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Author Topic: A QUESTION FOR THE DEEP THINKER  (Read 5986 times)

Bob K

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #25 on: May 01, 2012, 11:41:00 PM »

how long is a piece of string?

Now we are into String Theory, which makes no sense at all except to mathematicians. 
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RAAArtyGunner

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #26 on: May 02, 2012, 12:19:41 AM »

Now we are into String Theory, which makes no sense at all except to mathematicians. 

Next to come is what came first the chicken or the egg.

Thank you Neil mayhem abounds O0 O0 %% %% {-) {-)
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dodgy geezer

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #27 on: May 02, 2012, 01:04:50 AM »

Here it is........what is the penultimate real number (not an algebraic equation) to INFINITY %) %) %)

Umm... Which infinity?

Before around 1870, mathematical discussions of this kind would be answered by explaining that infinity was not a number, but rather a conceptual limit which marked the end of certain kinds of mathematical process, such as series.

Then Cantor gave us the transfinite numbers, and upset a lot of apple carts. These are numbers which can be shown to be bigger than 'infinity' by using a principle called 'cardinality'. The concept is complex, and is best dealt with in set theory (which Cantor invented to describe it), but briefly, if there exists a simple 'pairing' between two sets of numbers, those number sets have the same cardinality. Cantor showed that that, for instance, the set of real numbers (R) and the powerset of the set of real numbers (P(R)) do not have this simple pairing, and hence P(R)>R under all circumstances, including when R is infinite.  Cantor used the Hebrew term 'aleph' to depict a cardinality, and thus increasing sizes of infinities which are bigger than each other are described by the terms 'aleph-zero', 'aleph-one' ...etc

Useful mathematics can be done with these concepts. Cantor's set theory underlies all sorts of things, such as Turing's 'halting' work. Alas, the limitations of the standard set of characters on this board make it difficult to go further. The Wiki provides some useful introductions:

http://en.wikipedia.org/wiki/Cantor's_theorem
http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel
http://en.wikipedia.org/wiki/Cardinality
http://en.wikipedia.org/wiki/Hyperreal_number
...






   
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tt1

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #28 on: May 02, 2012, 01:30:26 AM »

Jeeze !!!!!!!!!!!!!!!!!!
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Peter Fitness

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #29 on: May 02, 2012, 02:21:27 AM »

I'm astounded at how many deep thinkers we have on Mayhem :o About as deep as my thinking gets is what boat will I build next or... will I have a cup of tea or coffee %% {-)

Peter.
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RAAArtyGunner

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #30 on: May 02, 2012, 03:03:32 AM »

I'm with you as I thought 2 + 2 model boats equaled four model boats but I can't see five yet can see three model boats.

Strewth am I confused  %% %% %% %%
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essex2visuvesi

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #31 on: May 02, 2012, 06:42:14 AM »

Here's one for you

Why are chinese Amps smaller than the rest of the world?
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boatmadman

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #32 on: May 02, 2012, 07:17:12 AM »

And another:
If infinity means going on for ever then it has no beginning and no end, therefore, if there is no beginning we arent really here. :D
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Artistmike

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #33 on: May 02, 2012, 07:27:26 AM »

Next to come is what came first the chicken or the egg.

That's an easy one...... Fish and later on Amphibians were laying eggs long before birds evolved on the planet, so the Egg as a means of reproduction was established long before the advent of the Chicken..   :}
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dodgy geezer

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #34 on: May 02, 2012, 01:53:04 PM »

I'm astounded at how many deep thinkers we have on Mayhem .....

Amongst other people, Galileo addressed the issue of adding and subtracting from infinity in his Two New Sciences (1638), and 'concluded that the ideas of less, equal, and greater apply to finite sets, but not to infinite sets.' That last phrase is directly lifted from a wiki entry - see http://en.wikipedia.org/wiki/Galileo's_paradox for the reasoning behind that statement. So Galileo's answer would be that infinity-1 breaks the rules and does not really exist.

