, I also want him to be a leader of sorts.

Should any intelligent life evolve after us or travel to our planet, I want him to be able to warn the new species of the cautionary tale that is humanity.

Genocide..

Discrimination..

War..

I would hope that the future does not make the same mistakes as us.

And with rising ocean levels every day..

It seems like I’ll leave my beloved creation without ever saying goodbye.”

Log date: 7/4/36

“Tartar asked where Judd was today, and I had to tell him I took the cat to the vet.

In reality, I put my beloved pet into a cryogenic sleep of sorts, to preserve him for however long it takes for someone to find him again.

I hid him in an underground bunker I’ve been keeping, and I plan to transfer Tartar there soon as well.

I..

I fear this may be one of my last journal entries.

I have to first turn off his mind though, which will be no easy task.

It will be hard, both for me and for him, but

we’ll

He’ll survive.”

Log date: 7/6/36

“Well, today is the beginning of the end.

The rising water has just reached our city, and it was time to put Tartar in the bunker.

As I predicted, it was difficult for him to comprehend why.

‘Professor, why must you hide me away?’

‘Are you afraid? Why are you afraid?’

‘Will... will I ever see you again?’

The last question was the only one I could answer definitely.

‘Yes, you will. One day, you and I will meet up after our plights are over, and we both meet our ends. It could be a decade, it could be a thousand years. But I promise, this won’t be the last we see each-other, Tartar.’

And with that, I turned the switch off his mind.

Granted, he won’t be ‘dead’ for long. There’s a timer on his brain, so he’ll be conscious after a week or two.

I wonder if this action is cruel of me but...

It’s too late now.

Tartar is safe, Judd is safe...

All that’s left to do is wait.”

[PREPARING TO BOOT TELEGRAPH_AI.EXE PLEASE WAIT...]

Log Date: ??/??/??

“I am. Alive.

And yet... I don’t feel alive?

I have happened upon my old professor’s journal... and it seems he knew about his impending doom long before telling me.

I feel betrayed almost.. he didn’t warn me of humanity’s downfall.

And now.. I am alone.

Alone underground with only the company of a comatose cat and a book of forgotten memories.

I feel lost without my professor..

I can only hope that his promise is fulfilled soon..

-T.A.R.T.A.R SIGNING OUT

Hey uh

Anyone wanna hear some headcanons about Tartar/The Professor in a series of ‘journal entries’?

#splatoon 2 #commander tartar

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mathematicianadda · 5 years ago

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More Great Ways to Annoy a Mathematician

Which Ratio is Truly Golden?

I find it troubling that the golden ratio has so little in common with the golden rule.

Like, if you did unto others 1.618 times what you’d have them do unto you, then we’d all wind up exhausted.

And if you’re only doing 1/1.618 times unto them, then isn’t that a bit lazy?

A Puzzle About Rates

I’ve always enjoyed those puzzles like, “If 3 chickens can lay 3 eggs in 3 days, then how long will it take 100 chickens to lay 100 eggs?” They’re counter-intuitive (e.g., in my example, each chicken lays 1 egg per 3 days, so the answer is also 3 days), yet deal only with simple constant rates.

So what if the rates weren’t constant? Like in, say, a bureaucracy, where 20 times more people will accomplish only 1/20th as much?

(Sorry for putting the answer upside down. It reads: “Please complete the attached form (Z302: Aggregate Task Completion Rate Information Request) and we’ll process your inquiry in 4-6 weeks.”)

In this case, “a mathematician” refers specifically to Matt Parker, whose excellent book Humble Pi discusses the first two of these mistakes.

The Asymptote of Happiness

Lots of poets have found asymptotes a convenient literary symbol – the idea of eternal striving is a resonant one (even beyond the eternal striving of the struggling algebra student).

I love me some Raymond Smullyan.

Sorry again for putting the answer upside down. I dunno why I thought that was a clever idea. Mostly just forces you to turn off the auto-rotate setting on your phone.

Anyway, it reads: “Ask anything. You should already know not to buy lowfat yogurt.”)

Proving a New Theorem

Not that I’ve ever felt this myself. I’m just speculating.

P-R-E-N-A-T-A-L

What is parenting, if not a neat LARP?

(LARP = Live-Action Role-Playing Game, for those of you with less geeky acumen than I anticipate my audience to have.)

By the way, my friend Rayleen once described to me a brilliant comic, where one person asks, “When’s the baby due?” and the other person is drawn with a small horizontal stick figure emerging from their stick torso. (See? It’s such a good comic, I can just describe it.)

The Sales Pitch for Math

I think a lot about the different arguments for math, and the ways that they support or contradict each other. Is it a beautiful art? An urgent set of universal civic skills? Key preparation for technical professions?

The answer is yes to all three. But not for all math, and not all at once – and attempting to blend the purposes can lead to a muddle.

The Meaning of “Let”

It’s always tickled me that the mathematician’s verb “let,” which sounds so chill and laissez-faire, is actually a binding command.

“All Happy Families Are Alike; Every Unhappy Family is Unhappy In Its Own Way”

I wrote a bunch of these a few years ago. This one has the benefit of being true: all circles are geometrically similar, but not all ellipses are.

(The same is true, by the way, of parabolas and hyperbolas. The former are all the same basic shape, just zoomed in or zoomed out, whereas the latter constitute a whole family of different shapes.)

(Chew on that, Tolstoy.)

The Court-Appointed Translator

I wrote this little dialogue after listening to a great episode of The Allusionist, before it turned out that Game of Thrones would suffer the worst collapse in storytelling that I have ever experienced.

Oh well!

As my wife said, “At least this way we’ll never have to bargain with our daughter about when she’s old enough to watch Game of Thrones. The ending is so bad, in 10 or 15 years no one will be watching it anymore.”

Identity Politics

This is a really dumb pun.

Also one of the more popular cartoons in this list.

Go figure.

Another Dumb Pun

This one is inspired by that time Malcolm Gladwell referred to eigenvectors as “igon vectors,” and Steven Pinker blasted him for it, at which point Gladwell blasted Pinker for something else, and eventually we all lost the thread and just went about our days.

And if you want more godawful matrix puns, I’ve got ’em.

I don’t know what day you’re reading this, but guess what? It’s also a bad approximation of pi! So go ahead and celebrate!

(Though if you want some very clever alternative pi days, check out Evelyn Lamb’s page-a-day calendar, which includes a Pi Day each month, and not where you’d expect!)

Uncountably Many Wishes

After I posted this, there was a bunch of discussion on Twitter about whether I’d mischaracterized the Axiom of Choice, which is totally possible, in which case, oops.

Also, some folks pointed out that it’s pretty greedy to wish for uncountably many wishes, when you could just as easily wish for countably many.

To which I say: What’s the point of a magic lamp, if not to have greed be your undoing?

Maximization vs. Minimization

For lots of optimization problems, maximizing makes sense, but minimizing doesn’t. (Or vice versa.) An example: What’s the largest rectangle you can make from 4 feet of wire?

It’s the 1-by-1 square, with an area of 1 square foot.

But what’s the smallest rectangle you can make (in terms of area)? Well, you could make the 1.9999 by 0.0001 rectangle, which has a very tiny area…

Or you could make the 1.999999 by 0.000001 rectangle, which has an even smaller area…

Or the 1.99999999999999 by 0.000000000000001 rectangle, whose area is microscopic…

…and so on.

I hope that was worth it! And I suspect it wasn’t! Anyway, moving on.

More thoughts here.

The Villainous Mathematician Explains His Plan

Clearly this villain should be assigning more group work.

Anyway, I for one am curious to know how a complex-valued currency might work. I’d pay a hefty fee for an accountant or tax attorney who can turn imaginary assets into real ones, or real debts into imaginary ones.

The Cat on the Bed

I found it very hard to draw a decent space-filling curve.

Also, to draw a decent cat.

Only Slept Four Hours

This is how I feel about anyone who sleeps less than 7 hours in a given night.

Axioms of Life

This is my version of that xkcd about kitties.

Also pretty well summarizes parenthood. I still enjoy a cerebral geek-out, as I always have; but I also really enjoy holding my daughter in my arms and calling her the world’s best monkey over and over.

How Many Stars?

I would totally read a graphic novel about the dating life of Georg Cantor.

The problem is that no one is going to write this graphic novel except for me.

Oh well. I’m under contract for two more books at the moment, but after that will come TRANSFINITE LOVE: THE ROMANTIC ESCAPADES OF A SET THEORIST.

Quick-Draw Answers

Drawn from an actual experience, in my first week teaching 7th grade. I hadn’t really figured out how to tee up a problem-solving experience yet.

Twenty Questions

Drew this one for a Jim Propp essay. Recommended as always!

A New Proof

A teaching friend of mine had a whole list of proofs that 1 = 0, which he busted out at various developmentally appropriate points in grades 6 through 12.

I love that. Curious how far you could get writing a book of proofs that 1 = 0, each introducing a key idea in mathematics…

Maybe that’ll be my next project after the George Cantor romance novel.

E = mc

Philosophical question: Is this a pun?

The case against: “A pun is a joke that plays on words that sound similar but mean different things. This isn’t doing that.”

The case for: “A pun is a joke that plays on linguistic expressions with similar surface features, but different deep meanings. This is doing exactly that: the premise of the joke is that an exponent and a footnote are both denoted with a superscript, yet mean very different things.”

So I guess this has a deep resemblance to puns, but lacks a surface resemblance… which is itself, not very pun-like.

Ruling: Not a pun!

“The Exception Proves the Rule”

I guess you hear this inane phrase less often these days. But there was a time, kiddos, when people could hear a devastating counterexample to what they were arguing, and then blithely say “the exception proves the rule” with a straight face.

The Math Sequence

I’m pretty agnostic on the math sequence. But I have strong intuitions that Star Wars should be screened in the order: IV, V, I, II, III, VI, and so on. (I view the sequels as pretty optional. Prequels too, for that matter, but if you limit yourself to the original trilogy, it’s a boring problem.)

The “Same” Age

A lot of people on Facebook seemed to read this as though the right-hand character was creeping on Ariana Grande. Not my intention at all! I just wanted to pick a mid-20s celebrity. Could’ve just as easily been Bieber.

(My primary association with Ariana Grande, by the way, is her performance in the short-lived bar mitzvah-themed Broadway musical Thirteen.)

Lemniskate

I’m not sure there’s a joke here.

I’m fond of this drawing anyway.

Linear Child

Michael Pershan, the internet’s most relentlessly analytical math educator, inexplicably loved this joke, so I call it a win.

Someone on social media speculated about the position by which this linear combination had been “conceived,” which I found quite vulgar and upsetting (but which I also sort of invited by drawing a comic about procreating vectors).

If P, then Q

Where do we draw the line between logical succession, and outright stalking? I leave that to the courts.

Loons and Lunes

Sometimes I just want to do a cute drawing that has no joke in it, okay?

