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#1 2015-03-05 19:36:58

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
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Different Laws of Thought

I've this friend who asked me to ask this to some respectable mathematician or physicist. So, I decided to post this here.

> Can there be universe with different laws of mathematics?

I tried to tell him that mathematics is how we define it.

He asked me if 2+2 could be 3. I do not have a clue what that means, so I think he wants to know if the [Laws of Thought](https://brilliant.org/wiki/the-laws-of-thought/) could be violated.

I said that even if it is, we cannot think of it so why bother?

The subsequent discussion was very cryptic for me but in conclusion he asked me to post it here.

So, please leave your comments. Thank You.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#2 2015-03-05 19:42:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Different Laws of Thought

I was lucky enough to be perusing another forum where one of the brightest guys there had this to say:

"The ultimate goal of mathematics is to eliminate any need for intelligent thought." Whitehead may have been prophetic in that view. The Discretists led by Zeilberger and us computational boys could not agree more. The formalists think that mathematics is just a game with rules invented by humans for humans.

Now how is that for poignant!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2015-03-05 20:03:39

David
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From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Re: Different Laws of Thought

Different laws of mathematics? It depends of what he thinks by different laws of mathematics. I have 2 answers.

Yes.
Perhaps you live in a parallel universe that had totally the different sets of physics.

No.
Physics is the same everywhere in the universe. Mathematics is the medium we use to explain and prove physics. If there are aliens, they probably would use another medium to prove and explain physics. If a alien have 12 fingers, maybe they will use base 12? Maybe they don't have a concept of zero?


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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#4 2015-03-05 20:15:01

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Different Laws of Thought

I was not talking about the purpose of Mathematics at all.

I was asking if there could be an universe where fundamental consistency is violated. For example, could there be a universe where people accepted contradicting ideas.

I am not talking about physics, either.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#5 2015-03-05 20:18:36

bob bundy
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Registered: 2010-06-20
Posts: 8,137

Re: Different Laws of Thought

hi Agnishom,

The laws of quantum mechanics may well disobey those laws.

2 + 2 = 3

Easy:

TkftfgW.gif

In this vector space 2 + 2 = 3

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2015-03-05 20:21:08

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Different Laws of Thought

What does this grid mean?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#7 2015-03-05 20:27:09

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,137

Re: Different Laws of Thought

There are vectors going across, vectors going at an angle of cos-1 (-I/8)

A vector journey consists of going across the grid then up the sloping line.

Check the measurements and you'll find that 2 + 2 = 3

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#8 2015-03-05 21:21:14

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,137

Re: Different Laws of Thought

On the planet Zarkon in the Triplex Quadrant lies the city of Vectos.  The city has a grid structure road system like some US cities but the roads do not run North-South and East-West.  For religious reasons the road in Vectos run East-West and Phi-Kog like this:

TkftfgW.gif

The Vectons have invented a comms unit that you might mistake for a mobile phone.  But it is subtly different.  They haven't invented the phone mast.  If you want to use the comms to speak to another Vecton you have to have line-of-sight between your unit and theirs.  In this respect, the units are more like walkie-talkies.

If you are both on the same road it's easy as you can see each other along the road.  But, if the two are on different roads on the grid, the buildings get in the way and stop communication.  To get around this problem, the Vectons have built towers at every intersection.  A native Vecton is a good climber from birth, so they are for ever climbing the towers to get line-of-sight comms.

[The building regulations in Vectos say that every intersection must have a tower of a specific height and other buildings may be anywhere else but must not exceed the tower height.]

Comms units are sold by transmitting strength.  eg. a 6-unit will have sufficient transmitting power to reach a distance of 6 vecs from the unit.  Naturally the more power, the higher the cost so Vectons have to weigh up cost against transmitting distance when making a purchase.

At school, young Vectons are made to learn their distance rules just like we have to learn our tables.

For example,
2 + 2 = 3
2 + 5 = 5.6
7 + 5 = 9.1

and so on.   A mother might say to her child. "You may go out to play but don't go further than 6 vecs, so I can call you back for dinner."

One day humans and Vectons will meet and we will explain about phone masts.  On that day, the Vecton way of life will change for ever.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2015-03-06 00:26:48

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Different Laws of Thought

It all depends on the metric..


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#10 2015-03-06 11:13:12

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Different Laws of Thought

I was asking if there could be an universe where fundamental consistency is violated.

Fundamental consistency? What is that? Why are our set of rules any better than any other?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#11 2015-03-06 13:05:38

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: Different Laws of Thought

I am asking if it is.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#12 2015-03-06 13:19:09

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Different Laws of Thought

Since human mathematics is just a game meaning it is a logical ( to us ) set of rules, it is not hard to believe that there are an infinite number of equally valid rules.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#13 2015-03-07 03:40:59

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Different Laws of Thought

Hi Bob,

It's not correct to say there that 2+2=3. Plus is an operation on the lines, not their distances.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#14 2015-03-07 04:14:15

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,137

Re: Different Laws of Thought

hi Stefy,

I wondered when you'd get involved.

It's not correct to say there that 2+2=3. Plus is an operation on the lines, not their distances.

Have you been to Vectos?  The professors of maths there (funnily enough they spell it that way too) would disagree with you.  They say that they define it differently.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#15 2015-03-07 04:30:02

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Different Laws of Thought

The 2, 3 and + they are using are not the same as ours.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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