Missing "The Future"

[Eldan]

To me Donnadogsoth is the worst kind of stupid. The stupid that thinks he's smart.

You all would do better just ignoring him.

I find it fascinating, though.

[Donnadogsoth]

I never claimed to be smart, but I do claim to be on to something. This “something” is associated from what I have read with the word “principle” and examples of it in math are doubling the square and the Pythagorean theorem, in physics universal gravitation, in economics infrastructure, in statesmanship the general welfare, in metaphysics sufficient reason, and in art the sublime.

I am looking for a definition that explains all of these things, but in this thread I have submitted only the physics and mathematical “somethings” and in return received examples from ecology, neuroscience, and genetics, and someone mentioned something about “chaos theory” whatever exactly that is. I am not sure that these referenced things fit into the inchoate definition of “principle” which motivates me to speak of them, though it seems likely (if we're going to roll %) that some of them do.

You help me: what is the commonality between all I have referred to in my first paragraph above, and does that “something” cohere with the examples that you others have helpfully given?

[Perch]

We humans suck and they'll corrupt any and all forms of tecnology for evil, twisted and nefarious reasons. Just look at the airplane, atomic studies and artificial inteligence.

Look at this: https://www.google.com.br/amp/s/www....chatbot-racist humans suck and anything we make will also suck by extension.

[Wardog]

For other "major discoveries of the 20th C that fundamentally change our understanding of our world" I'd add "plate tectonics".

And for technology, the laser and GPS instruments that allow us to measure it in realtime.

stuff

Everything that has been listed seem to be "major discoveries about the nature of life, the universe, maths, etc".

I can't see what is the common feature of your "principle" that isn't shared by the others.

Can *you* explain what it is that sets them apart?

[Tvtyrant]

I never claimed to be smart, but I do claim to be on to something. This “something” is associated from what I have read with the word “principle” and examples of it in math are doubling the square and the Pythagorean theorem, in physics universal gravitation, in economics infrastructure, in statesmanship the general welfare, in metaphysics sufficient reason, and in art the sublime.

I am looking for a definition that explains all of these things, but in this thread I have submitted only the physics and mathematical “somethings” and in return received examples from ecology, neuroscience, and genetics, and someone mentioned something about “chaos theory” whatever exactly that is. I am not sure that these referenced things fit into the inchoate definition of “principle” which motivates me to speak of them, though it seems likely (if we're going to roll %) that some of them do.

You help me: what is the commonality between all I have referred to in my first paragraph above, and does that “something” cohere with the examples that you others have helpfully given?

They are all things you believe in and understand. That is the connection between those things.

Art's relationship to the "sublime" is as subjective a preposition as is possible, general welfare statesmanship is a particular ideology, and the first two are mathematical proofs. The common element between those things is you.

James' definition of pragmatism is a principle (under your definition of the word) that I suspect you would not agree with but I would. A person believes things not based on their fidelity to reality but their value to the believer, and is incapable of perceiving the difference.

[Lvl 2 Expert]

and someone mentioned something about “chaos theory” whatever exactly that is.

We have beautiful weather prediction models, very complete, yet we can't predict the weather if us staying dry depends on it. And that's because if you take a great weather model, and you run it several times with just slightly different starting conditions, you get several very different results just hours down the line. That's how weather works, it turns out. You've probably heard that line about a butterfly flapping its wings causing a hurricane from about a dozen different movies. Well, this is what it was trying to say. It's the polar opposite to say what happens when you pour alcohol into a glass of water and stir. That interaction has a very predictable outcome, entropy dictates the molecules will mix, and the universe often doesn't have a good reason to go against entropy.

There are of course more areas where this same principle applies. Think social studies, the right riot at the right time can make a difference of several fallen governments. Would World War One have happened if the guy driving the archduke hadn't gotten lost? Financial systems. And of course dinosaur cloning research. Life will find a way. Chaos theory is the branch of mathematics that tries to codify and make sense of this kind of interactions, and then use them. Excession mentioned cryptography (just by the words he mentioned I can tell he knows more about it than I do). A good encryption has chaotic properties. If you take a traditional coded message using a code word and someone guesses the word almost right you get an almost readable message, which can help you figure out its meaning or the real code word. If you guess the key to a really good encryption algorithm almost right the decoded message will still be scrambled garbage.