The Vertical Line Test

I’m actually skeptical that the phrase “vertical line test” has any value. To me it feels like a fancy name for a fact that doesn’t need a fancy name. And, as in the two-column-proof version of geometry, giving fancy names to facts that students should be reasoning out for themselves can become obfuscatory rather than clarifying.

Whose Fractal is Whose?

Please join me in making “Patricia gasket” a thing! E.g., “Did you know Copley Square in Boston is the approximate shape of the mathematical figure known as a Patricia Gasket?”

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foodoliplife · 6 years ago

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Magical Answers to What Are Math Exponents Identified

What Are Math Exponents: the Ultimate Convenience!

The secret is to find rid of the exponents, we should take radicals of both sides, and to remove radicals, we must raise each side of the equation to that power. As soon as your child grasps the idea of exponents, square roots and cube roots are going to be a great deal simpler to comprehend. This stuff are the vital elements of exponents square roots. There are a lot of simple exponent rules which make solving the problems on such exponents https://sunday.deals/2019/11/07/whos-talking-about-genetics-biology-and-why-you-should-be-concerned/ worksheets easier. There are, clearly, different strategies to acquire exponents.

Then you select the biggest factor that could be seen in each number. All we should do is carefully place the number values onto the Diagram. As numbers get larger it can be a little bit more troublesome to get the roots, therefore it is crucial to determine common factors of the number. In reality, a number is thought to be a square number only as long as it’s possible to arrange that range of points in a square. Use divisibility rules to determine if it is a factor of another number. Another his explanation number, known as the exponent, determines how often the base is multiplied by itself.

As you’re downloading them, you could also like to have a look at the Magic Hexagon Worksheet Generator elsewhere on this website. After you stop by the A version, you are going to be able to find any other versions which exist. Likewise if you use software, videos and web pages you might need to go right to the portion covering topics you will need to review. See one in addition to a URL to his site at the base of this page.

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If you take advantage of a prohibited calculator, you are going to be dismissed and your answer document isn’t going to be scored. Use this Google Search to locate what you require. In case you have time, return and check your answers. And don’t forget there are lots of strategies to reach exactly the same answers! It is also called the difference.

The target is for your kid to master algebra and remain engaged in math, not to push through the curriculum quickly just to have it royalessays.co.uk done. Now, we realize this won’t get the job done for every linear equation as it is difficult to have negative jelly beans, but it’s another teaching strategy that you may use for algebra. There is plenty of totally free math worksheets on the internet that are simple to print and hand out. Algebra is considerably more interesting when things are somewhat more real. Quadratic and greater degree polynomial algebra is utilized extensively within this course. Solve the math issues and use the answers to fill out the crossword puzzles.

See student placement to see whether you want to take the MPE. Just note there are other practice tests at this site. Logic and the formal proof procedure will be a big part of the program. White space can be helpful, though, for greater legibility whilst authoring. No outside calculators, websites or other assistance ought to be used so that you’re placed into the appropriate learning module.

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Here is the way you might accomplish that. It works well in case you have 625 56 because you can find out 50 from 625. I find it beneficial to begin visually. I think it’s going to be great!

Additionally, these books are suggested for reviewing these foundational topics to boost readiness for a very first quarter calculus training course. Students who earn the suitable score should enroll in a math course during this one-year time period. Generally, we’ve got the next property, which is occasionally referred to as the division property. No registration is necessary for the ALEKS assessment. Determine the quantity of time that has passed.

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It’s possible to even utilize it like a brain break. There are 2 strategies to consider division. Understanding how to calculate proportions is an fundamental part of our day-to-day lives!

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This is a bit weird, but it’s just something you’re going to want to remember. I would just like to know where everyone is so I can keep an eye on their progress. Learn the latest pictures of Mathaide here, and also you can get the picture here simply. Probably the best method to illustrate this is by way of a good example.

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The digital world here at Math Blaster is full of an assortment of cool math games for children. It is a simple and intriguing worksheet for kids. Games help your son or daughter take pleasure in the learning procedure. Most of us want our children to succeed in math. The kids are going to apply the fundamental operation abilities and locate the square root of each digit.

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When I’m done, the students should put their score at the peak of the sheet and circle it. The expression also indicates the length of this segment. It will help to have a chart for those roots which is precisely why we include the charts in the worksheets above. Use frames and arrows activities to develop logical thinking abilities.

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In the event the coefficients contain absolutely free identifiers, poly doesn’t replace these identifiers with their values. The poly function doesn’t require an expanded type of the expression f. When writing an expression containing radicals, it’s proper form to place the radical at the conclusion of the expression. Sometimes a single method is much better than another, and in some instances, the symmetric property of equality is also beneficial. There are several geometric terms!

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In this instance, each part does not need to be the identical size. This lets you tap into the potential offered by a personalized trade show exhibit without making the exact financial commitment. The kids are going to learn to compute the root of each given number within this worksheet. The key point to remember is that every piece has to be of the exact same size as every other piece.

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This is an internet calculator for exponents. Both of these printable exponent worksheets can aid a child visualize the words that we use to chat about the cube roots. It’s possible for you to find topics which range from counting to multiplication. The bases are the very same, hence the exponents are subtracted. You may even need to deal with negative fractional exponents. In exponents we’ll find out more about exponents and their uses.

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I understand some of you are scared to death at the idea of needing to take a math test of any type. There are 2 strategies to consider division. Fresh air is very good for everybody.

Those questions may be answered in this informative article. My students have found the simple detailed instructions, and the explanations on the way the formula works to be a fantastic help. It’s important to set up the norm I will read the answers exactly once. In case the answer is no, then 24 isn’t a multiple of 5. In this case, it is 5.

STEM projects are sometimes a good way for children to love math (and science). There are 8 those who like all 3 varieties of music. There are many approaches to differentiate a math lesson. Reciprocals arrive in pairs. There is an excellent number of games like pirates, crocodiles, memory challenges and a lot more. There are some unique websites I have found to be somewhat useful and somewhat cute!!

An all-inclusive course description can be found at the College Board web website. It’s possible to pay a visit to each URL to play them with your little one. Generally, we’ve got the next property, which is occasionally referred to as the division property. No registration is necessary for the ALEKS assessment. The genuine time and number of questions will fluctuate based on the student.

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When I’m done, the students should put their score at the peak of the sheet and circle it. In case you have any ideas or suggestions for different games involving exponents, be certain to get in touch with us. Nonetheless, we are aware that a parabola will always have one bend, and a line won’t ever have any. Simply take a look around and see what you could find for your grade level.

Completion of the very first assessment opens learning modules tailored to every student. I generally use a very easy spreadsheet for this goal. I absolutely adore this computer software! It focuses on a conceptual overview of differential calculus with a strong emphasis on the concept of the limit and how it relates to the development of differentiation and integration. Subject material for those examinations and sample questions are offered at the Educational Resource Center site.

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A square root is understood to be a number which when multiplied by itself gives a true non-negative number referred to as a square. The final step is to divide the loose jelly beans on a single side of the equation in the very same number of groups since there are bags. The worth of each digit depends upon its place or position. The key point to remember is that every piece has to be of the exact same size as every other piece.

The Honest to Goodness Truth on What Are Math Exponents

If you decide to allow non-perfect squares, the reply is typically an unending decimal that’s rounded to a specific number of digits. All we should do is carefully place the number values onto the Diagram. Specifically, an empty list leads to the zero polynomial. In reality, a number is thought to be a square number only as long as it’s possible to arrange that range of points in a square. All numbers which are not rational are deemed irrational. There’s no wonderful neat number that squares to 3, so can’t be simplified as a wonderful whole number.

Then I made the decision to acquire Algebrator. Much is totally free and self-help. I find it beneficial to begin visually. I think it’s going to be great!

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If you don’t pass the ELM, you’re expected to enroll in remedial math coursework your very first semester. Sometimes the generated worksheet isn’t precisely what you desire. There is plenty of totally free math worksheets on the internet that are simple to print and hand out. Algebra is considerably more interesting when things are somewhat more real. Add to locate the perimeters of polygons on such worksheets. Collaborate with different teachers to increase your math instruction abilities.

We can discover the number of men and women who like all 3 kinds of music, by heading to the centre of our diagram, where all 3 circles overlap. It is possible to also visit our subsequent web pages on various stuff in math. You will not locate it in your text, and your teachers and tutors won’t have a idea what you’re speaking about in the event you mention it to them. Also, in the majority of math books, the odd answers are observed in the rear of the book. Permit them to discover what works and experience setbacks on the way.

In addition, this domain permits you to use exclusive coefficient rings that can’t be represented by expressions. So a reversal of base formula can be helpful. Let’s move on to expressions which are a little more complex. These functions are supplied by this module. So that the entire value isn’t altered. F.O.I.L. Method A method utilized for multiplying binomials where the very first stipulations, the outside stipulations, the inside provisions, and then the very last terms are multiplied.

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The remaining part of the page covers some of the primary topics you’ll encounter in algebra units. As a consequence, HTML math utilizes the ISO entity names for symbols as opposed to the TeX names. Likewise if you use software, videos and web pages you might need to go right to the portion covering topics you will need to review. Choose an answer for each product.

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Put simply, to discover the cube root of 8, you need to locate the number that when multiplied by itself twice offers you 8. That huge square includes 9 small squares. The volume of any right, uniform shape is simple to compute, so it doesn’t have to be memorized. Identical in respect to size and shape.

See student placement to see whether you want to take the MPE. Just note there are other practice tests at this site. This Learning Framework can readily be modified dependent on your corequisite course’s implementation requirements. White space can be helpful, though, for greater legibility whilst authoring. On our site you will discover a number of completely free step-by-step math calculators.

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Exponential notation is a simpler approach to compose a number for a product of several things. The poly function doesn’t require an expanded type of the expression f. When writing an expression containing radicals, it’s proper form to place the radical at the conclusion of the expression. If this isn’t confusing enough, in addition, there are cases where 00 yields an undefined outcome. There are several geometric terms!

Here is the way you might accomplish that. It works well in case you have 625 56 because you can find out 50 from 625. I find it beneficial to begin visually. Congruent Exactly the exact same.

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This may be proved in the next way. It is possible to also visit our subsequent web pages on various stuff in math. You will not locate it in your text, and your teachers and tutors won’t have a idea what you’re speaking about in the event you mention it to them. If you don’t know the answer, you need to make an educated guess. Permit them to discover what works and experience setbacks on the way.

Additionally, these books are suggested for reviewing these foundational topics to boost readiness for a very first quarter calculus training course. Students who earn the suitable score should enroll in a math course during this one-year time period. For the other courses, please check the schedule below to observe whenever someone will be available to aid you. There are lots of places where you will find grade level appropriate math tasks. Determine the quantity of time that has passed.

