[yor_on]

Sweet thinking BC. We all must have intuitive ways of doing mathematics. The real problems comes when one want to formalize it into a system. Like adding numbers 34 + 44 + 76 f.ex. The easiest way is to take the 'tens' and then count up the single digits, but that's not the way I saw it presented in school. I guess a lot of us do it this way as it is simpler, and that some even might question why bother to learn a slower system? One good resource I think is the so called vedic mathematics, as they seem pretty intuitive. http://mathlearners.com/

what I'm thinking of is that we must all 'know mathematics' because how else do I know how to lift that cup of tea? And I'm guessing that the first waterclocks came from this intuitive understanding.

[Bored chemist]

Sweet thinking BC. We all must have intuitive ways of doing mathematics. The real problems comes when one want to formalize it into a system. Like adding numbers 34 + 44 + 76 f.ex. The easiest way is to take the 'tens' and then count up the single digits, but that's not the way I saw it presented in school. I guess a lot of us do it this way as it is simpler, and that some even might question why bother to learn a slower system? One good resource I think is the so called vedic mathematics, as they seem pretty intuitive. http://mathlearners.com/

what I'm thinking of is that we must all 'know mathematics' because how else do I know how to lift that cup of tea? And I'm guessing that the first waterclocks came from this intuitive understanding.

There's a story, I don't know if it's true, about a research group trying to make a robot that could catch a ball.
They set out by getting lots of computing power so they could take data from a camera and solve the differential equations to calculate the trajectory. It was very difficult.
Then they asked someone who played cricket how he caught the ball. He thought about it and said
"If the ball looks like it's going up, move backwards. If it looks like it's coming down, move forwards.
If it's to your left, move left. If it's to your right move right.
The ball will hit you in the face."

No maths required.

[evan_au]

It is a mystery why Earth has a magnetic field, and Mars doesn't (any more).
Mars is slightly smaller than Earth, so it would have cooled slightly quicker - but not much quicker.

Perhaps the collision that produced the Moon might have injected a pulse of energy into the Earth's interior, keeping it hotter for longer? The iron core of the impactor would have sunk towards the center of the earth, merging with Earth's core.
See: https://en.wikipedia.org/wiki/Giant-impact_hypothesis

[Janus]

It is a mystery why Earth has a magnetic field, and Mars doesn't (any more).
Mars is slightly smaller than Earth, so it would have cooled slightly quicker - but not much quicker.

Perhaps the collision that produced the Moon might have injected a pulse of energy into the Earth's interior, keeping it hotter for longer? The iron core of the impactor would have sunk towards the center of the earth, merging with Earth's core.
See: https://en.wikipedia.org/wiki/Giant-impact_hypothesis

Earth's radius is ~1.87 times that of Mars,  This gives it ~3.5 times the surface area, but  ~6.5 times the volume of Mars.  Earth also has a density of 5.52 g/cc to Mars 3.93g/cc,  which makes the Earth over 9 times more massive.   All in all, Earth's mass to surface area ratio is ~2.66 times that of Mars.   Surface area determines how fast the heat can radiate away and mass determines the total heat contained for objects of the same temperature and like make up.  Thus Mars should be expected to lose its heat fairly quickly compared to the Earth

[yor_on]

Well BC. I would say that is mathematics, same as with lifting something, judging a distance, etc. I would also call it intuitive.

[evan_au]

Earth also has a density of 5.52 g/cc to Mars 3.93g/cc

This density difference may be another clue as to why Earth's magnetic field is longer-lasting than Mars.
- Mars has a density closer to rock (basalt: 3g/cm³)
- Earth has a density which is closer to iron (iron: 8g/cm³)
- This suggests that Mars has a fairly small iron core, while Earth has a much larger iron core in relation to its size
- Some versions of the impact hypothesis have much of Earth's rocky crust ending up in the Moon, and much of the Mars-sized impactor's iron core joining the Earth's iron core.

[yor_on]

Actually I seem to remember experiments done with analog small  'robots' that seemed to adapt much easier to different milieus than those defined by binary logic handling it. Which should put the type of mathematics the brain use as 'non linear' adjusted by inputs from the environment, as you described there BC. https://en.wikipedia.org/wiki/Nonlinear_system
=

The wiki and I disagree on one thing though. "  It follows that some aspects of the dynamic behavior of a nonlinear system can appear to be counterintuitive, unpredictable or even chaotic. Although such chaotic behavior may resemble random behavior, it is in fact not random. For example, some aspects of the weather are seen to be chaotic, where simple changes in one part of the system produce complex effects throughout. This nonlinearity is one of the reasons why accurate long-term forecasts are impossible with current technology.  "

I'll put a dollar on that this seemingly expected 'technology' accurately describing and predicting the outcome of every 'chaotic system' never will exist.

[Bored chemist]

I'll put a dollar on that this seemingly expected 'technology' accurately describing and predicting the outcome of every 'chaotic system' never will exist.

Nobody suggested otherwise.

[yor_on]

Heh, seems we're not the only one able to intuitively 'calculate'. "  honeybees can apparently understand the concept of zero, and learn to correctly indicate which of two groups of objects is the smaller.  But now they say insects can learn to carry out exact numerical calculations such as adding and subtracting a given number. “Their brain can manage a long-term rule and applying that to a mathematical problem to come up with a correct answer,” said Dr Adrian Dyer, co-author of the research from RMIT University in Australia. “That is a different type of number processing to spontaneous quantity judgments.”

If the team are right, the insects are in good company. While it was once thought that only humans could manage such calculations, the authors note recent research has revealed a veritable menagerie of creatures can keep track of numbers or even add or subtract. “[There was] evidence that other primates could do it and then an African grey parrot, Alex, famously could do it, but also some spiders could do it,” said Dyer.