I'm not a mathematician either (I'm in applied pharmaceutical research with a focus on drug release and delivery solutions, still not sure if say an idea like using targeted drug containing nanoparticles could count as a discovered principle), but especially that last application seems to be pretty big right now.

[S@tanicoaldo]

Is stuff like Higgs boson, advances in prosthetic limbs, magnetic resonance imaging, efficient electrolysis, functional neuroimaging, the four quark particle and many species and animal discoveries pretty big name changes in modern science?

Are we just going to ignore that?

[jayem]

Is stuff like Higgs boson, advances in prosthetic limbs, magnetic resonance imaging, efficient electrolysis, functional neuroimaging, the four quark particle and many species and animal discoveries pretty big name changes in modern science?

Are we just going to ignore that?

Probably not when combined with the stuff that's happening and will get the prizes in 20 years time.
But there is a bit of a Morton's fork where if it's either not practically useful (yet, because it's new) or is just a final iteration of an earlier discovery that's crossed a threshold.

E.g being deliberately harsh and unfair

Spoiler

Show

Higg's was proposed in 1964, in some senses the LHC is 'just'* a bigger what they had there in 57.
MRI dates back to the 70's
The tetraquark is just another thing in the meson, hadron sequence, cool but a bit like the difference between Columbus and Hudson.
Efficient electrolysis and Better phrosphetic's have the weaselly words in the name.
Quite a few of the species, we've really known about it's just the separation (the last I saw was a subset of Siberian Tigers).
Functional neuroimagery is just an application of improvements to MRI (and similarly earlier technology).

*there is an awful lot hiding behind that just, the collisions are 6 orders of magnitude bigger.

[Frozen_Feet]

The problem here is not that Donna hasn't given a working definition of "principle". They did, just one page ago:

So, that's my understanding of a principle: a thought-object or idea resulting from the working-through of an ontological paradox (such as the the problem of generating a second square double the area of a first square).

The problem here is that they have not pointed out which examples fit, which now has been proven to be because they can't. Like I surmised, they plain do not know enough to evaluate the examples, as best evidenced by them not knowing what Chaos Theory is.

[Donnadogsoth]

The problem here is not that Donna hasn't given a working definition of "principle". They did, just one page ago:

The problem here is that they have not pointed out which examples fit, which now has been proven to be because they can't. Like I surmised, they plain do not know enough to evaluate the examples, as best evidenced by them not knowing what Chaos Theory is.

Can you point out which examples fit my definition?

[Grey_Wolf_c]

Can you point out which examples fit my definition?

Can you? Because I fail to see how doubling the area of a square is an ontological paradox of any description.

On the other hand, the theory that addresses that some systems have effects whose impact is orders of magnitude larger than the difference between its causes is, by any definition I can imagine, and ontological paradox.

GW

[Zen]

Has the potential for human potential to be expressed been equally apportioned across all time and space? Did the average individual in ancient China have much in the way of opportunity to become educated and think? What about a Paleolithic individual? Did they have any opportunities for thought and education? So, there is a progression of increase of potential, chiefly embodied in the history of the West, whereby individuals have increasingly had the opportunity to become educated and think, and so make discoveries of all sorts.

Ewww, do you know how racist and western-centric this is? Besides wasn't the gunpowder created in ancient China? How can you top that?

[Excession]

The problem here is not that Donna hasn't given a working definition of "principle". They did, just one page ago:

The problem here is that they have not pointed out which examples fit, which now has been proven to be because they can't. Like I surmised, they plain do not know enough to evaluate the examples, as best evidenced by them not knowing what Chaos Theory is.

For me a big part of the problem is that the definition doesn't make sense. Initially I thought that was because I had the wrong meaning for "ontological paradox" but taking that as "something that seems impossible but obstinately exists anyway" hasn't helped much. Doubling the area of a square is just a geometry problem, right? There's maths there with square roots and algebra if you want to get into that, but isn't the solution just to cut the second square along both diagonals and arrange in the obvious manner? If that's supposed to be meaningful I don't see why. They used to print harder problems on the back of matchboxes when I was a kid.

I was hoping for a better explanation from Donnadogsoth, but at this point I'm not expecting one.

[Donnadogsoth]

Can you? Because I fail to see how doubling the area of a square is an ontological paradox of any description.