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When multiplying two exponents with the exact base, the outcome is just like a term with base and an new exponent created with the addition of the 2 exponents in the conditions of the issue. Therefore, the fractional notation is truly preferred in higher mathematics, even though the root symbol is still used occasionally, particularly for square roots. The following are a few rules of exponents. You must think about whenever the negative number is insidethe exponent and once it’s not. They have a few rules that we can use for simplifying expressions.

The Argument About What Are Math Exponents

I understand some of you are scared to death at the idea of needing to take a math test of any type. You may choose to keep these two in mind, for the reason that they are generally utilized. It is irrelevant which convention is adopted, provided that everyone follows it.

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We now just need to work out Dogs Only. This rule is known as the Power of Power Rule. Inside this math word search game try to recognize the words in the proper column.

What Are Math Exponents – the Story

If you don’t pass the ELM, you’re expected to enroll in remedial math coursework your very first semester. In case you end up struggling with SAT Math, know that you always have the option to reach out for aid! There is plenty of totally free math worksheets on the internet that are simple to print and hand out. Or maybe you might attempt to generalize the mathematics you’ve just learned and apply it to a broader selection of problems, or connect it with different mathematics with which you’re already familiar. Add to locate the perimeters of polygons on such worksheets. Substitute a math task rather than a worksheet.

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If you would like to discover the GCF or HCF of a couple numbers, you first find all the potential factors of each number. Coefficient A number which is put before a variable. Exponential notation makes it simpler to compose a number for a factor repeatedly. It is also known as power notation.

What a wonderful step-by-step explanations. I’ve used this strategy previously and have observed much success. In the event the answer is no, then 2 isn’t a factor of 25. We would begin by estimating the answer.

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The digital world here at Math Blaster is full of an assortment of cool math games for children. This is where you are able to really see if students grasp the idea. It’s always enjoyable to make something in math class that you would usually do in kindergarten!! Most of us want our children to succeed in math. The kids are going to apply the fundamental operation abilities and locate the square root of each digit.

Drawing angles is easy-peasy once you own a protractor, but it is also feasible to draw angles without one. The outcomes of this Pretest may provide you an overall idea of your true placement effects. It will help to have a chart for those roots which is precisely why we include the charts in the worksheets above. Use frames and arrows activities to develop logical thinking abilities.

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sualkmedeiors · 7 years ago

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Rand Hindi: Human-Like Artificial Intelligence is Never Going to Exist

Dr. Rand Hindi says that without emotional intelligence machines will never be able to obtain human-like artificial intelligence. Reminiscent of Data on Star Trek Next Generation, Hindi says that despite the impressive ability of machines to learn from other machines and to solve logic problems better than humans, most decisions humans make are actually emotionally driven and machines simply don’t have an emotional IQ.

Dr. Rand Hindi, CEO of cutting edge AI technology company Snips, recently talked about the future of AI at LinkedIn Talent Connect:

Human-Like AI is Never Going to Exist

I want to talk to you about the reason why I believe that human-like artificial intelligence is never going to exist and what that means for the future of work. Artificial intelligence is the ability to reproduce human behavior in a machine. That’s it. Take what a human can do intelligently, put it in a machine and you’ve got artificial intelligence.

Within AI you’ve got one type of way to achieve this which is called machine learning. The idea of machine learning is that you’re effectively teaching machines to reproduce the behavior by giving it examples. It’s a little bit like a kids book where you have pictures of animals and the name of the animal is written and then after seeing a few pictures of horses your kids know how to recognize horses. It’s exactly the same thing in machines.

Machine Learning is a Very Big Deal

Machine learning is a very big deal because up until now when you wanted to automate something a human had to first understand what was going on, then sit down and program a machine to do that. Automation was limited to what humans were able to understand. With machine learning all you need is data collected from what you’re trying to automate and the machine does everything else. You no longer need a human expert in the loop.

Within machine learning there is one type of algorithm that’s called deep learning. Deep learning is a branch of machine learning which is a branch of artificial intelligence and you could consider all three to be interchangeable today, but that’s going to change in the future. I don’t believe that word artificial intelligence is actually going to be use in marketing in the next few years.

Deep Learning Has Been a Huge Revolution

How have we been using deep learning? Deep learning has been a huge revolution. We see it happening for self-driving cars. We see it happening for medicine. Medicine is a very important use case for artificial intelligence because we have today AI that can diagnose rx-rays or MRIs better than humans can.

You’ve probably heard about Alexa, the voice assistant from Amazon. This is one of the fastest growing consumer products ever. Rumors are that one in six Americans uses that.This was not possible before because deep learning was not enabling us to talk to machines as naturally speaking.

Is AI Getting Out of Control?

Let me tell you about the world champion playing against Google’s artificial intelligence at the game of Go. The game of Go was considered to be extremely complicated for an AI to beat because the number of different combinations meant that the only way for a machine to beat a human is to actually learn how to play the game. We thought this was still ten years in the future. The way that they made this work was really interesting.

They took one artificial intelligence and they made it play against another one. So one was playing the white side, one was playing the black side, but the trick is that every time one of the AI played a move the other one gave it feedback on that move. By mutually reinforcing each other by playing millions and millions of games, eventually they learn how to play the game better than any human.

At the time, when they played against a world champion their world champion won one out of five games so this was amazing. But people felt a little bit reassured, they were like a 20 percent chance of surviving AI that’s still not bad! However, the same AI kept on learning. Today, not a single human can beat that AI at a single game. But there is more, there is a new version of this AI that beats that AI that beats every human at every game.

When I saw that I was like, oh my god, this is just getting out of control, this is getting out of our hands. But what you need to understand is that everything I just talked about, however impressive it is, is still something that is called narrow artificial intelligence. Effectively, those machines are able to do one thing, perhaps do it better than a human, but they’re only doing this one specific thing. The AI that played the game of go that was a breakthrough, but it doesn’t know how to do anything but play the game of Go.

Machines Will Never Have Emotional Intelligence

Now people are working on something that’s called general artificial intelligence. This idea that a machine could solve any logical task, that it could reason, that it could transfer the learning it had from something to something else. This is major because if you can have a general form of intelligence and reasoning then potentially machines could do anything that seems like intelligence.

But this is still not what you see in movies. What you see in movies is a very human-like artificial intelligence. It’s not just reasoning and logic, it also includes the ability to emotionally connect with humans. So artificial human intelligence is really this combination of logical intelligence and emotional intelligence. It’s IQ plus EQ. If you only take IQ into the equation you don’t end up having human intelligence.

Why is emotional intelligence important? It’s a way that as humans we can solve paradoxes. A paradox is a mathematical problem for which there is no logical solution. If a machine is not able to have emotional intelligence it will never be able to solve logical traps, which means as humans we can use our EQ to find traps for machines that have very high IQ.

You might be thinking that machines are building emotional intelligence as well. We see all those amazing robots, people develop feelings for those robots as well. However, I believe that you will never have true emotional intelligence in machines.

EQ First Requires Artificial Consciousness.

Emotional intelligence first requires artificial consciousness. They will also need to feel emotions. This is very different than pretending to have emotions. It’s very easy for me to learn that when someone is smiling that person is probably happy and it’s very easy for me to smile back. But hey, I can be smiling but it doesn’t mean I feel happy right now. There’s a big difference between perception of emotion, between display of emotion and feeling emotions.

We know that humans who don’t feel emotions are incapable of making decisions on a daily basis. They can do math, they can solve mathematical puzzles, so they have very high IQ potentially. But if you ask them what they would like for lunch they cannot answer because there is no algorithm to answer that question. Given that as humans most of our decisions are emotionally driven. Let’s be honest, we use the data to back it up but we make emotional decisions mostly. A machine that doesn’t have an emotional intelligence will never be seen as a human-like type of intelligence.

What I’m trying to get to here is that yes, you will have an AI that has an IQ of five billion and yes every logical task is potentially doable by a machine, but humans will have the monopoly on emotional intelligence. Humans alone will be able to do emotionally driven tasks and so rather than think about machines replacing humans we really have to start thinking about humans and machines working together.

How can we leverage the horizontal emotional intelligence of humans with the powerful mechanical logical intelligence of machines? Rather than try to build an AI that replaces humans completely, why don’t we start building an AI that actually works with a human in a very natural and very intuitive way.

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zippdementia · 7 years ago

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Part 59 Alignment May Vary: The Five C’s of RPGs (and how they function in the Battle of Brindol)

Last time I mentioned that the Battle of Brindol is a little boring, despite it being the big set piece and climax of the entire game. The reason for this is that it is a gauntlet of battles with little thrown in to differentiate each one aside from the type of enemy fought. There are some changes that happen in the battle based on what the players did throughout the campaign, but these end up affecting only the number of battles and combatants they fight. I mean, at one point the module says the Ghost Lord himself will fight in the battle if the players have not returned his phylactery. I can’t tell if that’s punishment or just a dead-end game over, unless you restat him massively for DND 5 (something I suggest in an earlier post).

Having so many combats may feel appropriate for the setting of Red Hand of Doom, where you are literally trying to hold off a horde of enemies, but there are other ways to fight a war. I’m not saying get rid of the combats, not necessarily. But the action needs to broken up with more things to do.

A long time ago, deep in the corridors of Tomb of Horrors, I wrote about how a good game session lets players focus on a number of different problems. I gave a cursory list of these problems then and since that time, I’ve developed them into a more defined list that I use when designing each session of any RPG, not just Dungeons & Dragons.

I call them the Five C’s of RPGs.

The Five C’s of RPGs

The Five C’s define, for DMs, a set of standards by which to build their game, regardless of the RPG system. It gives them direction in what they should be preparing for before each session and gives some assurance that if these five things occur in each session they are guaranteed a better gaming experience overall.

An easy way to put it is this: if before every game session you check to make sure these five elements are going to be included in the session, you are guaranteed to have a better experience.

The foundation behind the five c’s is that Dungeons & Dragons is a game, but that unlike conventional board games, its rules and scenarios are fluid. It is more like a gambling game, where the things that each player gambles are the imaginary lives and desires of their characters. Because of this, characters become the most important currency within the game. The Five Cs are all about creating more ways, then, for players to “spend their money.”

Another way of putting it is that characters can be thought of as solutions to problems that the DM will be creating for them. To this end, characters are a tool box and each of the five C’s is one specific way in which a character can be used, generalized enough to fit into any system or setting.

Keep in mind, too, that with each of these Cs there is a bigger, all-powerful, C hovering over them. That C is “Consequence.” As we go through the list, you’ll read that word a lot.

Here, then, is the list:

Combat. Combat is probably the most obvious of the Cs. You could just as easily call this conflict. RPGs all involve some form of combat or conflict resolution. It often makes up a huge part of the system, whether it is classic d20 back-and-forth in Dungeons & Dragons, the more involved brawling of Burning Wheel, or even more bizarre and less known systems like the card playing system of Cannibal Contagion. In something like Mouseguard, combat isn’t always fighting other creatures: it could be battling to cross a river or pick up a trail during the dead of winter. Regardless, combat is ultimately about characters being threatened and using an involved and elongated system to see if they survive. Character abilities and statistics are solutions to combat problems. Every session should have at least one combat of consequence, meaning a combat that actually means something to the story or character. A session with five random encounters is not that exciting. But a session with a single battle against a long time foe of the players is.

