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Author Topic: A more detailed civilization (game)  (Read 387 times)
Julie.chan
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Re: A more detailed civilization (game)
« Reply #15 on: June 19, 2017, 08:39:59 pm »

No, I know nothing about that book. But unless that book argues that experimentation is unnecessary, I don't see how it could be relevant.
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Re: A more detailed civilization (game)
« Reply #16 on: June 19, 2017, 10:10:02 pm »

The hard part of making a radical new discovery is not the being radical and new, but the part where you're right. This is harder than it seems.
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Zanthius
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Re: A more detailed civilization (game)
« Reply #17 on: June 19, 2017, 10:24:09 pm »

No, I know nothing about that book. But unless that book argues that experimentation is unnecessary, I don't see how it could be relevant.



What you talk about "making small incremental improvements" would be like what Kuhn calls "ordinary science". Changing the educational system completely, would be more like what Kuhn calls "revolutionary science". One example of such revolutionary science would be when quantum physics started to replace Newtonian physics, or when Copernican heliocentrism started to replace Ptolemy's geocentric model of the solar system. Similarly, this "revolution", could be regarded as Montessorian student-centered education starting to replace classical teacher-centered education.

The Kuhnian model of scientific progress is similar to the theory of punctuated equilibrium in evolutionary biology. https://en.wikipedia.org/wiki/Punctuated_equilibrium
« Last Edit: June 19, 2017, 11:44:37 pm by Zanthius » Logged
Julie.chan
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Re: A more detailed civilization (game)
« Reply #18 on: June 20, 2017, 07:28:08 am »

Quote
One example of such revolutionary science would be when quantum physics started to replace Newtonian physics, or when Copernican heliocentrism started to replace Ptolemy's geocentric model of the solar system.
I don't know anything about Kuhn's ideas. But revolutionary scientific discoveries don't happen because philosophers think of new paradigms. They happen when testing shows that what we thought we knew before was wrong. This isn't an apt analogy anyway because schools try to accomplish something while science only tries to understand something. But if we were to make an analogy between them, it would be between new scientific paradigms being tested and new teaching methods being tested. Just thinking about ideas for different teaching methods is more akin to armchair junk science.

A more apt analogy would be with engineering, and at that, engineering for structures which are incredibly important. Consider this: it could be that there is a much better way to build bridges than we know, which causes the bridge to be sturdier, cheaper, and safer. But since the failure of a bridge can easily lead to the death of hundreds of people, it would be foolish for non-engineers to come up with random ideas for different bridge designs, and then for society to pick one of those ideas as the new bridge design model, demolish all bridges, and rebuild them in that manner. If it works, maybe it's better. If it doesn't, it could lead to more deaths than would otherwise happen.

I think education is so important that it is similar. Granted, it's not a matter of life and death per se, but screwing up education could lead to massive societal and/or economic harm. Given this, any improvements to education should be verified reasonably before being made widespread. Better to stick with what we know kind of works than to try something new with too many children and have it backfire next generation.
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Zanthius
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Re: A more detailed civilization (game)
« Reply #19 on: June 20, 2017, 09:17:41 am »

I don't know anything about Kuhn's ideas. But revolutionary scientific discoveries don't happen because philosophers think of new paradigms. They happen when testing shows that what we thought we knew before was wrong.

Actually, the Copernican heliocentric model of the solar system didn't give more accurate predictions than the old Ptolemaic geocentric model with retrograde motion. One might however argue that the apparent retrograde motion in the geocentric model made it less elegant.

A more apt analogy would be with engineering, and at that, engineering for structures which are incredibly important. Consider this: it could be that there is a much better way to build bridges than we know, which causes the bridge to be sturdier, cheaper, and safer. But since the failure of a bridge can easily lead to the death of hundreds of people, it would be foolish for non-engineers to come up with random ideas for different bridge designs, and then for society to pick one of those ideas as the new bridge design model, demolish all bridges, and rebuild them in that manner. If it works, maybe it's better. If it doesn't, it could lead to more deaths than would otherwise happen.