On the other hand, the theory that addresses that some systems have effects whose impact is orders of magnitude larger than the difference between its causes is, by any definition I can imagine, and ontological paradox.

GW

It's a paradox because its solution is impervious to rational magnitudes and requires non-deductive creativity. So long as one looks at it in terms of counting numbers or even algebra it is insoluble. One can cheat and look up the solution, of course, but to discover it oneself, as through being questioned as in the Meno dialogue, is to demonstrate a quality of creativity that no lower animal possesses. It's that quality that I attach to "principle", distinguishing it from an arbitrary axiom, and for which I hunt amongst these candidates.

I'm not sure that "small things can have big consequences" has this sort of quality. Venomous spiders spring to mind.

[Chen]

It's a paradox because its solution is impervious to rational magnitudes and requires non-deductive creativity. So long as one looks at it in terms of counting numbers or even algebra it is insoluble. One can cheat and look up the solution, of course, but to discover it oneself, as through being questioned as in the Meno dialogue, is to demonstrate a quality of creativity that no lower animal possesses. It's that quality that I attach to "principle", distinguishing it from an arbitrary axiom, and for which I hunt amongst these candidates.

I'm not sure that "small things can have big consequences" has this sort of quality. Venomous spiders spring to mind.

Im pretty sure no lower animal could solve that algebraically either though. I mean creativity no lower animal posses is an extremely low bar. Just plain reading falls into that category.

[Grey_Wolf_c]

It's a paradox because its solution is impervious to rational magnitudes and requires non-deductive creativity. [...]
I'm not sure that "small things can have big consequences" has this sort of quality.

So a trivial problem you can solve with a compass and a straight edge is somehow "a paradox" but a problem equally "impervious to rational magnitudes and requires non-deductive creativity" and that can furthermore only be partially approached with advanced mathematics and a lot of supercomputer time is not. Special pleading at its best. But then, that's really Donna in a nutshell.

GW

[Fawkes]

Ewww, do you know how racist and western-centric this is? Besides wasn't the gunpowder created in ancient China? How can you top that?

That's a whole other can of worms that it's best not to open with Donny D. Instead:

Since this is in the "Media Discussions" sub forum, how about more suggestions for fiction with futuristic (instead of "alternate") settings?

It is sort of fascinating how many of our cultural 'future' touchstones have been surpassed by the present.

Fahrenheit 451 was originally set in the future of 1960 - later editions pushed it back to 1990 and now 2022.

1984 was a vision of the future, written in 1949.

The voyages in Lost in Space take place in 1997 - the same year as Terminator 2's Judgment Day Snake Plissken's Escape from New York, and the first Guy Fawkes day in the original V for Vendetta.

Then we passed 2001: A Space Odyssey, the birth of Astro Boy (2003), Timecop (2004), and just so many video games set in the early 2000s.

Then in 2015, we passed the 'future' from Back to the Future 2.

Blade Runner is coming up next: the original film took place in 2019. We're still a long ways off from Star Trek and Buck Rogers, though.

[Excession]

Fahrenheit 451 was originally set in the future of 1960 - later editions pushed it back to 1990 and now 2022.

Perhaps Fahrenheit 451, like fusion power, is always 10 years away.

[Ramza00]

[This is mostly addressed at the OP even though he barely participated in his own thread and other people went and expanded it.]

The sense of wonder we have as children can't be accessed in the same way as adults, but it still can be accessed, we just merely have to learn a different way to access it.

Yorokobe Shounen (Rejoice, Boy / Young Man)

[Earlier in the scene, a young man is talking to a priest about what his wish is, and he wishes to be a superhero, a literal champion of justice.

Differing from fighting for the sake of others (altruism) or oneself (glory) as a hero, those who hold the concept of being a hero of justice will fight for the concepts of benevolence, justice, loyalty, and love in which they believe.

Aka literally a Power Ranger.

Well the young "hero" is about to enter into a "Holy Grail War" that will have the possibility of turning the city into a literal hellscape of war.]