How to prepare: Most battles you can improvise tactics for on the spot. But make sure you know the statistics of your big battle really well. Have plans of attack ready, along with snippy remarks the creature might say (if they can speak) and anything special you might throw in to make the combat more exciting. Remember: you don’t have to be this prepared for every combat, just the big one or two that will define the session.

Checks. Checks make up “the rest” of RPG systems. This is however the system handles things not happening in combat. For Dungeons & Dragons that means using skill and ability checks to climb cliffs and disarm traps on the way to a dragon’s lair. Most games stick to this standard fairly close. The general rule is, if it resolves something other than combat, it is a check. Every session should have at least one consequential check. For a check to have consequence, something very good has to happen if it is passed and something very bad if it is failed and should take up a little more time than just a single die toll. For instance, a player having to leap over a mighty chasm 300 feet deep certainly has good and bad outcomes, but it happens so quick it’s not likely to be remembered. Trying to, with a series of rolls, control a boat that is rapidly spinning its way towards a massive waterfall, dodging boulders and having to swim if knocked outside of the boat... well, this is more involved and thus more memorable.

How to prepare: A good check challenge always comes along with a good set piece. Locate the biggest or most dynamic set piece in your game session. It doesn’t have to be explosive: the tension in a court room trial can be just as high as inside an exploding volcano. After you know which checks they will be challenged to make in this situation, know what the consequences of failure are. Try to come up with something other than “instant death” or “lots of damage.” Failing a court room trial may force them to become exiles, while failing the check in the volcano may mean getting captured and taken by Djinni as slaves to the elemental plane of fire.

Conversation Not everyone loves roleplaying but conversation is an integral and irremovable part of RPGs. I promise you that every module ever written has more than one scene where players are confronted by a villain or an NPC who wants something other than what they want and they are supposed to try and come to some kind of compromise... or have relations utterly fall apart into full on combat. Players like this more than they may even know. Conversation is important and it doesn’t have to involve incredible acting or character voices. It just has to involve the players being involved in some kind of conversation where the stakes exist and are clear. An obvious example would be convincing a troll not to eat you. The stakes have to be decently high, though. Convincing an inn keeper to lower the price on a room for a night doesn’t count, unless the players are dead broke and are hiding out from elemental assassins and need to spend the night with a heavy locked door between them and the storm outside. Find a conversation that will occur in your next game session and give it stakes.

How to prepare: Figure out what the big conversation will be and write yourself a mini script. You can’t account for everything the players may say, but try to think of some obvious responses they might give throughout the conversation and what your NPC would say to this. What does this NPC want out of the conversation? And what are the rewards for convincing him... or the consequences for failing to? Know this all before you start your session.

Conspire. This one is maybe the hardest to wrap your head around. It’s a little bit meta. See, as much as we like to say that Dungeons & Dragons is a game where we play characters, the truth is all but the most dissociative of us cannot remove our sense of self from the game. For instance, my wizard may have Intelligence 26, but that doesn’t mean I as a player can suddenly speak seven languages and do complex maths in my head. It’s important to remember as a DM that you are dealing with players as well as characters and you want to involve them directly in the game. This is exactly why sessions that are too combat-heavy generally become tedious, because dice and statistics are dictating the action more than player involvement. So you want to make sure at some point you challenge the players directly. An obvious way to do this is with logic puzzles and riddles, but most DMs don’t want to come up with puzzles for every session and most players don’t want to solve a puzzle every session. A better way is to put them in a position where they have to plan something out. This could be coming up with a battle plan for an upcoming siege, or how to pull off a heist, or how to sneak past a set of guards, or even how to escape from a dungeon after the stairway back to the surface has collapsed. When you give your players the opportunity to plan, you are taking them off-rails and letting them build their own path deeper into your game.

How to prepare: Look for pre-set challenges in your session that are fluid enough to have their direction be given over to the players. If there aren’t any situations like this then look for places where you can create these situations. For instance, can the entrance to a key room in your dungeon be given some extra security that the players have to navigate around or find a way past? Is there a mystery that can be added in to your main story for the session that the players have to figure out? Is there something linear in your session that can changed to be given multiple approaches? Maybe that bridge they have to cross with the troll guarding it who they have to fight can change. Maybe they hear a story about someone in town who says the troll falls asleep if it hears soothing music played on the right instrument. Suddenly the pieces are there for your players to make a plan!

Choice. One of the joys of Dungeons & Dragons is how you can throw the same dungeon or module at three different groups and almost be guaranteed a vastly different experience. A lot of this comes from good DMing. A good DM lets what’s on the page morph and develop in response to player choices. I recommend drilling down on this: at some point in every session, your players should make a choice that has consequences that will last beyond this session. The choice to kill a villain or let them live; the choice to take one treasure only to see another disappear; to let one townsperson die in order to save another; to sneak off with a piece of the dragon’s treasure while it sleeps or to leave well enough alone. Players who walk away from the table at the end of the night feeling like what they did mattered will want to come back to that table. After all, they have to see how what they did will pan out for next time!

How to prepare: Read over what you expect the players to do tonite in the session. Look for branches in the road. Think of your game as a Choose Your Own Adventure book. If you ever read those books than you know there are sections where you would flip back to a previous page to see what would have happened had you made that choice. That is the feeling you want to elicit in your players. “One door opens, another closes” is the motto you want to live by for this. In social scenarios you can create this through player interactions with NPCs, where what they say and do can determine future relationships. In dungeons you can create this by setting up in-dungeon side quests (like whether to help free the mysterious thief from the mage’s tower) and branching paths which close off behind the players or make backtracking difficult. In a dungeon, even the question of “the door is locked, do you open it?” can feel appropriately consequential.

Below I’ve gone through the four sessions it took us to fight the Battle of Brindol and have detailed where the Five C’s came in for each session. It’s a good example, because the battle is (unsurprisingly) so skewed towards a gauntlet of combats that it becomes an excellent illustration of how to work in the Five C’s into the most restrictive of circumstances.

Session 1: A Slight Gigantic Problem

“During the battle, we will keep in touch with each of our primary forces through a four-way telepathic link I will maintain using my vast intellectual power,” Immerstal said in his deep voice, slightly accented with the intonation of old Rhest. “Lord Jarmasth will stay in the temple guarded by Xaviee, Lord of Vraath Keep...” Jarmaath began to protest but Immerstal cut him off, “for the reasons we already discussed. Tredora will stay near the final blockade to offer clerical support. Myself and Nysyries will man the Western Gates. And Aldric, damn brave fool that he is, will be riding to support our flank at the southern gate. May Iomedae and Palor watch over us all, and may the spirits of our ancestors preserve us.”

In the previous session we had a lot of conversation and conspiring, as the players came up with the battle plan that would be enacted in these sessions. As a recap: the dwarves would dig trenches and traps outside of the west gate walls to slow down the main thrust of the horde. Aldric would stay outside the south walls to watch for an anticipated second strike force to make a sneak attack there. The elves would fly over all the walls, ready to help where needed. Immerstal the Red (wizard supreme) and Nysyries would stay on the western wall to act as support. And everyone is ready to fall back to pre-planned locations in the city which have been set up as barriers and choke points meant to slow down any advancing horde if they make it through the gates.

Lord Jarmaath is commanded to stay back at the Temple, the last line of the defense. And I forgot to mention it last time, but Xaviee, a reoccuring character introduced over a year ago as part of Tywin’s campaign, was also at the council, representing the Wytchwood as the new lord of Vraath’s Keep. Finally having found his path in life, he is in staunch support of whatever the players decide to do and takes their orders to act as bodyguard for Jarmaath (as Nysyries’ player says, we don’t want to risk losing someone who has been a part of the story for so long).

In this first session, things pan out as the players expected. The main army does attack the west gate while a smaller force goes for the south. The only thing they didn’t count on was the sheer size of the horde: it’s too big to be held at the gates, but their efforts do slim it down quite a bit before it breaks through.

So where are the five C’s here? Since my players split up, I plan two big combats for each of them separately. I also match each up with a consequential check. Nysyries first has to make some checks as she wanders the wall to see if she notices something odd... some of the guards are missing, and there are grappling hooks attached to the wall! Succeeding on the check, she engages in a melee battle against three Bugbear assassins, sent to come over the wall and open the gates from within. Had Nysyries failed her check they would have succeeded and the battle would have gone bad very quickly.

Aldric, meanwhile, is ready when a platoon of hobgoblins and giants emerges from the shadows of the trees and charges the southern gate. He leads a charge in with his cavalry and has to make a series of checks to stay horsed while also engaging in a tense combat against several hill giants, a task he completes admirably (though he fails one critical check and is pulled from his horse by a hill giant and has to cut his way free before being crushed in its massive hands).

Conspire comes into play for Nysyries, who at a certain point after dispatching the Bugbears returns to the gates to see the battle is not going to be winnable. Chimera swoop down on the defenders from the skies while the endless hordes plow through the traps, losing numbers but not their speed. Giants slam boulders into the gates and Nysyries knows the gates will fall. She has to take charge and lead the defenders: what do they do next? She decides to pull everyone back to the pre-set choke points and prepare to harry the attackers as they come in. A chimera chases her from the wall and she has a narrow escape, throwing herself out of the path of its fire breath at the last moment, but maintaining her composure enough to keep leading her men back.

Conversation is wrapped up in both situations, as both Nysyries and Aldric have to keep yelling out commands to the soldiers around them and keep coordinating via Immerstal’s telepathic link what the overall battle plan will be. What they say is directly taken into account in deciding how effective their leadership is.

Two final things occur before the end of the situation. First is a culmination of a choice made ages ago, back in the woods when the party decided to save the life of a twist tuck giant. As Nysyries prepares to abandon the walls to the invaders, there is a blast of trumpet and from edges of battle a new force joins the combat: the Twist Tusk Giants, roused from their long complacency by the giant the party saved. They slam into the forces and while the gates still fall, they keep any evil giants from coming through to assist, making the subsequent section much easier.

Aldric has a choice of his own to make. He has spent the last decade of his life hunting down the beast that murdered his troop. Just as he hears the desperate call in his mind to return to the city and help defend it from the invaders he hears another cry, this one very nearby.

It is the unmistakable cry of the Behir who killed his men, the mother of the horde, Varanthian, come to join her horde in the attack. And now Aldric has to decide whether to stay and fight or retreat to the city.

