i just learnt some new maths(!)

[bigegg]

No it's not philosophy

I may not be totally correct but how many numbers between 0 and 1? Is one infinity and the infinite hotel example is another, smaller infinity

its still philosophy:
"infinity" is a concept, not a number.

to use your examples:
"how many numbers between 0 and 1?
the same as the number of rooms in the infinite hotel.

 

[Pigeon_Droppings2]

Thats an excellent bit of trivia...I like that...just rearranging everything:

x% = x/100
y% = y/100

so x% of y = (x/100)*y = (x*y)/100 = x*(y/100) = (y/100)*x = y% of x

Thats a nice bit of trivia because it isn't apparent when you first look at it.

I once saw someone simplify Sin(x)/Cos(x)....and ended up with in/Co ....was quite funny!

 

[Screwdriver]

I have (quite recently) had a long argument on another forum to defend my assertion that mathematics is an invention, numbers are an invention and infinity (all varieties) and zero do not exist in reality.

I hesitate to drag it out here except that I agree, infinity is an abstract mathematical tool and there are several different kinds so that some types of infinities are larger than others. You would have to delve into set theory and frankly, that's not an iPad friendly topic to post.

The concept of zero is itself a relatively recent invention. The Romans didn't have a zero and their mathematics was excruciatingly limited and cumbersome. Amazing that they got as far as they did.

I went on to suggest 1+1 does not equal 2 since in reality, there is only geometry and there is no thing in this universe which is the same as any other. There can be no "2" unless you make an assumption (lit. Axiom) that one physically real object can be said to be identical to another.

 

[Pigeon_Droppings2]

I think you were doing OK....until you got to 1+1 <> 2!

Dunno about 0....thats an interesting one....have to think about that...I guess it's like a construct.

I think infinity is in the same category as "i" (square root of -1)...they are constructs but they are useful....the square root of -1 for example...utter nonsense....but i^2 = -1 is quite handy!

Been far far too long since I did this stuff in anger....like another life ago!

 

[Screwdriver]

Yes, numbers and mathematics are certainly useful but they are still a human invention. They are not a fundamental property of the universe which we observe as a geometric structure.

Warning: I am sitting at the computer now. Ready for battle...

 

[Pigeon_Droppings2]

Screwdriver....Think you've moved onto philosophy which isn't my area

It's an interesting thought exercise though.

I remember studying how to calculate the lift on various shapes of aircraft wings...it's very complex maths as you can imagine. When I pointed out that the Wright brothers came up with the wing first without the complex maths....and the maths was just used to explain what had already been invented....yea that didn't go down well at all!

 

[bigegg]

Yes, numbers and mathematics are certainly useful but they are still a human invention. They are not a fundamental property of the universe which we observe as a geometric structure.

Warning: I am sitting at the computer now. Ready for battle...

I see your "geometric structure" and raise you "mental construct" - which we explain as a geometric structure, but could be explained by a completely different *PHILOSOPHY".
But now we're getting towards tensor calculus.

 

[bigegg]

I read a long time ago - in "new scientist", I think:
At higher levels:

Maths is actually philosophy
Physics is actually maths
Chemistry is physics
Biology is Chemistry
and
Philosophy is actually biology

 

[bwservices]

maths is made up.with more flaws than Gordon ramseys scrotum

we all know the hypotenuse theory from squaring out stuff


longest side A squared = B squared + C squared

if B is 1 meter, and C is one meter, we think we can get a 'real' value for A?

1.41421356237309504880168872420969807856967187537694807317667973799......

I couldn't find it on my my measuring tape

 

[Pigeon_Droppings2]

Wasn't it the Greeks who discovered irrational numbers by accident....then it became an official secret! No idea if thats true....its what we were taught. Apparently their whole society was based on everything having an absolute measurement....then "that bloke" ruined it with his funny triangles!

....I was literally typing this when your triangle appeared!

 

[Screwdriver]

I see your "geometric structure" and raise you "mental construct" - which we explain as a geometric structure, but could be explained by a completely different *PHILOSOPHY".
But now we're getting towards tensor calculus.

Yes but everything is a mental construct and that process itself reveals the geometry of nature. They are not incompatible descriptions. Mathematics is the tool we use to describe observed geometry. What goes on inside an individuals head when the observation gets there is an entirely other subject I suggest and best left where it is. I'm having enough trouble inside my own head thanks.

Tensor calculus is a step too far for informal discussion, a simple snapshot of a static 3d world is deep enough to discuss the reality or otherwise of mathematics. There is no doubt the numbers "work" but again, those predictions and the validity of any more complex theory are confirmed by making further observations of pure geometry.

 

[rtbcomp]

I think you were doing OK....until you got to 1+1 <> 2!

...

2! = 2

 

[Screwdriver]

I couldn't find it on my my measuring tape

IKR and of course some irrational numbers are more irrational than others! It's a minefield...

 

[Pigeon_Droppings2]

2! = 2

Very good....and 3! = 6

 

[Screwdriver]

I think you were doing OK....until you got to 1+1 ≠ 2 (!)

Well if you can show me two of something, I'll show you where you're going wrong...

 

[Pigeon_Droppings2]

Yea...philosophy really isn't my bag.

From my perspective we've defined each number "1" as identical to every other number "1" in our construct....so in the construct 1+1=2.

Does that apply in the physical universe...well only if you can find something physical that is entirely uniform in nature. If it is uniform you can divide it into 2 identical parts...but probably only in theory!

 

[Olderisbetter]

As i am wired a bit funny in the brain my way to work most maths out is pretty much to flip it around and work it out, As soon it was discovered i could do this i was told i was clever? like see 17 x 89 written down but instantly i convert it to 890 + 445 + 160 +18 so i am doing addition not multiplication more

 

[Screwdriver]

As i am wired a bit funny in the brain my way to work most maths out is pretty much to flip it around and work it out, As soon it was discovered i could do this i was told i was clever? like see 17 x 89 written down but instantly i convert it to 890 + 445 + 160 +18 so i am doing addition not multiplication more

That's a very common method for any kind of maths, especially for people without the gift of a savant. There are two or three examples of partitioning in this very thread...

 

[Burdekin]

Yes, numbers and mathematics are certainly useful but they are still a human invention. They are not a fundamental property of the universe which we observe as a geometric structure.

Warning: I am sitting at the computer now. Ready for battle...

Maths is a life skill, it's like reading you can get by without it but it's better if you can do it. Algebra, geometry, trig, statistics etc, use them all the time. The maths we're talking about here is all what we all would have learnt in primary school. My wife works in a language based environment and she is the maths guru, she can work out percentages. :-)

 

[bigegg]

As i am wired a bit funny in the brain my way to work most maths out is pretty much to flip it around and work it out, As soon it was discovered i could do this i was told i was clever? like see 17 x 89 written down but instantly i convert it to 890 + 445 + 160 +18 so i am doing addition not multiplication more

i'm the same, but i'd do 89x17 as
(100-11) * 17
(100*17) - (11*17)
(100*17) - (10*17)-(1*17)
1700 - 170 - 17