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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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valamhic

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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=12at²
This was the concept until a Cavan farmer advanced the theory. There is no such thing as an object. There is just a collection of atoms. There is no such thing as a fall. There is just just the suspension/prevention on a collection of atoms from complying with space time and the release of that suspension/prevention

The use of square and cube is simply the dimensions of space viz: length breath and width, The 4th dimension being time. No one here could answer what the square root of minus 36 is,
 
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valamhic

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The concept of empty space is not correct either. Atoms can form in empty space. The moment an atom is formed it warps the space time it is in .
 

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.

 

valamhic

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I have postulated the theory that the reason there is no square root of a minus number is that man has dictated it to make maths work as he wanted. A minus by a minus is not a plus at all. There is no such thing as a minus figure in nature.
 

valamhic

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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.

That's the shape of the universe. It has to have a shape.

When counting length 3 +3 = 6
When counting length by breath there is no 3 + 3 there is only 3 X 3.
When counting length by breath be width there is no 3 + 3 or 3 x3 there is just 3 x 3 x 3 = 27.
 
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valamhic

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Where is U2?

What about parallel universes? Where are an infinite number of universes some almost identical to ours but with slight differences.
 
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Tadhg Gaelach

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Did you ever wonder why any number or variable to the power of zero is one?

 

valamhic

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Did you ever wonder why any number or variable to the power of zero is one?

I did.

4 (power 3) = 64. 4( power 3 - 1) = 16. 4(power 3 - 3) = 4
4 multiplied by itself zero times = 4 (not one).
A line is 8 meters (long measure.) We decide to make it a square 0 meters wide It is a line not a square. Therefore a number multiplied by itself zero times is not 1.

2 squared / 2 squared = 1 ------ a patio 2 meters square

2 meter (power 0) does not give 1 meter.
 

valamhic

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Like in your bonce, Val?



Jaze, you're some man for one man, Val.



Bono - Dalkey

Adam - Danesmoat (Rathfarnham)

Edge - Los Angeles

Larry - On his Harley
I was up at 6.40 am, why were you so late getting up. You're too fond of that auld scratchier.
 

Mowl

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Well, 0640 for you is 0840 for me due to the GMT factor.

Besides, I thought farmers never slept?

I sometimes have to take pills to sleep - I'm a lifelong insomniac. When I was a kid I used to sleepwalk too. Some nights I'd come back down the stairs after being sent to bed due to school the next day, and I'd wander into the kitchen and make a sandwich. Mam said that she'd be asking me what I was doing but I'd be oblivious to her, and everything else around me.

It got worse over the years and one time I went camping with the crew from the Saint John's Ambulance Brigade at a spot we rented from a farmer at the bottom of Bray Head on the Greystones side. I got up in the middle of the night, and the lads thought I was going to take a leak but after a while I didn't come back so one of them grabbed a torch to search for me.

I'd walked up through the fields, over the grass verge of the Greystones tunnel, and onto the cliffs that line the sea all the way down to Greystones village itself. Apparently he asked me what I was doing but again I was sleep walking and was unaware of him. They say you're not supposed to startle a sleep walker into waking up suddenly as it can have disastrous effects on them, but he had to wake me, he thought I was going to either fall or jump off the edge and plummet several meters down onto the rocks below.

But that said, I was up at the same time as you - around quarter to nine local time, I had a hospital appointment about my surgery at ten.
 
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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.

 

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
 

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?
 

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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