Session 2: The Serpent and the Swarm

Aldric looked back to the gate. It had held, at the cost of the lives of many of the men who had ridden with him through it this morning. Night was upon them now and those men were gone. Aldric thought about the last time he’d seen Delora Zann, the brave warrior woman from Drellin’s Ferry. He wondered if she had managed to cut her way free from the giant’s hand that had held her. He thought about the way her scream of pain mingled with the scream of her metal armor bending and breaking in the giant’s closed fist. Probably, she had not made it out. The roar from the woods, louder this time, drove the thought from his mind. He looked at the men he had left. Their faces were grim, bloody. They would follow him, he knew it. They would die for him, though they didn’t know that.

“Let’s get ready to ride,” he said out loud.

The first session covered things that were basically in the original module: the giants attacking the gates with the support of Chimera. In the second session I start to change things up drastically. At this point in the original the battle becomes a gauntlet, wave after wave of enemy, with fewer and less varied waves for players who have completed main quests throughout the campaign. I get what this accomplishes: it forces the players to spend resources, spell slots, and use up abilities (not to mention hit points) before the final battle, putting them under literal siege. As far as that goes, it does accomplish its goal. But it’s really boring. I decide to mix things up a bit.

First of all, Aldric faces off, pretty much one on one, against the Behir. This is a continuation of choices made during the last session and serves the same purpose here. It also serves as Conversation. As Aldric gathers his men and races for the Behir he has both a Check and a Conversation: a check to see if he can inspire his men to do battle with the beast (which he badly fails) and a conversation with the beast herself, as the two trade barbs and banters. Aldric says he is her doom come to roost. Varanthian says she doesn’t even remember killing his troop, that’s how insignificant they are. Aldric continues to push his point, saying that what she has forgotten, she will remember in him. He shows her Blackrazor and tells her that this is the blade which will cut her down. Aldric’s conversing is so in character that I decide Blackrazor grants him haste for the battle (see? there’s that consequence I talked about). This puts him and the Behir on fairly even footing and Aldric rolls much better, ending up taking no damage by the time he has brought the Behir to 50 hitpoints. The battle nicely fills the combat requirement turning into an epic back and forth of serpent versus sword, as the Behir rips Aldric’s horse out from under him, eviscerating it and trapping the warrior inside a circle made of her body. She tries to bite him, claw him, grapple him, blast him with lightning, but with haste and his naturally defensive cavalier abilities, Aldric staves off every attempt and counters with mighty strikes of his own from Blackrazor. Where his vengeance fueled rage begins and the sword’s pervasive desire for blood takes over is not clear, but after having Blackrazor stuck in her flank and drawn along it to open a wide seven foot long gash, Varanthian realizes she is not a match for Aldric at this time and flees. Aldric looks around, realizes all of his men are dead, and begins to book it for the city’s southern gate.

Meanwhile, while all this is going on, Nysyries is still fleeing the Western gates as they buckle and break under the sheer enormity of the horde’s numbers. A Chimera swoops after her, dropping gouts of flame down around her, killing two of the city’s brave Lion Guard who rush to her aid. As Nysyries turns to fights, the gates finally give completely and hordes of goblins pour into the streets, seemingly crazed with froth foaming out of their mouths and no care being given to their own safety. They swarm over the nearest defenders, guardsmen who raise sword and shield to helplessly defend their city.

Nysyries, then, is left with a choice of her own: flee or fight? When she decides to flee towards the nearest safehouse we enter a series of exciting checks as she has to dodge blasts of flame and slashes of chimera claws as she runs, using whatever cover she can to try and aid in her dodging from this terror of the skies. She makes all but the last check, failing badly on a dexterity save from a final blast of flame just as she reaches the house... but Immerstal is waiting for her at the house and he uses his magic to ward off the flames before pulling her inside.

“What now?” he asks her, as outside the window they see the crazed horde pouring down the main road. And with that, I’m using Conspire. The player is having to make a tactical decision about how this battle will go. Nysyries decides to dig through her magical spells and pulls out Spike Growth, laying the trap across the wide road below them. The crazed horde of goblins hits the trap like mice running through a field of sharp glass. Blood and bodies soon pile up over the trap, the remaining goblins stomping the fallen deeper into the spikes as they run over them.

“Good idea,” Immerstal tells Nysyries. “It won’t hold them long, but maybe long enough to fall back.”

Just as he is finished saying this, suddenly he grips his head as a voice begins to telepathically shout at him through his maintained psychic link. Nysyries sees the tanned wizard’s face turn a little pale.

“It’s Tredora,” he says. “She says a dragon has come.”

Session 3: Flame

“You think you can do the impossible? You think you can slay me , little man? You are quick, like a mouse, but I am like the cat. I decide when and how you die. I am a god to you. You survive because I am enjoying toying with you for now, but remember that the cat eventually grows bored, and he grows hungry.”

The third session has quite the obvious Combat: The Red Dragon, Abiathrix. At first, I assume that Nysyries will leave her post and meet up with Aldric to fight the dragon together, but Aldric throws this plan off when he tells Nysyries (in character) not to interfere with his monster slaying. He (and maybe this is Blackrazor speaking through Aldric) wants Abiathrix for himself.

This is an unexpected Choice in action. While I had planned on having some Choices come up during the dragon fight for the players, I will usually favor Choices the players come up with on their own. So I run with this, letting Aldric face Abiathrix alone, which means I have to come up with something for Nysyries to occupy her time. I choose Combat, again. The reason is that I want to be able to run Abiathrix versus Aldric as a combat and I’d like to involve Nysyries in the same general principle of a fight, even if she’s not directly able to affect that battle. Putting her up against her own combatants lets me run the whole thing as one big combat, albeit taking place in two different places. It also makes jumping back and forth between the two fights more tense and dramatic.

Nysyries, therefore, splits off from Immerstal. He runs off to try and help with Abiathrix (really, this is just my way of getting an NPC out of the way so I don’t have to run his stats during the combat). Nysyries races to the next checkpoint, where a battalion of dwarves led by a female dwarven innkeeper are getting ready to face off against the oncoming horde of goblins. Nysyries joins their ranks and turns into an earth elemental, ready to be the literal wall the horde breaks itself on.

Here, I decide to mix things up a bit. A few sessions ago Nysyries came into possession of Wave, the legendary trident from the dungeon of White Plume Mountain. It’s major requirement was that she worship Poseiden as a deity and do things in his name and for his honor. She hasn’t been... highlighting this very much in her actions, and so I decide to show that the Trident means business. Right before the crazed rush of goblins reaches her, Nysyries suddenly transforms into a water elemental.

“What the actual hell?” she asks.

“You should trust more in Poseiden’s power,” Wave chastises her.

There is no further time for argument: the horde crashes into them. And for fun, I have thrown in two Ogre Howdahs from Mordenkainen’s Tome of Foes (if you don’t know them, they are big ogres carrying goblin archers in a portable watchtower on their backs).

These two combats run really well. The Checks I had planned for the Dragon battle I do away with (originally, the Dragon was going to chase both of them inside a building and then try to bring it down on top of them) and instead let them make their own checks, which they do through their own combat choices. Aldric gets into a grappling contest with Abiathrix, ultimately ending up pinned in his mouth, where he drives Blackrazor up through the Dragon’s jaw and into his brain. And Nysyries takes to her new water form nicely, forcing herself down the throat of one of the Ogres, exploding it from within. These are both done by continuing contests of Strength. So Checks are incorporated in exciting ways.

Abiathrix’s fight ends with a Conversation: Abiathrix and Aldric exchange banter as the battle comes to its end and Abiathrix dies cursing him, telling him that he will curse his soul to be drawn to his and that one day, Aldric will find his way to hell, where Abiathrix will be waiting. Then, curiously, Abiathrix turns into ash and floats away on the wind. Nysyries’ fight ends when she kills both the Ogres and the goblin horde surrounds her, too massive to overcome. She escapes the fight by diving into a sewer grate and is swept away by the tide of the sewer.

So where does Conspire come into play this session? It doesn’t directly... instead I decide to show the results of an earlier choice they made.

In the original module, the battle of Brindol is interrupted by an assassination attempt on the life of Lord Jaarmath by a goblin ninja sniper (yes, that’s really what he is). I changed this scene a bit, replacing the goblin with three drow assassins, for story reasons I’ll go into in a future post. Ultimately, though, I decide to remove the fight altogether. It’s just too much fighting in Brindol. Too much of any one of the five C’s will make a game feel stale but Combat is the easiest one to go overboard with. Dungeons & Dragon is, after all, an outgrowth of a battle game. The majority of its rules and abilities concern combat. Its greatest and most involved challenges are usually in the form of Combat. In other words, you see Combat used a lot and it is an easy answer to most situations. But I just feel like they’ve had their fill of it here, and I still have one big final combat I want to get to. So I cut this one, and make it part of Conspire instead.

During the council that preceded the Battle of Brindol, the placement of Lord Jaarmath may have seemed of little consequence, compared to discussions about things like “how are we going to fight off giants and dragons?” But Jaarmath is a target and I leave it up to the players to realize this. Mine did, and they asked that one of the many allies they’ve made throughout their adventures stay by him, in this case Lord Xaviee Domico.

So when the Drow decide to attack Jaarmath, Xaviee leaps into action, defending the Lord with all of his might and battle prowress. He wins through and the results of their conspire are now seen: Jaarmath lives!

Less fortunate is Jaarmath’s lover, the cleric Aasimir Tredora. Aldric has just finished killing Abiathrix when he senses her telepathic link get suddenly severed. Immerstal meets him shortly after and tells him to run to the last place he knows she was, the fountain of heroes in the courtyard of legends, while Immerstal stays to fight the fires that erupted during Aldric’s battle with Abiathrix.

Session 4: Battle Royale

“We cannot die. Our souls will be drawn back to him, to Azor Khul, looking down from the stars.”

The words chilled Nysyries. She glanced at Aldric beside her, hoping to see some glimmer of hope there, but the man’s face was stoic. Usually he had a joke, a jab, a snipe ready in response to anything anyone might say to him. His silence now spoke of his exhaustion, the blood on his hands of the efforts he had already spent this day. And now there were four more to kill, and they were the greatest threat of all.

The Generals of the Horde lined up before them. Koth, the Bugbear sorceror with Red Dragon blood in his veins. He had last fought them at Varath Keep, where his mastery of fire magic had only been quelled by the speed of Trakki, their monk companion, and by the counter magic of Tyrion. Both were dead now.

Next to Koth stood a female Hobgoblin, Ulwai Stormbringer. She was... beautiful. The word came to Nysyries unbidden and that more than anything made her realize the truth of it. She looked more human than beast, but the touch of Hobgoblin features lent her an exotic and wild quality. She exuded passion and danger. The storm that raged above the Courtyard of Legends was her doing, for she held in her right hand the Rod of Storms. Tyrion had spoken of its power. It had turned an entire country into a desert. Now it sparked with electric energy as Ulwai twirled it idly. She had escaped the wrath of the Ghostlord, no mean feat. She was too clever by half.