• Kirei Kotomine: "Rejoice, boy. Your wish will finally come true."
  The priest says, as if declaring an oracle.
• Shirou Emiya: "What are you saying all of a sudden?"
• Kirei Kotomine: "You should know. Your wish will not come true unless there is a clear evil. Even if it is not something you approve of, a superhero requires a villain to defeat."
• Shirou Emiya: "---------------!"
• Shirou Emiya's inner thoughts / monologue: I feel like everything has turned black. The priest said it. The greatest wish and the ugliest wish I have are the same. …Yes, the desire to protect something… …Is, at the same time, none other than the wish for something to violate it
• Shirou Emiya: "-------------You..."
• Shirou Emiya's inner thoughts / monologue: But there's no way I'd wish for something like that. I don't remember a moment when I've wished for that. Such an insecure wish… …Just means the target ideals are inconsistent. But the priest says as if to pierce my heart,
• Kirei Kotomine: "Good thing you have an enemy now."
• Kirei Kotomine: "No, you do not have to gloss over it. Your worries are normal for a human being."
• Kirei Kotomine:
• The priest smiles.
• Shirou Emiya's inner thoughts / monologue: "---------!"
• Shirou Emiya's inner thoughts / monologue: I shake off the priest's words and walk to the door.

Science Fiction at its core is the exploration of the Unknown for it deals with

1) What Could Be

and

2) What Will Be

And through 1 and 2, two different forms of perception that deals with pattern recognition, you explore two different forms of perception 3) What is happening now, and 4) What happened earlier / What Was.

Science Fiction can also explore what we value and not just our perceptions.

But Good Science Fiction has a sense of wonder tied to it, for wonder is the thing that links different styles of perception and different styles of assigning value to things, concepts, ideas, objects, etc into a unified whole.

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But wonder does not have to come from a single place. It does not need "space" to have a sense of wonder, a sense of the future, I would argue some of the earliest sci fi stories such as The Modern Promethesus (Mary Shelly, arguably the first modern sci fi novel this is arguably) and L'Ève future / The Future Eve / Tommorrows Eve, the Eve of the Future (Auguste Villiers de l'Isle-Adam) and other sci fi stories are well captured in a modern telling with the HBO scifi show WestWorld.

Thinking space as the future and find it frustrating where space is "less wondrous" than it was in the 1950s and 1960s is I think missing out what makes good sci fi, it is not the stuff but can the stuff create a sense of wonder.

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So lets bring this back 360 degrees, so you as a child found space to be wondrous and are frustrated out of nostalgia that there are less good stories involving space, and even if they are good stories they seem less wondrous than they used to be as your childhood sense of wonder.

Well we adults find lots of stuff that we used to find as a child mysterious to be mudane and normal. But we can find wonder in new things such as the OP (2D8HP) mentioned here.

I mean. I think it's a pretty awesome idea that we can print organs. That's not something we'd have thought 50 years ago. 3D printing? Going to change the face of...well so many things when the tech is up and running. Does that count? Probably not...not for you...at any rate.

.
That is pretty awesome (I didn't know that before this thread) !

We don't have lunar landings or supersonic trans-atlantic passenger jets anymore, but damn actual replicators!

My moods a little better.

Literally 3D printing organs like in the westworld opening is now happening. We are finding out that with stem cells (either embryonic or reprogrammed stem cells from your skin or fat, turning a more developed almost stem cell into a stem cell similar to an embryonic stem cell) that as long as they have the right genes (and are not cancerous for many forms of cancers are turning off certain genes) put them next to the right cells and they automatically convert to the right thing we need to create organs. And thus 3D printing organs is literally assembling a blue print that is biodegradable, doing a basic lattice out of the appropriate transplant as a foundation, and then letting nature happen.

This was not even conceivable 5 years ago as practical, but it is now happening.

https://www.usatoday.com/story/tech/...plant/2370079/

https://cv2i.org/louisville-research...ng-3-d-hearts/

-----

So repeating my point, the future is happening, sci fi is happening, the future is happening but you have to be open to a form of wonder that is different than your childhood form, but it is really the same feeling, but finding it in different places as an adult.

[2D8HP]

The sense of wonder we have...

....but finding it in different places as an adult.

.
Thank you very much for your wonderfully Illuminating and encouraging post.

[Ramza00]

.
Thank you very much for your wonderfully Illuminating and encouraging post.

Awww sucks, *blush*

Hmm. Are there any other principles in Chaos Theory other than the quoted one? Could you tell me them?

