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Interesting Concepts in Science and Mathematics

Tadhg Gaelach

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Before Galileo, it was known that objects in freefall sped up on their way down, but nobody had a quantitative measure of how that speed increased. It was generally assumed that if an object fell distance y in the first second, it would fall 2y in the second second, 3y during the third, etc.

When Galileo dropped or rolled objects, he discovered that if an object fell/rolled a distance y in the first second, it fell three times as far, 3y, during the second, 5y during the third, 7y during the fourth, 9y, 11y, etc. In other words, not consecutive numbers, but rather the odd numbers.

To get the cumulative total distance after a given time, it is only necessary to add up all the numbers corresponding to each elapsed time. And we get:

1
+3 = 4
+5 = 9
+7= 16
+9 = 25
+11=36, etc.

So we have 1, 4, 9, 16, 25, 36….

If those numbers look familiar, they should. They are the perfect squares.

So the distance y traveled by an object is proportional to the square of the time, t² . To get a numerical answer, you multiply t² by the distance fallen in the first second, call it c, which for a freefall object is (in current-day SI units) 4.90 m. Nowadays we don’t use 4.90, which is the average speed for the first second, but rather 2c = 9.81, which is the speed it’s going at the end of the first second, which we call the acceleration, a.

So the formula becomes:

y=1/2 at²
 
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Tadhg Gaelach

Tadhg Gaelach

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I found it remarkable that the distance covered by a freefalling body increases in proportion to the perfect square of the time taken. Such patterns led the likes of Plato to consider Mathematics to be the language of God. It seems completely impossible that such patterns could be random. Here's an interesting lecture on this topic.

 
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Tadhg Gaelach

Tadhg Gaelach

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Apart from Val's video above explaining why negative numbers don't exist so there cannot be a square root of minus one, this is probably Ireland's greatest contribution to mathematics. And strangely enough, it also involves the square root of minus one.

 
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Tadhg Gaelach

Tadhg Gaelach

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Regarding the above video, William Rowen Hamilton was a rather brilliant fellow. Besides being a professor of mathematics and astronomy at Trinity College, he also spoke 13 languages. But, although he lived all his life in Ireland, and during his day (1805 - 1865) a full half of the Irish people spoke Irish as their daily language, he claimed himself that he couldn't speak a word of Irish. That really shows the system of almost total Apartheid that existed between the Anglo-Irish and the Native Gael in the 19th Century.
 
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valamhic

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Regarding the above video, William Rowen Hamilton was a rather brilliant fellow. Besides being a professor of mathematics and astronomy at Trinity College, he also spoke 13 languages. But, although he lived all his life in Ireland, and during his day (1805 - 1865) a full half of the Irish people spoke Irish as their daily language, he claimed himself that he couldn't speak a word of Irish. That really shows the system of almost total Apartheid that existed between the Anglo-Irish and the Native Gael in the 19th Century.
To the victor goes the spoils and the Southern Irish did not help O'Neil. You can never get the IRISH TO PULL TOGETHER
 

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I was wondering whether this is an "Intelligent Design" thread (Tadhg's sneaky like that) :)
Btw, I've never really understood the (compelling) reason for eh, mathematical regularities in the Universe to be a reason for a 'Creator' 🤔
 
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Tadhg Gaelach

Tadhg Gaelach

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Btw, I've never really understood the (compelling) reason for eh, mathematical regularities in the Universe to be a reason for a 'Creator' 🤔


I think the way Plato looked on it was that figures like a triangle - he called them forms - are thoughts. Who who is having these thoughts? Only a Supreme Being could have such thoughts.
 

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I think the way Plato looked on it was that figures like a triangle - he called them forms - are thoughts. Who who is having these thoughts? Only a Supreme Being could have such thoughts.
Why are they thoughts?
 
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Tadhg Gaelach

Tadhg Gaelach

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Why are they thoughts?


That's the way Plato saw it. I think there's some merit to that view. What do you think of the idea that we are really a hologram - 2D information on the surface of a black hole. One could view that information as thoughts.
 

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That's the way Plato saw it. I think there's some merit to that view. What do you think of the idea that we are really a hologram - 2D information on the surface of a black hole. One could view that information as thoughts.
Well how do we know, think of something as a triangle? I suppose it's that the angles add up to 180 degrees.. But how does something like that indicate a Creator?
 
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Tadhg Gaelach

Tadhg Gaelach

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Well how do we know, think of something as a triangle? I suppose it's that the angles add up to 180 degrees.. But how does something like that indicate a Creator?


People find it hard to believe that a universe that seems to work so perfectly could be the result of random chance.
 

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I don't think it is random. I personally believe that the universe itself is an intelligence.
Yes, sorry, I'm frequently guilty of jumping the gun a little bit..

Let me rephrase, you say that it isn't random, it's ordered, we can notice patterns, sequences, we can predict things (with remarkable accuracy) and so on but why is that not random, why is that evidence for intelligence.. and not just the way things are?
 

valamhic

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This is an entertaining video to watch (if you're feeling insomniac)

Richard Feynman: The Man Who Asked Why? (I made up that title) -

Note he says the relationship between gravity and the electromagnetic force is unknown.It would make a good topic here in a few weeks.
 

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How does the rotating object experiencing centrifugal force and the central object retaining it by centripetal force (unit) know that it is spinning round and that its not the universe which is spinning round? If it is the universe which is spinning round at the exact same speed as the unit, then the two objects are stationary and if applied to the moon and earth, the moon should collapse into the earth.

Question me on this so you get the concept in your head. I believe I have the answer and that answer was never discovered before and is not in any book that I know of . I will reveal it later in about 3 days.

If a single planet solar system (unit) same size as ours has a sun and an earth in orbit. What reference frame is the earth spinning in? We assume the universe is stationary in relation to the unit, but how does the unit know this?
Well, it is well known that the universe is not rotating as it can be directly observed. (I admit I'm finding it very hard to follow your thinking).

But thinking about the fact that our planet has a rotation, it rotates around the sun, the sun rotates around the massive black hole at the centre of our milky way, our milky way is part of a local galaxy group of 50+ galaxies, which in turn is part of the Virgo cluster, which is part of the Laniaka Supercluster... (granted the expansion of space overtakes gravitational attraction at the scale of the space between galaxies, so we could probably discount anything outside the milky way, at least to get going with the calculation).

So let's say you're briskly striding down your field at 7 mph one morning, twirling your sheepdog whistle around on a 15cm piece of twine from your finger at the rate of one and a half revolutions per second. Can you interpolate the real 3D rotation of your dog whistle relative to the whole stationary universe, every half second, using that great distinguished Irish mathematical invention, quaternions?

PS It's not at all helpful to talk about centrifugal force from rotation in the same breath as gravitational force. Even on the earth's surface we don't explicitly separate out centrifugal forces but rather lump them in with gravitational forces. But they are completely different forces. Gravitational force is completely independent of centrifugal force. And in the above, we're talking purely about rotation, we don't need to deal with gravitational attraction. It's always best to take one property alone at a time in these kinds of maths problems, otherwise you just end up confusing yourself.
 
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