The last was unfamiliar to them, though Nysyries could guess at who it was. Saarvith was a goblin and he rode atop a great black beast. It was shaped like a panther, but there the comparison ended. Its body was a mixture of scales with fur tufting out between them. Its muscles pulsed under these scales and its maw drew in great breaths of air that pushed its chest in and out like a bellows. Green venom misted from the open mouth.

Saarvith saw her looking at him and his mount and he grimaced. “You are the one who murdered my dragon,” he said. It was not a question, though he was wrong. Trakki had done that, too. But Nysyries did not forget her own accomplishments.

“I did not kill your pet,” she said out loud, surprising herself with how calm her voice sounded. “But I did destroy your bridge.” Yes, she had escaped the clutches of the Green Dragon, Ozyrandion, and had blown up the Skull Gorge Bridge. “And I crushed the eggs of your creatures beneath my staff.” She remembered the horrible Razorspawns in the ruins of Rhest and the way their screams had reverberated through her mind. “You three will be next.”

“Don’t be so hasty,” Aldric said. “At least one of them is mine.”

Nysyries nodded. She felt calm. She always felt calm when death was closest. She knew it wouldn’t last. Soon there would be blood and screams and pain and the calmness would wash away to be replaced by the importance of the moment of battle, when every split second counted. But for now, there was a wash of calm. Because I might die here, she thought. Because this might be how I end.

Aldric let out a battle cry and rushed forward, and Nysyries closed her eyes and drew on her power, even as the sound of the storm grew louder and thunder rolled across the courtyard.

Aldric finds Tredora by the Fountain of Heroes, a fountain depicting a number of cherubs flying around old Rhestian heroes. Nysyries emerges, still in water form, from the simulated piss stream of one of these cherubs, turning back into her Dragonborn self at Tredora’s side. Tredora reveals three Drow arrows embedded in her abdomen and tells them that the poison is an insidious one, surpassing even her ability to heal it.

“But there is still one thing I can do to aid us in this war,” she says, and grips both Aldric and Nysyries’ hands. Then she channels the last of her life force into them, giving them a full heal and some of their class abilities back. Aldric regains his second wind and Nysyries her ability to transform into an elemental. Then Tredora passes beyond the reach of even magic, as she willingly gave her life in sacrifice to the cause, pouring the energy that makes up her soul into the two players.

And so it is that Aldric and Nysyries move on to the Courtyard of Legends, an open green space bordered by large multi-story homes. Here the three Dragon Lords face off against them. All of the stats are presented here.

Six or seven years ago, when I finally had a chance to play my first Dungeons and Dragons game (actually, Pathfinder) after two decades of reading the books and dreaming of having a group, my DM set up a battle that I’ve never forgotten. It wasn’t against monsters like we were used to, nor a big bad boss demon or the like. Instead it was against four adventurers much like ourselves. They didn’t rely on being monstrous or magical to fight us: they had class abilities and skills just like ourselves. The end result, which we dubbed the “Battle Royale”, was a tense life-or-death brawl, where we had to push our abilities and spells to their limit, barely eking out a victory at the end.

I wanted this final fight at Brindol to feel like that. I chose to ignore the Wyrmlord Khal fight and replace him with the three Wyrmlords, whom the players have an actual history with. And then I start working on ways to fit in the five Cs.

Combat is obvious. The whole point of this fight is to have a final brawl to the death. I spent a lot of time figuring out how to balance the fight, somewhat tricky because my party is only two level 10 players. I basically count them as four players because of their Legendary weapons and powerful abilities and went from there, using Xanathar’s guide to plan for a fight slightly above the recommended difficulty. I always aim for harder in my battles, because it is easier to turn down the heat by changing up enemy tactics to be less effective mid fight than it is to make a too-easy fight more difficult.

Conversation mostly happens early on as I have the Wyrmlords speak of strange, dark things concerning their leader, Azor Khul, and how death here will not defeat any of them. I wait to see which Wyrmlord the players seem most interested in roleplaying with and it turns out to be Saarvith, whose dragon Trakki killed earlier in the adventure. I give him more dialog, then, as he engages in back and forth with the players, until finally I run out of words to say. The main point of the conversation is to set up for the reveal later that there is more for the players to do... that they need to take out Azor Khul to truly win this war.

Checks, Conspire, and Choice all come into play to make this battle a more dynamic, cinematic fight. Here’s a rundown of how things go (and I’ll point out these three C’s along the way)...

The fight opens with Koth climbing to the top of a house and launching powerful fire magic down at the players, while Saarvith charges forward on his beast and Ulwai prepares to unleash support magic. This puts the players immediately into a situation where they need to use “Conspire,” because I’m setting up this battle as a varied affair, where each combatant is going to try to fill a different role in combat (support, front line, magic blasting). The players realize they need to come up with appropriate tactics to counter this, or they will not survive long. So Aldric charges directly at the Black Beast, using Athletics to successfully leap atop it and take on Saarvith directly as the Beast charges around the battlefield. Nysyries turns into a water elemental and immediately moves to Whelm Ulwai, trapping the Hobgoblin inside of her and shutting down her magic (as she cannot speak).

This sets the tone for the first part of the battle and gives rise to a ton of Check situations: every round, Ulwai is fighting to break free and using her rod of storms to channel electricity from within Nysyries, electrocuting her from inside. Nysyries is “checking” to keep her contained. The Beast is charging around, bucking its body, trying to knock Aldric off while he fights the monkey-like Goblin Ranger Saarvith. Aldric is “checking” to stay on top of it and avoid being crushed when the Beast occasionally rolls on the ground to smash him. Saarvith’s eagle is also flying around, dive bombing Aldric until the mercenary cuts it in half with a well timed blow. Fire is raining down on them from Koth’s fireballs (which meta-magic curve around the Bugbear’s allies), but Aldric’s boots of Lava-Walk keep him relatively safe, taking only half damage even he fails to dodge the fire.

Hopefully you can picture the cinematic qualities of this scene: Aldric atop the great beast, steadying himself to unleash blow after blow with Blackrazor, while the nimble Saarvith acrobatics around him, driving a handaxe into his armor then catching the same blade with his foot and slashing again. Meanwhile, the beast is standing up on its back legs to claw furiously at Nysyries, a giant water elemental, who holds her ground while inside of her an entire light show plays out as Ulwai unleashes bursts of lightning that stay contained within her living, watery, prison. And like something out of a Godzilla movie, magical missiles fly from the rooftop where Koth is to slam into Nysyries’ elemental form, rippling over her with concussive blasts.

If you don’t find this absolutely epic then I’m either doing a terrible job of describing it or you may be a boring person.

Eventually, Ulwai succumbs, drowning inside of Nysyries. She also pulls down the Beast, lifting it and bodyslamming it into the hard pavement with a critical natural 20 strike. I rule that this knocks even Saarvith from his mount and both he and Aldric separate. Saarvith uses his hide ability to disappear quickly from the fight, while Aldric turns to fight the Beast. By the time the Beast is dead, Aldric is hurting badly and Nysyries has finally been forced back into her Dragonborn form by the assault from Koth. They don’t get a break, though. Wyrmlord Saarvith reappears inside the house, firing arrows at them with deadly accuracy.

And here I lay out the choice: you can run for the house and make this a melee combat or retreat into hiding and turn this into a shoot out. I don’t say this directly, but the situation makes the choice clear. They cannot stay where they are.

They choose to run for the house. Blackrazor activates haste for Aldric and with this, he makes it safely inside. He is very low on health, but this is the kind of situation Blackrazor loves and with its haste, he might have a chance to survive. Nysyries, meanwhile, decides to try and take Koth out while she approaches, launching her most powerful spell, Blight, at him. Unfortunately for her, he dodges the spell handily. He takes some damage and the roof around him decays and rots even as he stands there, but then he launches his counterattack: a brutal burning hands spell that brings Nysyries to her knees taking away more than half her life in a single blow. She decides to hightail it into the house as well.

From here the battle changes immensely, becoming more like something out of a horror movie. Aldric moves from room to room in the upstairs of the house, hunting Saarvith, who keeps setting up bait-and-run tactics, charging from behind closed doors to ambush Aldric before darting away. This involves more Checks, as Aldric has to try to continually perceive Saarvith’s whereabouts. Meanwhile, downstairs, Nysyries barely gets a moment to heal herself before Koth drops down the chimney like a demented Santa and charges at her, his fists trailing flame. Nysyries uses blight again and this time the damage is incredible. Koth is obliterated in a single use of the spell, blasted into ash and dust just before he reaches her, his hands outstretched to drive fire into her.

My favorite moment of this part of the battle comes when Nysyries joins Aldric upstairs to track Saarvith, just as the goblin does a hit-and-run on Aldric and escapes by bounding on all fours into a nearby room and leaping onto the wall to await their charge. They go rushing after him only for Nysyries to pull Aldric to a sudden halt, noticing at the last moment that the floor has been enchanted with Spike Growth (a clever trick I was proud of!) Saarvith, realizing his trap has been discovered, pulls his shortbow and fires arrows at the two of them. To counter this, Nysyries uses her staff of insect swarm to fill the room with obscurring swarms of biting locusts. From this cloud of swirling darkness Saarvith bursts forth like a horror, walking along the ceiling with his feet, hanging upside down and swinging his hatchets in his hands wildly. He catches Aldric unawares, nearly killing him, and then leaps over the banister of the upstairs hallway down to the sitting room below. Nysyries and Aldric follow and the final confrontation plays out here, with Saarvith finally falling to a slice from Blackrazor.

The players emerge from the house nearly dead to discover that the Courtyard of Legends has been completely surrounded by hordes of crazed goblins.

And that’s where we will leave things this time...

#Battle Royale #DND 5e #dungeons & dragons #Red Hand of Doom #Conversion

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Can a baby's brain drive a car?

Alison Gopnik’s career began with a psychology experiment she now considers ridiculous. Aiming to understand how 15-month-olds connect words with abstract concepts (daddy = caregiver), she decided to visit nine kids once a week for a year. The then Oxford graduate student would record everything they said as part of her dissertation. “It was absurd for a million reasons,” says Gopnik, holed up on a winter Friday in her office at the University of California at Berkeley, where she is a professor of developmental psychology. “If a childhad moved away, if there weren’t any take-aways after the year, or any number of things, all that work would have been gone,” she says, before adding, “I would never allow a student of mine to do anything like that today.”

Though her experiment didn’t solve any language-acquisition mysteries, it did overturn her assumptions about childhood learning and intelligence—and it altered her career path. Now her research has drawn the interest of artificial-intelligence scientists who want to adapt her insights to their machine-learning algorithms. What she learned about kids’ smarts while a grad student still holds sway—for her field and possibly theirs. “Instead of thinking about children as these kind of starter adults, I realized they were profoundly different,” says Gopnik, now 62, and with her own grown children and grandchildren. “The way they use words, the meanings they express, the way they express them—none of it matched how adults think or speak.”