The whole idea of jerks^{a physic / calculus term also known as jolt, surge, lurch}, aka the 3rd derivative of position over time, is basic chaos theory.

https://en.wikipedia.org/wiki/Chaos_theory#Jerk_systems

And I find it so ironic that most jerks in real life with human society really do not get the concept of a jerk in chaos theory, physics, calculus, general systems, etc.

Put another way.

Hammond: I really hate that man.




-----

Personally though I prefer talking about snap, crackle, and pop instead of talking about jerks, but to talk about snap^{also known as jounce}, crackle, and pop we first have to address the jerks in the system.

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But seriously Donnadogsoth you mentioned Plato earlier, go back and reread Philebus. Understand the distinction between the 3rd and 4th kind of being, and why Socrates (really Plato since it was a later dialogue of Plato) laughed at himself when describing the 3rd kind of being for he realized via articulating the 3rd kind of being that there had to be a 4th kind of being separate from the 3rd even though the 3rd and 4th both come from the mixture of the limited and the limitless with the idea of "counting" the things in the universe.

Realize the difference Donnasdogsoth for I think it will provide you some insight into what you think is so beautiful.

[Frozen_Feet]

Can you point out which examples fit my definition?

Yes. Gödel's incompleteness theorems, Heisenberg's uncertainty Principle (it's in the God-damned name), Lotka-Volterra Equations, computational decidability and undecidability, Universal Assemblers (AKA Von Neumann machines), the Turing Machine, Turing Completeness and Incompleteness, cellular automatons, the observer effect, the butterfly effect, the ideas that DNA and RNA encode genetic information and especially how they do that, etc.

The biggest mistake most of the other posters made is that they listed discoveries, whole theories, fields or applications. These are not the new principles you seek, they are larger bodies which contain them. For example, Chaos theory is not a principle, but it contains principles such as the butterfly effect, chaos attractors, feedback loops etc.

Sometimes, the classification is not wholly clear or a thing may fall in multiple categories. For example, the Turing machine was not a model of a real computer, it was a thought experiment which can be used in principle to explore limits and functionsof computation. (Which then gives rise to the concept of Turing completeness, that is, the idea of different machines which in principle are exactly as computationally powerfull.) Yet, you can also build a Turing machine if you want. Out of Legos if desired.

---

Can [Donna tell which examples count as principles]?

Obviously they can't. That's why we're all mocking them.

Because I fail to see how doubling the area of a square is an ontological paradox of any description.

I can. It's simple: get in the head of the child being taught. They are the one to whom there is a paradox. More detailed explanation below.

On the other hand, the theory that addresses that some systems have effects whose impact is orders of magnitude larger than the difference between its causes is, by any definition I can imagine, and ontological paradox.

GW

You are correct. The problem, again, is that Donna knows nill about the theory.

---

For me a big part of the problem is that the definition doesn't make sense. Initially I thought that was because I had the wrong meaning for "ontological paradox" but taking that as "something that seems impossible but obstinately exists anyway" hasn't helped much. Doubling the area of a square is just a geometry problem, right? There's maths there with square roots and algebra if you want to get into that, but isn't the solution just to cut the second square along both diagonals and arrange in the obvious manner? If that's supposed to be meaningful I don't see why. They used to print harder problems on the back of matchboxes when I was a kid.

Do you remember how those geometry problems looked to you as kid before you learned how to solve them?

That is the key to understanding the example.

The kid in the dialogue does not know geometry, so when asked to double a square, they naively double the length of its sides. However, the naive solution proves to be wrong - if you double the sides of a square, the area is quadrupled instead. The kid is stymied - they understand that a square that's double the size must exist, but they have no idea how to get there. Solving the problems requires understanding key mathematic qualities of squares, and codifying that understanding leads to mathematical principles which apply to squares universally.

Tl;dr: no such thing as "just a geometry problem" for someone who does not know geometry.

Sure, it is basic, compared to, say, Lotka-Volterra equations which are non-linear differential equations. ("Non-linear differential equations" can also be read "a sure sign that God hates you.") But even the basics had to be come up by somebody, and to someone who doesn't know a whole lot, even basic things can trigger the feeling of ontological paradox.

A non-scientific example: I am an amateur martial artist. I sometimes punch solid, hard objects for training or out of boredom. It's quite common for some people to stop and stare wide-eyed if they catch me doing this barehanded. They ask "Doesn't it hurt?"