After Cantor, an alternative approach, and the one usually used by current mathematicians, is the use of transfinite arithmetic, as evidenced by Hilbert in his famous 'Hotel' illustration, where he uses Cantor's pairing argument to show that 'infinity+1=infinity' (at aleph-null cardinality). Similarly, infinity-1 would also equal infinity. And, before you ask, yes, there is an aleph-infinity cardinality. It's called aleph-aleph null ....

Have a look here: http://io9.com/5809689/a-brief-introduction-to-infinity   Nothing deep with this - it's just maths, which is a simple process of following the rules. Unlike some the problems in life that I do have difficulty with, such as why I cannot get the transom on my boats to stay at 90 deg to the keel, and why my wife complains if I use her shoes to hold a sheet of balsa down when gluing....
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andrewh

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #35 on: May 02, 2012, 04:34:48 PM »

I'm not a deep thinker, at least I can't remember if I am

But going back to the original question it's clear that its a trick(ish) question

because

infinity isn't a number,  its a reference to a conceptual number, so in itself its a formula (for a given value of formula)

So if the brians of Mayhem are nicely warmed up:

What is red and invisible?

andrew
 
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Netleyned

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #36 on: May 02, 2012, 04:44:34 PM »

Come on you Brians  {-) {-)

Ned
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davidm1945

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #37 on: May 02, 2012, 07:18:48 PM »


What is red and invisible?

andrew
 

A submerged Russian submarine?

Dave
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Bob K

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #38 on: May 02, 2012, 07:33:32 PM »


What is red and invisible?
andrew
 

Infra Dread, as opposed to Ultra Violent ?   
[ another Douglas Adams quote, he has some interesting mathamatical concepts too ]
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Martin [Admin]

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #39 on: May 02, 2012, 08:35:32 PM »


3 men check into a hotel and the cost for the room is £30, they each pay £10 and go to their room.
 
After they have gone the man on the reception realises he has over charged and the room should be £25 not £30.
 
He takes 5 x £1 coins out of the till. realising he cannot split the refund 3 ways he decides to pocket £2 and give each of his guests £1 back.
 
So each man in the room has now paid £9.
 
3 x £9 is £27 and the £2 the receptionist pocketed = £29 , where has the other £1 gone?
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malcolmfrary

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #40 on: May 02, 2012, 09:34:38 PM »

9 quid each = £27, LESS the £2 in the receptionists pocket = the £25 it should have been.

Quote
What is red and invisible?
a/ Stealth post office van.
b/ No tomatoes.

And for really deep thinkers -  http://www.youtube.com/watch?v=6zkZ3f8DnKs
An old one, but well worth the visit.
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Norseman

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #41 on: May 02, 2012, 11:17:29 PM »

To add to the confusion:

I know that the square root of minus one utiises i the imaginary number
and that has allowed amazing technologies to arrive ....... but that does take
us right back to our capacity to imagine

I imagine I am late for work now <:( - gotta go >>>>>>>>>>>>>

Dave
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dreadnought72

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #42 on: May 03, 2012, 10:17:09 PM »

I don't have a problem with the square root of minus one - I met in, head on, in trying to understand quaternions.  %%

Seeing it as a "y axis" to the real number "x axis" was good enough for my head. That it ultimately Doesn't Make Sense is neither here nor there.  :-))

Andy
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Norseman

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Re: A QUESTION FOR THE DEEP THINKER
« Reply #43 on: May 03, 2012, 10:42:59 PM »

That it ultimately Doesn't Make Sense is neither here nor there.  :-))
Andy - that might be the most sensible thing said on Mayhem since the meltdown

A woman on a tv documentary said earlier '1 in 7 of men in the UK suffer with depression'
I think the rest of us simply enjoy it;  being depressed is the best it's going to get anytime soon.
....... ah well, I'm just off to work now :((

Dave
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