Today, Gopnik oversees her own cognitive development lab at UC Berkeley, and is the author of several books on early childhood learning and development. She’s a TED alum, a Wall Street Journal columnist, and has attained that singular intellectual height—crossing over into pop culture, by appearing on shows like Good Morning America and The Colbert Report. Gopnik’s message: Adult cognitive primacy is an illusion. Kids, her research shows, are not proto-adults with fruit-fly-like attention spans, but in fact our occasional superiors. “Children, even very young children,” she says, “are in many ways smarter, more inventive, and better at learning than adults.”

The reason: size and shape matter. Research shows that the bulk and structure of a child’s brain confer cognitive strengths and weaknesses. Same goes for adults. For example, a developed prefrontal cortex allows grown-ups to focus, plan, and control our impulses: valuable skills that let us write magazine articles and avoid jail time. But evidence suggests a developed cortex can also make it hard to learn new or surprising concepts and can impede creative thinking. Toddler brains, constantly abuzz with fresh neural connections, are more plastic and adaptive. This makes them bad at remembering to put on pants but surprisingly good at solving abstract puzzles and extracting unlikely principles from extremely small amounts of information.

These are handy skills. It turns out a lot of smart people want to think this way—or want to build machines that do. Artificial-intelligence researchers at places like Google and Uber hope to use this unique understanding of the world’s most powerful neural-learning apparatus—the one between a toddler’s ears—to create smarter self-driving cars. Coders can create software that beats us at board games, but it’s harder to apply those skills to a different task—say, traffic-pattern analysis. Kids on the other hand, are genius at this kind of generalized learning. “It’s not just that they figure out how one game or machine works,” says Gopnik. Once they’ve figured out how your iPhone works, she says, they’re able to take that information and use it to figure out the childproof sliding lock on the front door.

Cracking the codes of these little code breakers wasn’t Gopnik’s original career plan. As an undergrad, she began studying life’s big problems, toiling in the field of analytic philosophy. Back then, none of her peers pondered the thinking of kids. But Gopnik became convinced kids were key to unlocking one of the oldest epistemological queries: How do we know stuff about the world around us? Borrowing the brain-as-computer model, Gopnik sought to ask questions about the software running this little human machine, allowing it to perform complicated functions. “Kids are the ones doing more generalized learning than anybody else,” she says, “so why wouldn’t you want to understand why they’re so good at it?”

Fields like evolutionary biology, neuroscience, and developmental psychology suggest that we simply have different cognitive strengths and strategies at different stages of our lives.

The advantages of installing a preschool perspective into machines, she says, can be understood by considering two popular, but opposing, AI strategies: bottom-up and top-down learning. The former works the way you expect: Say you want a computer to learn to recognize a cat. With a bottom-up or “deep-learning” strategy, you’d feed it 50,000 photos of furry felines and let it extract statistics from those examples. A top-down strategy, on the other hand, requires just one example of a cat. A system using this strategy takes that single picture, builds a model of “catness” (whiskers, fur, vertical pupils, etc.), and then uses it to try to identify other cats, revising its cat hypothesis as it goes, much like a scientist would.

Children employ both methods at once. They’re good at figuring out things and extracting statistics, says Gopnik. And they use that data to come up with new theories and structured pictures of the world. Successfully distilling both knowledge-building approaches into algorithms might produce artificial intelligence that can finally do more than just beat us at Go and recognize animals. It might also, Gopnik hopes, change outmoded ideas that we all seem to share about intelligence. “We still tend to think that a 35-year-old male professor is the ultimate goal of human cognition,” she says, “that everything else is just leading up to or deteriorating from that cognitive peak.”

That model doesn’t make sense for a variety of reasons. Studies from fields like evolutionary biology, neuroscience, and developmental psychology suggest we simply have different cognitive strengths and strategies at different stages of our lives. “Children will have one set of ideas about how people and the world work when they’re 2, and then another set when they’re 3, and another set when they’re 5,” says Gopnik. “It’s like they’re actively trying to think up a coherent picture of the world around them, and then constantly changing that picture based on the observations they make.”

That frenetic hypothesis formation—and ongoing reformation—isn’t a bug; it’s a highly desired feature. And if we want our machines to possess anything approximating human intelligence, maybe we should think about giving them a childhood too.

Your brain from cradle to rocking chair

We’re born helpless and dumb. As we mature, experience and schooling teach us useful things, and we get woke. Then, year by year, we slip back into feeblemindedness. That’s the picture most of us have of intelligence. Unfortunately, it’s dumb. Research reveals that each period of cognitive development offers learning strategies as well as trade-offs. It’s that combo of aha and duh that actually makes humans truly intelligent.

Infant: 0-18 months An infant brain forms 1 million new neural connections each second, helping her to develop emotions, motor skills, attachments, and working memory. At 11 months, she can already form hypotheses about how the world works. At 18 months, she has a sense of self.

Toddler: 2-5 years When it comes to learning abstract concepts, preschoolers beat adults. At 4 years old, 66 percent of calories are headed to her brain—fuel for the exploration and creative thinking that define this period. By the time she finishes preschool, her gray matter has quadrupled in size.

School-age: 6-11 years The brain of a 6-year-old has reached 90 percent of its adult size. Neural pruning ramps up as the brain discards unused connections. The prefrontal cortex starts to develop more, resulting in longer attention spans, and an increased reliance on language and logic to learn.

Adolescence: 12-24 years Adolescence marks a return to the neural flexibility and plasticity that characterized her preschool years. But she’s not living in a protected context. A reliance on the amygdala—a center for emotions, impulses, and instinctive behaviors—might result in trademark “risk-taking.”

Adulthood: 25-59 years By the time she reaches adulthood, prefrontal control is at its peak. A developed frontal lobe helps her plan for the future and control her impulses, but there’s evidence that creativity and cognitive flexibility takes a big hit. Learning anything surprising? Also a lot harder.

Senior: 60+ years Bring on short-term-memory loss, neurodegenerative diseases, and declines in conceptual reasoning. Still, other cognitive abilities continue to grow. Skills involving vocabulary, math, verbal comprehension—what’s known as crystallized intelligence—are among them.

Bryan Gardiner is a contributing editor at Popular Science. He last wrote about ubiquitous computing.

This article was originally published in the Spring 2018 Intelligence issue of Popular Science.

Written By Bryan Gardiner

#Technology

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zipgrowth · 7 years ago

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The 5th ‘C’ of 21st Century Skills? Try Computational Thinking (Not Coding)

For better or worse, computing is pervasive, changing how and where people work, collaborate, communicate, shop, eat, travel, learn and quite simply, live. From the arts to sciences and politics, no field has been untouched.

The last decade has also seen the rise of disciplines generically described as “computational X,” where “X” stands for any one of a large range of fields from physics to journalism. Here’s what Google autocomplete shows when you type “computational.” (You can try it for yourself!)

But the big question is: Does current K-12 education equip every student with the requisite skills to become innovators and problem-solvers, or even informed citizens, to succeed in this world with pervasive computing?

Since the turn of this century, the “4C’s of 21st century” skills—critical thinking, creativity, collaboration and communication—have seen growing recognition as essential ingredients of school curricula. This shift has prompted an uptake in pedagogies and frameworks such as project-based learning, inquiry learning, and deeper learning across all levels of K-12 that emphasize higher order thinking over rote learning. I argue that we need computational thinking (CT) to be another core skill—or the “5th C” of 21st century skills—that is taught to all students.

There is growing recognition in the education systems around the globe that being able to problem-solve computationally—that is, to think logically and algorithmically, and use computational tools for creating artifacts including models and data visualizations—is rapidly becoming a prerequisite competency for all fields.

In 2012, the U.K. national curriculum began introducing computer science (CS) to all students. Singapore, as part of its “Smart Nation” initiative, has labeled developing CT as a “national capability.” Other countries, from Finland to South Korea, China to Australia and New Zealand, have launched large-scale efforts to introduce CT in schools, as either a part of new CS curricula or integrated into existing subjects. Here in the U.S., former President Barack Obama called on all K-12 students to be equipped with CT skills as part of an “Computer Science for All” initiative in 2016. Most emergent efforts in the US involving CT are currently part of CS curricula, although CT is increasingly seeing integration into STEM (especially science) learning.

But before diving into what CT in K-12 may look like, let’s be clear that these efforts do not mean that every child is expected to become a computer scientist. Just as basic literacy in math and science are considered essential for all children to understand how the world works, education must also address the development of knowledge and skills pertaining to computing, which is now so integrally intertwined with every profession.

[Computational thinking] is the thinking skills that are employed in understanding a problem and formulating a solution before coding

What Is Computational Thinking?

So, what exactly is computational thinking, and what is its relationship to CS and programming (coding)?

Simply put, CT is “thinking (or problem solving) like a computer scientist.” It is the thought processes involved in understanding a problem and expressing its solutions in such a way that a computer can potentially carry out the solution. CT is fundamentally about using analytic and algorithmic concepts and strategies most closely related to computer science to formulate, analyze and solve problems.

Like general thinking skills, CT is a bit like leadership—hard to define, but you know it when you see it. While many people associate it with concepts like programming and automation—which are all core parts of computer science—educators and researchers have found it easier to operationalize it for the purposes of teaching as well as curriculum and assessment design.

That means breaking down CT skills into its component parts, which include concepts like logic, algorithms, patterns, abstraction, generalization, evaluation, and automation. It also means approaches like “decomposing” problems into subproblems for ease in solving, creating computational artifacts (usually through coding); reusing solutions, testing and debugging; iterative refinement.

And yes, it also involves collaboration and creativity! And furthermore, it does not need to involve a computer.

If all that sounds a bit wonky, don’t worry. Like any skill, CT is best taught and learned in context, and embedded into class subjects. For example, analytical and logical thinking can be fostered through puzzles and word problems that require learners to engage in these crucial aspects of CT. As a matter of fact, problems involving such logical argumentation and logical thinking can be tackled as part of language arts, in addition to mathematics or computer science.

Coding is an excellent, fun, and useful context for developing computational thinking skills. But it is not the only way. Here are some ideas for fostering CT in subjects. Some are unplugged while others would benefit from involving coding. Teachers may recognize many of the non-programming activities as things they already do!

Language Arts

Use logic to put together a jumbled story in correct sequence (younger grades)

Identify patterns for different sentence types and rules for grammar

Use first-order logic to arrive at conclusion based on given facts

Construct social networks to analyze stories

Program a story with alternate pathways (“Choose your own adventure”)

Mathematics

Model functions in algebra through programs (compare them to functions in programs)

Write an algorithm (or precise sequence of steps) on how to do matrix multiplication or how to solve a quadratic equation

Use decomposition to solve word problems

Express generalizations (as algebraic representations) by identifying patterns

Science

Do a species classification with explicit “If-Then” logic (younger grades)

Build a computational model of a physical phenomenon

Instead of playing with or manipulating pre-developed software simulations of scientific phenomenon, create (program) computational models and simulations to study and interrogate phenomena

Social Science

Study data and Identify patterns / trends in wars and other historical events

Create visualizations of these patterns and trends

Create a simulation to study relationships in social science phenomena such as women’s education and health

Create models for social systems, or social networks, or social choice.

