The Ur-Quan Masters Discussion Forum

I am playing civilization 5, to see if it has educational value for children. I like how one invention/discovery leads to something else, and so on. But it could have been MUCH more detailed. They could have used real theorems from the history of mathematics (https://en.wikipedia.org/wiki/Timeline_of_mathematics (https://en.wikipedia.org/wiki/Timeline_of_mathematics)), and real discoveries from the history of physics (https://en.wikipedia.org/wiki/Timeline_of_fundamental_physics_discoveries (https://en.wikipedia.org/wiki/Timeline_of_fundamental_physics_discoveries)) or (https://en.wikipedia.org/wiki/Timeline_of_scientific_discoveries (https://en.wikipedia.org/wiki/Timeline_of_scientific_discoveries)). Such a game could have huge educational value.

If you feel that way, there's nothing stopping you from forking Freeciv into an educational game.

You sure talk about education a lot. Are you a teacher/professor, or are you just studying to be one?

Thank you for the information, I didn't know about Freeciv.. That actually sounds like a good idea. 


No. I am just starting to realize that the only way to change the world in a "good" way, must be from reforming how we are educating people.

Oh? How old are you, out of curiosity?

Old enough that I played Star Control 2 on a 386 16mhz a few years after it was released.

Anyone know about any branching diagram for the history of mathematics/science? I cannot find any such diagrams from this search https://www.google.no/search?q=branching+diagram+history+of+science&source=lnms&tbm=isch&sa=X (https://www.google.no/search?q=branching+diagram+history+of+science&source=lnms&tbm=isch&sa=X)

But I think it must be possible to relate theorems and scientific discoveries to each other in a branching diagram.

So... at least 22 then. Fair enough.

What gave you this epiphany, and what exactly are you trying to accomplish by posting about this stuff to strangers who, like you, have no involvement or expertise in the field of education?

Onpon, I forget, were you around for his Rainbow Planet Dxun days?

That doesn't sound familiar, so I guess not.

I feel like we have neglected the education of the very young. If kids in China can learn the Chinese alphabet, why can't they also learn equally many chemical structures? I believe the human brain is best suited for learning "ground structures", such as  phonemes, words, Chinese characters, atoms, quarks, or chemical structures, when we are very young. When the kids get a bit older, the brain is probably better suited for making relationships between "ground structures" in the brain. And as we get older and older, these relationships become more and more complex....

Most of the people working in kindergarten or in primary, secondary or high school, have much less education than me. They also often think "within" the box, which is not very useful if you are trying to reshape the box (or reform a system). In general, I write here because I feel like I often get intelligent out-of-the-box feedback, probably because people that are attracted to star control 2 often are prone to intelligent out-of-the-box thinking. Star control 2 is also my favorite game of all time.

But I also talk to other people. Last summer for example, I asked a guy that was taking a master degree in pedagogy why they weren't teaching languages to kids much earlier. He (being bilingual himself) thought it was a great idea, and said he might write his master thesis about it.

Who says those in China specializing in chemistry don't learn these chemical structures? Also, who says that every Chinese person learns the entire Chinese alphabet? :)


Beware the Dunning-Krueger effect.


Maybe you should train to be a teacher, since the subject apparently interests you. It's really easy to talk about what you think others should do, and it doesn't convince anyone else to change. Do it yourself, however, and your then-peers will notice your success and emulate it (assuming it is a success, that is).

issue is, with teaching a success can only be confirmed after two decades, or so. That's far too slow for political decision makers nowadays... You need to put in much effort upfront, and due to this latency times, you might never see the rewards...

That makes it hard to even tell if you're doing a good job at all, which slows down optimization even for people with a lot of patience.

Yeah.. I am starting to realize that maybe I should start working at a Montessori school. I even sent them an email and asked what the requirements are for working there, but they haven't responded yet. There is a 2 year study program I can take to become a Montessori teacher, but it is in a different city, and it seems to require that I have the 1 year normal pedagogy course. So, maybe 3 years just to get the education needed to work as a Montessori teacher.


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.

Perhaps, but you can't change the education system overnight anyway. It's too complex.


I think in the case of teaching methods, what makes them stronger is demonstration of efficacy by being put into practice. There are so many things that seem perfect on paper, but just don't work out the way you expect in the real world.

You can't just figure out the perfect education system and implement it right away. You have to take it one step at a time, within the system. A really tiny incremental change every generation. You're never going to live to see a perfect education system no matter what, but you can work from the inside to make it a little better.

You haven't read Thomas Kuhn? This is actually a quite famous book, and required reading for many university courses about the philosophy/history of science.

https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Revolutions (https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Revolutions)

https://www.amazon.com/Structure-Scientific-Revolutions-50th-Anniversary/dp/0226458121/ (https://www.amazon.com/Structure-Scientific-Revolutions-50th-Anniversary/dp/0226458121/)

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.

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.

(https://image.ibb.co/j26vF5/diagram.png)

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 (https://en.wikipedia.org/wiki/Punctuated_equilibrium)

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.

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.


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 (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 (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/ (https://exploringyourmind.com/5-discoveries-neuroscience-support-montessori-teaching/)


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.

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!

Thanks.  ;)

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.

(https://image.ibb.co/ctghCk/branching.png)

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.  :)

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?

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?

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...

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 (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 (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".


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...

(http://cdn.huodongxing.com/file/20160328/11F63FFF75E85CC5DEE5DD6862B159544F/30932453876427911.jpeg)

(https://elog.by/wp-content/uploads/2016/08/MathLearnMap-1024x657.gif)

(http://www2.stetson.edu/~mhale/logic/tree.gif)

(https://lh5.googleusercontent.com/proxy/JHOY5Rwmdo-5CObgzA6isy0rpGCiguUj1ICAE_gmgstwrZ0LJzEQCeGw49kKNmDUhNiHdU5TloCZ9hHzCwo6o-lc85eIqXq7SQCFF8xi_2AMq5yLW16kirultXCro_I1Slve_7YV1JB32KC2jAZTdsU=w1200-h630-p-k-no-nu)

Remember, these are maps for how to implement mathematical/scientific development into the game Freeciv (http://www.freeciv.org/ (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.

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...

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