It's a pretty silly question, of course it hurts. But that is the paradox to them: why would someone voluntarily hit a hard, solid object with their bare hands like that if it hurts? There's obviously nothing physically impossible about it, but it is so counter to intuition, so absurd, so insane that they can't get in the head of a person who does it. (Hint: absurd/insane is what paradox literally meant in Greek.) The reasons are literally unthinkable to them.

So I agree with what was said by one of the other posters: it is a low bar to pass. The high bar to pass is noticing paradoxes which have not been noticed by others or figuring out principles which solve those paradoxes that no-one else has thought of before.

It has happened within last hundred years, and is continuing to happen, but quite often the paradoxes and the principles are far removed from everyday life, or you don't need to pay attention to them to function in society. For example, it is a simple fact that most people using modern communicatiom devices such as my smartphone know nothing at all about the principles that make them tick.

[Grey_Wolf_c]

Obviously they can't. That's why we're all mocking them.

I can. It's simple: get in the head of the child being taught. They are the one to whom there is a paradox. More detailed explanation below.

OK, so if I am understanding you correctly, what Donna means by "ontological paradox" is a side-effect of the Dunning-Kruger effect: someone that knows nothing, therefore believe themselves to be experts in everything, therefore anything they can't explain is an ontological paradox.

That makes a scary amount of sense.

(Also, no-one taught me how to double the area of a square - it was set as a class exercise, and I simply figured it out. So I'm guessing this "child" needs to be a particularly stupid child, because I'd hesitate to think of a more trivial geometrical problem than "double the area of a square")

GW

[Frozen_Feet]

OK, so if I am understanding you correctly, what Donna means by "ontological paradox" is a side-effect of the Dunning-Kruger effect: someone that knows nothing, therefore believe themselves to be experts in everything, therefore anything they can't explain is an ontological paradox.

Even simpler than that. I'm merely saying that a lot of things can seem impossible when you don't know how they're possible. When you're then faced with them obstinately existing anyway, that will trigger the sense of paradox.

Overestimating one's expertise is not required. Being self-aware and honest about not knowing anything will not make the feeling of paradox go away.

That makes a scary amount of sense.

Well, I'm mildly happy you say that. The main point I was making is that there's an interpretation of Donna's exact words which is sensical and serves as a functional definition. Unless Donna feels the pressing need to contradict my interpretation and clarify that what they mean is nothing like I claim, harping on the lack of a definition is just rude.

Also, no-one taught me how to double the area of a square - it was set as a class exercise, and I simply figured it out. So I'm guessing this "child" needs to be a particularly stupid child, because I'd hesitate to think of a more trivial geometrical problem than "double the area of a square".

Or maybe you were a particularly smart child. You didn't tell which grade you were on when you did this, so it's hard to tell. Either way, the difficulty of the particular example is besides the point. Because there's still an observed paradox, the process of working it through, and the resultant principle about the traits of squares. It is the same process which can be codified into a system of philosophy or science, such as thesis-antithesis-synthesis, or observation-hypothesis-experimentation-theory.

Or in other words: I wholly agree with you that basics are trivial. This never meant that they're unimportant. Nor that the process by which basic principles are figured out is fundamentally dissimilar to figuring out advanced principles.

[Lvl 2 Expert]

Or maybe you were a particularly smart child. You didn't tell which grade you were on when you did this, so it's hard to tell.

The grade where they explained what the root of a number is, because that's when you would give the class the exercise of finding how much longer the sides of a cube become for its surface to become a certain amount bigger. (If the teacher was not working on roots she wouldn't have tried to let the kids double the area, quadruple would have been much more intuitive.)

As a rule of thumb: if you figured something out while answering a school exercise that was probably what the teacher was trying to accomplish in the first place. (Except in the case of Gauss.)

[Excession]

Do you remember how those geometry problems looked to you as kid before you learned how to solve them?

That is the key to understanding the example.

The kid in the dialogue does not know geometry, so when asked to double a square, they naively double the length of its sides. However, the naive solution proves to be wrong - if you double the sides of a square, the area is quadrupled instead. The kid is stymied - they understand that a square that's double the size must exist, but they have no idea how to get there. Solving the problems requires understanding key mathematic qualities of squares, and codifying that understanding leads to mathematical principles which apply to squares universally.