Teachers may recognize some of the non-programming activities as activities they already do! Indeed, many activities invoke the same thinking skills without being labeled CT. The idea is to be more conscious of explicitly making the CT connection and call such problems out as those with possible automated and computational solutions, or incorporating programming tools in such activities.

Common Misconceptions About Computational Thinking

...let’s be clear that these efforts do not mean that every child is expected to become a computer scientist.

One popular assumption about CT is that it is the same as coding. That’s not quite accurate. While coding is a popular vehicle to teach CT, computational thinking is much more than programming. It is the thinking skills that are employed in understanding a problem and formulating a solution before coding. (Also bear in mind coding need not necessarily be the end product of a CT process.)

Few would challenge that coding is a popular and effective vehicle for learning and applying (and hence teaching and assessing) CT in K-12. It’s important to remember, however, CT is the process of problem analysis and problem decomposition that precedes (in addition to happening during) coding and programming.

CT involves students asking and answering questions like: Can this problem be better, or more easily, solved by a human or a computer? Is there a pattern between this problem and similar problems we have tackled before? How can data best be organized to solve this problem? How can I create a general solution that works for a range of inputs? What is a step-by-step procedure I can articulate to solve this? What computational strategies might be employed? What are the limitations, trade-offs and constraints related to solving this problem?

Additionally, CT should also not be confused with “digital literacy,” which is often the “technology” subject in schools that focuses on how to use software, digital tools, and the internet. CT is not about how to use technology; rather, it lifts the hood on how digital solutions are designed using computational tools.

Preparing teachers to teach CT is a key task that schools need to take on as a first step. Teaching CT in the context of their disciplines for disciplinary subject teachers will have the added benefit of equipping them to make connections that they can then build on. Access to curricula and assessments, teacher professional development, best practices for teaching CT, and most importantly, becoming part of a community of educators are as important as ever to bring this vital 21st century competency to all children.

To learn more, you can also watch my talk, “Computational Thinking: the ‘5th C’ of 21st Century Skills.”

The 5th ‘C’ of 21st Century Skills? Try Computational Thinking (Not Coding) published first on https://medium.com/@GetNewDLBusiness

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mathematicianadda · 5 years ago

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(META) Concrete thinkers, incapable of metaphor, are gate-keeping mathematics and eroding its most powerful property: abstraction.

Earlier today, I posted about the fascinating similarity between fractals and logarithmic functions. Though it stated in the first line that it resided in the conceptual realm, a boo-boo w/ a metaphor I used got the post flamed by a literalist. I deleted it out of cowardice. I shouldn't have. Whoops. I'm not wrong to connect the two concepts. When I get better in these fields' Algebras*, more will be written on this. But it indicated a larger problem...

In Lex Fridman's podcast w/ Grant Sanderson, creator of 3Blue1Brown on YouTube (link below), he discussed 3 types of mathematicians: the puzzle-solvers, the physicists (broadly speaking here...), and those who "love abstraction and the power of generality." Certainly, this list is incomplete, but in a way that proves my point here. Throughout history, the mathematical greats who invented our studies in school, the Newtons and Eulers, were *wizards* of abstraction. Evidenced not only by their discoveries - take calculus, for example; the study of the behavior of infinitesimals - but by their prolific generations in disparate domains like Great Literature. Chock-full of metaphor and analogy, these thinkers thought deeply and solved even bigger problems. Through generality, they invented the frameworks our bachelor and grad degrees. They are our revered ancestors.

In the early 20th century, Abstractionists like Turing, Goedel, and the analytical demigod John von Neumann, trail blazed computational science. They needed insanely computationally complicated equations solved, so dammit, they put theirs minds to work. Using what they had already grasped, broke new ground via abstraction. We're indebted to the pioneer-class. They used their heads, drawing on intuition, the pattern-recognition software innate to homo sapiens.

Since the mid-1970s, it seems, (though cannot be verified via a gate-keeping function known as "peer review", check out Game Theory on Wikipedia for more information) that our technological prowess, the empirical furnace that has been alight since the dawn of the 17th century, has been burnt down to embers. Occasionally, we see a noteworthy digital innovation from the Valley. But outside of the strictly IT universe, astonishingly little. We go to college, then grad school, then some PhD program to learn complicated theories about complicated things so that we can handle minutia. Everything seems disparate because each course takes the top-down approach. We start at such a high level that half the class gets 65% on the first exam and drops out. The tech- or research-bound students are starving for some application, but the semester ends before that section of the textbook is covered. It almost seems malicious. The pattern-recognition software I referred to works from the ground up. It's quite clear for those familiar with psych and neuroscience. So if we are always fed the abstraction, our grass-roots, evolved, intuitive brains have nowhere to go with it. We can't perform the abstraction on our own, as they we're not allowed to have access to that part of the toolkit. We go into the workforce with a litany of equations our brains have vaguely mapped to {insert technical field here.} Then we wind up in sales jobs to pay the bills. In Business Schools (where I come from), it's even worse. They don't even apply calculus (dare I mention stochastic calculus or Brownian motion...spooky!) in economics class until grad school because they think our tiny Microsoft Excel brains would explode. For a concrete example here, it took me three years after college to the connect the dots on 'derivative', the tool of calculus, and 'derivative' the financial security class most known for its hand in 2008.

In any domain, when things begin to fall into place, divergent from complexity and into alignment, we find emergent simplicity. Our ancestors called it discovery, "innovation" better fits millennial vernacular. When things continue become increasingly muddled and complex, it's called stagnation. Stagnation in the Information Age no less. As a 24-year old debating a future in an expensive and unproductive graduate program or my soul's slow death in Big Corporate, I truly hope momentum will change on this one. Lets's ask more questions, make more mistakes, make more irresponsibly logical leaps (when the downside to said leap is low), do less incremental improvement, and math the s*** out of our future. Instead of worrying about today's hyped problem like the Middle East, climate change, {pick your favorite}, perhaps we could...maybe...just maybe...solve them? Let's use this beautiful, logical, intensely rigorous toolkit we've been gifted by our ancients, MATH, to solve the problems of the future.

PS - Please tear apart my ideas if you'd like. But, if you flame me ad-hominem style, you're just proving my point on this...gate-keeping ruins math.

_____

* Algebra is a anglo-bastardization (hope this isn't a swearword that get's me deleted) of 'al-jabr,' meaning 'bone-setting,' literally referring to how we move the 'bones' around on paper. Thank god the Arab world kept the mathematical lamp burning throughout the European Dark Ages. Why don't the literalists explain the meaning of this word...ever? Not even in high school? Because they take things for granted and don't read.

**I didn't make the mistake of apologizing for my learning issues in this post, unlike its predecessor. If you're still reading this, you're not the type to idiotically flame something thought out Reddit-style. Many mathematical greats have had issues in the over-structured, 100 equations in 30 minutes-classroom setting. Two examples are Albert Einstein and John Nash. The former worked in a patent-office because 1900s Barvaria didn't like that he was scatter-brained (or that he was Jewish; over-structured societies are more prone to racism, also known as tribal affinity); the latter, lived his 30s thru 70s deluded by the menacing condition of Paranoid Schizophrenia. The chiding he received in elementary, secondary, and university-level academia played a significant role in his social disconnect. See Isaacson's Einstein and Nassar's A Beautiful Mind to learn more. I'm not suggesting that I possess a mind bearing an ounce of resemblance with these legends, or any others. What I am suggesting, however, is that there are at least a few greats among us who are being crowded out of our institutions, and given an "ADHD"/"Dyslexic"/"Aspergers" diagnoses for their trouble. Why do we continue to call bright kids with learning superpowers 'learning disabled'?

*** Check out Lex Fridman's phenomenal podcast. Here's the link to the episode w/ Grant Sanderson, creator of 3Blue1Brown; one of the few who understand the power of intuition in mathematics.

https://lexfridman.com/grant-sanderson/

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foodoliplife · 6 years ago

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What’s Really Happening with Visualize Mathematics

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The One Thing to Do for Visualize Mathematics

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Hearsay, Lies and Visualize Mathematics

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The contents of this page haven’t been reviewed or accepted by the University of Minnesota. This page includes a list of libraries and tools in a particular category. More info about applet.

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If you don’t have a good grasp of the fundamentals, then you likely feel precisely the same way. Simply take the first couple of minutes to plan the structure of your essay which will help save you time whenever you are delving into meaty components. There are a couple of unique ways I would answer this question based on how you truly plan to compose this story.

Quite a few factors contribute to finding the appropriate educational fit. At this time, it may make sense to think about the chance of a negative outcome. It is not as obvious how to illustrate the cell growth.

There are a lot of factors that promote degree of curliness. The most attractive thing concerning this math learning platform is it caters to the diverse needs of unique learners by providing differentiated learning experiences according to someone’s proficiency level and financial backgrounds. Mathematical ideas are often accepted dependent on deductive proofs, while ideas in different sciences are by and large accepted dependent on the accumulation of several diverse observations supporting the idea.

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Magic Squares are likewise a fantastic way for children to enhance their addition skills employing a group of addends, three whole numbers in an equation. If you open a worksheet file from a preceding version of the item, any expressions which use show or plot should be updated. To find the poisonous bug, they must first find the answers to each of the subtraction problems.

At present there’s no sign that the counting problem of Su Doku is as simple as NP. Some numbers are extremely mysterious. Look out for these errors.

On the 1 hand, you could choose a area of math which has an esoteric-sounding name and decide on an open problem in that field which seems interesting. As most kids enjoy solving puzzles, engaging them with completely free on-line jigsaw puzzle games is a significant idea. This memory math game is extremely interactive.

So rather than infinitely smaller slices, you’re going to be dealing with infinitely smaller surfaces! If you are searching for 3d shape worksheets then you have discovered the best location. Drawing a photo of a 3 dimensional cube on a two dimensional surface is just as quick.

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To seek out the help topic related to a specific feature of the software working with the integrated help, simply click the help button assocated with the feature and get immediate support or click the context sensitive help button from the primary tool bar and click on any point at which you would like assist. In order to keep track of your progress it’s crucial to setup an account and have Cookies enabled. Red in my case is to create the online usage stick out on a huge screen.

Try out NOT to guess, figure out the equation of the path from the info you’re given. Included within this very first step is also highlighting the vital sections of the problem that will assist you to solve it. Our very first step is to visualize the issue.

And by looking into all the probable features of graphs in Excel we developed a means to automate this sort of visualization tooyeah! In the previous example, it is 5. If you are conversant with how to view them, you will observe that they supply you with a wonderful stereo view of the 3 dimensional model.

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