Flatlanders in the 3rd dimension "Hyperspace"

[ChrisisC]

Is the 4th dimension right under our noses?
In the book "Hyperspace" written by Machio Kaku (fantastic book, check it out), Kaku uses what he calls "flatlanders" to depict how, us, 3 dimensional people, could actually be involved in the 4th SPACIAL dimension (4th dimension is not used in the sense of "time" but space in this scenario). Kaku says that 2 dimensional flatlanders like on a line, to these flatlanders, they can only move Up,down,forward and backward, just like humans can only move up,down, forward, backward, and side to side. But Kaku says that a flatlander sciemctists studies this line and realizes that it's actually 3 dimensional. The people of flatland couldn't tell
they were on a 3 dimensional shape because the width of the line was just too small to
observe, so bringing that into real life... Are we humans those flatlanders? Could the 4th dimension be too small to observe directly? what are your thoughts?

 

[Drakkith]

Kaku says that 2 dimensional flatlanders like on a line,

I'm not sure what this means. Can you elaborate?

 

[jbriggs444]

Kaku says that 2 dimensional flatlanders like on a line

Traditionally a "flatlander" lives on a plane or, if one is trying to introduce curved geometry, a sphere. See https://en.wikipedia.org/wiki/Sphereland. A very good read.

 

[ChrisisC]

I'm not sure what this means. Can you elaborate?

In Kakus scenario, Flatlander people live on a line. Which is 2 dimensional.

 

[Drakkith]

In Kakus scenario, Flatlander people live on a line. Which is 2 dimensional.

You sure you don't mean a plane? A line is 1d while a plane is 2d.

 

[DrClaude]

By the way, Kaku did not invent Flatlanders: https://en.wikipedia.org/wiki/Flatland

 

[phinds]

@ChrisisC, Kaku used to be a serious physicist but has long since devolved into a popularizer and sensationalist of the worst sort so DO NOT try to learn physics from him.

PF is littered with threads disparaging him, which you can find with a forum search, and here are a smattering from other sources.

http://rationalwiki.org/wiki/Michio_Kaku
http://bigthink.com/ideas/26680
http://scienceblogs.com/pharyngula/2011/02/16/why-do-physicists-think-they-a/

 

[ChrisisC]

I'm reading his book "Hyperspace" which was written in the 1990's... It seems to make a ton of sense and the way he uses analogies to help the reader understand is quite fascinating, when particularly did he begin to stray away from his professionalism?

 

[ChrisisC]

You sure you don't mean a plane? A line is 1d while a plane is 2d.

Oops! I apologize I thought that a point like particle was 1 dimenstional, and then a like was 2. But a point like particle would be 0 dimensional? i don't understand how something could be 0 dimensional?

 

[jbriggs444]

Oops! I apologize I thought that a point like particle was 1 dimenstional, and then a like was 2. But a point like particle would be 0 dimensional? i don't understand how something could be 0 dimensional?

How many coordinate values does it take to describe the position of something already known to be on a particular plane: 2
How many coordinate values does it take to describe the position of something already known to be on a particular line: 1
How many coordinate values does it take to describe the position of something already known to be at a particular point: 0

The "dimension" of a space is [roughly translating the concept from linear algebra] the number of coordinate values it takes to define a position within that space.

 

[ChrisisC]

How many coordinate values does it take to describe the position of something already known to be on a particular plane: 2
How many coordinate values does it take to describe the position of something already known to be on a particular line: 1
How many coordinate values does it take to describe the position of something already known to be at a particular point: 0

The "dimension" of a space is [roughly translating the concept from linear algebra] the number of coordinate values it takes to define a position within that space.

Thanks for putting this in simpler terms! I'm trying to gather as much knowledge as possible

 

[phinds]

I'm reading his book "Hyperspace" which was written in the 1990's... It seems to make a ton of sense and the way he uses analogies to help the reader understand is quite fascinating, when particularly did he begin to stray away from his professionalism?

At least 10 years ago, probably more.

And he "strayed away from his professionalism" only in the sense that he CHANGED professions. He used to be a professional scientist, now he's a professional gadfly and I'm sure he gets paid much better now.