There are already tons of different types of bridges in the world, just like there already are many different educational systems in the world. In the United States for example, there are religious private schools and some parents are homeschooling their kids. There are also public Montessori schools in the United States. Different countries also have different educational systems. So it is already possible to do research on the efficacy of different educational systems.  Here is a publication that investigated the efficacy of Montessori education: https://www.researchgate.net/profile/Kathryn_Dohrmann/publication/230757162_High_School_Outcomes_for_Students_in_a_Public_Montessori_Program/links/56ef3cc508ae59dd41c730b4.pdf, and here is another one: http://www.montessori-science.org/Science_Evaluating_Montessori_Education_Lillard.pdf

We also have a branch of science called neuroscience today, and from neuroscience we might learn about how the brain changes from early childhood to adulthood. Here is an article that compares Montessori education to modern neuroscience: https://exploringyourmind.com/5-discoveries-neuroscience-support-montessori-teaching/

Better to stick with what we know kind of works than to try something new with too many children and have it backfire next generation.

You are never going to make me believe that the educational system in the United States is functional when so many of you voted for Donald Trump.
« Last Edit: June 20, 2017, 01:06:58 pm by Zanthius » Logged
Krulle
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Re: A more detailed civilization (game)
« Reply #20 on: June 20, 2017, 09:20:57 am »

I am much more interested in getting negative feedback, than in convincing you. Theories tend to grow stronger from negative feedback, not from convincing people.
This. Things like this is why I stick around.
I may find you an unrealistic idealist, but at least you ARE open to criticism, and you try to find a way to make it work, despite negative comments.

You, sir, have an attitude that's increasingly rare, and a real virtue to behold.

I wish the current management of economy whatever would think that way, but nearly everywhere criticism is unwanted and blocked, no matter how much arguments the critics bring forward, it all is swept under the rug with "you are just opposing change as such". I really lack counterarguments from managements (and some governments), when they are being opposed with arguments.
The discussion culture and grasp of basic democracy is lacking everywhere. (And I hope Macron won't fall for this too.)

My hats off to you, Sir!
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Zanthius
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Re: A more detailed civilization (game)
« Reply #21 on: June 20, 2017, 11:33:06 am »

My hats off to you, Sir!

Thanks.  Wink

Here is a branching diagram I have been working on for the early evolution of mathematics. Such an evolutionary map could be implemented into Freeciv. I am not a mathematician, so it is probably far from perfect.



The good thing about implementing this into Freeciv, is that even if this diagram becomes so complex that it becomes almost impossible to visualize it, it doesn't matter when it is implemented into Freeciv. Nor does it matter when it is implemented into the neural network of a brain.  Smiley
« Last Edit: June 20, 2017, 11:48:47 am by Zanthius » Logged
Krulle
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Re: A more detailed civilization (game)
« Reply #22 on: June 20, 2017, 01:34:34 pm »

I would go from Algebra to linear algebra, then to vector algebra, and from there to matrix algebra.
Easier to visualize, as linear algebra is understandable by every kid (1+1=2).
But matrix algebra and vector algebra have a lot less for intuitive grasp to keep hold on.
vecotr algebra comes together with physics, when you start handling 2-dimensional mathematics.
Which you then expand into matrix algebra.
Also, vector algebra is a subset of matrix algebra, and linear algebra is a subset of linear algebra.
Why start with general, when specific is so easy to understand?
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Zanthius
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Re: A more detailed civilization (game)
« Reply #23 on: June 20, 2017, 01:46:56 pm »

Also, vector algebra is a subset of matrix algebra, and linear algebra is a subset of linear algebra.