Tl;dr: no such thing as "just a geometry problem" for someone who does not know geometry.

Let me restate the problem slightly to remove some of the mathematics from it. You give the child two squares of paper, and ask them to cut up one or both squares and rearrange the pieces to form another square, with no overlaps or gaps at all. For younger children maybe have an adult run the scissors. This removes the need to explain what "twice the size" or "area" mean mathematically in this case. Is that still the same problem?

The key to solving this problem is to realise you need to cut along the diagonal, not parallel to the sides. To me it's a cute trick, a bit of an "Oh I see now" moment, but lots of geometry problems have that sort of solution. I don't, personally, see that as something fundamental, but maybe that isn't surprising, as Donna's idea of principles appears pretty subjective.

As a rule of thumb: if you figured something out while answering a school exercise that was probably what the teacher was trying to accomplish in the first place. (Except in the case of Gauss).

Huffman too, to some degree. Solving the problem was given as an option, but I don't think the professor expected any of them to answer it.

[Frozen_Feet]

@Excession: it is the same problem, you just stopped at solving the problem instead of continuing to codify why the solution works.

Or in other words: yes, it's possible to come up with special solutions to simple problems without bothering to turn them into general principles. This is entirely besides the point. The reason why the special solution works is still because of mathematical qualities of squares and you can still figure out the principles which govern those traits from the solution. The only subjective thing about that is your opinion on the difficulty of the particular example, which still does not matter.

That you don't see this as something fundamental is... well, let's put it this way: at its root, fundamental means foundational, basic. Principles which govern squares are exactly that, that is why we teach this stuff to kids! It serves as the foundation for learning and understanding more complex geometries.

[Donnadogsoth]

But seriously Donnadogsoth you mentioned Plato earlier, go back and reread Philebus. Understand the distinction between the 3rd and 4th kind of being, and why Socrates (really Plato since it was a later dialogue of Plato) laughed at himself when describing the 3rd kind of being for he realized via articulating the 3rd kind of being that there had to be a 4th kind of being separate from the 3rd even though the 3rd and 4th both come from the mixture of the limited and the limitless with the idea of "counting" the things in the universe.

Realize the difference Donnasdogsoth for I think it will provide you some insight into what you think is so beautiful.

That sounds like a good idea, thank you.

[Donnadogsoth]

So a trivial problem you can solve with a compass and a straight edge is somehow "a paradox" but a problem equally "impervious to rational magnitudes and requires non-deductive creativity" and that can furthermore only be partially approached with advanced mathematics and a lot of supercomputer time is not. Special pleading at its best. But then, that's really Donna in a nutshell.

I didn't say I know for sure chaos theory is not qualitatively the same as doubling the square, only that I was not sure. If I find out either way I will be happy, for it will increase my knowledge, but first I must understand the proper definition of principle, or whether there are many types, and whether those types have a commonality.

[Donnadogsoth]

Yes. Gödel's incompleteness theorems, Heisenberg's uncertainty Principle (it's in the God-damned name), Lotka-Volterra Equations, computational decidability and undecidability, Universal Assemblers (AKA Von Neumann machines), the Turing Machine, Turing Completeness and Incompleteness, cellular automatons, the observer effect, the butterfly effect, the ideas that DNA and RNA encode genetic information and especially how they do that, etc.

The biggest mistake most of the other posters made is that they listed discoveries, whole theories, fields or applications. These are not the new principles you seek, they are larger bodies which contain them. For example, Chaos theory is not a principle, but it contains principles such as the butterfly effect, chaos attractors, feedback loops etc.

Sometimes, the classification is not wholly clear or a thing may fall in multiple categories. For example, the Turing machine was not a model of a real computer, it was a thought experiment which can be used in principle to explore limits and functionsof computation. (Which then gives rise to the concept of Turing completeness, that is, the idea of different machines which in principle are exactly as computationally powerfull.) Yet, you can also build a Turing machine if you want. Out of Legos if desired.

I feel like I am in a cave watching shadow-puppets and you are suggesting there is a place of three dimensionality. For the questions I have are what about principles such as the general welfare. Do you count such a thing as a principle akin to scientific principles, or is it merely a convention?