Ok. I am not a mathematician. I just remember that I learned about both matrix algebra and vector algebra when I had the topic called "linear algebra", so I thought vector algebra and matrix algebra were subsets of linear algebra.  But maybe you can have nonlinear systems in matrix algebra and vector algebra?
« Last Edit: June 20, 2017, 01:49:32 pm by Zanthius » Logged
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Re: A more detailed civilization (game)
« Reply #24 on: June 20, 2017, 02:26:29 pm »

Linear mathematics is best visualised as walking along a line. Forward, backwards,.... but staying in this one dimension.
Linear mathematics knows only forward or backwards. Best visualised as plus/minus.

Vector mathematics is best visualised as walking on a plane. Left, right, forward, backwards. (2D-vectors).
3D-vectors would add up and down. For vectors you need to know the direction, so you also need angles.

Matrix mathematics can do all that, and add an infinite amount of additional dimensions.
Hence, matrix matrix can visualise the linear maths also very nicely, just most matrix elements would be zero, except for one position. It's much easier to simply write the equations known.

I don't really know what you mean with non-linear mathematics...
Integration and differential mathematics? Just another specific subset of vector/matrix/(linear) mathematics. Using time as a dimension.
They just appear prima facie as non-linear. But in the end it's not different from linear mathematics, it's just not that straightforward to visualise.

Or equations like
4x+7y=45   ?
Just another form of vector mathematics...
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Zanthius
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Re: A more detailed civilization (game)
« Reply #25 on: June 20, 2017, 02:35:22 pm »

I don't really know what you mean with non-linear mathematics...

From the wikipedia page about vector calculus:
The algebraic (non-differential) operations in vector calculus are referred to as vector algebra, being defined for a vector space and then globally applied to a vector field.  https://en.wikipedia.org/wiki/Vector_calculus

From the wikipedia page about vector algebra:
In mathematics and linear algebra, vector algebra refers to algebraic operations in vector spaces. Most commonly, it refers to operations on Euclidean vectors. https://en.wikipedia.org/wiki/Vector_algebra

I was thinking to make a box for "vector calculus" and draw an arrow from "vector algebra" to "vector calculus".

Matrix mathematics can do all that, and add an infinite amount of additional dimensions.

And since we can't visualize n-dimensional vectors.. vector algebra should evolve into matrix algebra.

I found some very nice maps! No need for me to do this...







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Zanthius
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Re: A more detailed civilization (game)
« Reply #26 on: June 20, 2017, 04:54:26 pm »

Why start with general, when specific is so easy to understand?

Remember, these are maps for how to implement mathematical/scientific development into the game Freeciv (http://www.freeciv.org/). I am not expecting kids to learn all of these mathematical/scientific disciplines when they are playing Freeciv, just to familiarize themselves with how mathematics/science has developed.

I think kids might benefit from mapping intellectual territories first, and rather go deeper into topics they already have mapped later. For example. I didn't have any clue about what to study when I had finished high school, because I hadn't spent enough time/energy on mapping intellectual territories. If kids spend more time on mapping intellectual territories, they might have a better idea of what they want to dig deeper into later.
« Last Edit: June 20, 2017, 05:03:23 pm by Zanthius » Logged
Krulle
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Re: A more detailed civilization (game)
« Reply #27 on: June 20, 2017, 06:59:55 pm »

Remember, these are maps for how to implement mathematical/scientific development into the game Freeciv (http://www.freeciv.org/). I am not expecting kids to learn all of these mathematical/scientific disciplines when they are playing Freeciv, just to familiarize themselves with how mathematics/science has developed.
And math started with necessities, like counting (which is linear algebra in its purest form). Then people startedto keep track who owned how many of the flock of sheep, cows, ....
Then came land measuring, especially in Nile flooded egypt, so that the fields could be staked again after the yearly flood, which is still the most importamt and simplest application of vector mathematics.
That was the order of historic development....

Whether the  "zero" came before or after land measuring is debateable, as its primary use was for traders...
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Re: A more detailed civilization (game)
« Reply #28 on: June 21, 2017, 02:25:55 pm »

I have split the discussion of Donald Trump into a separate topic.
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