Can we find the square root of two on the Real number line?
The following is a debate between Root Two and Lady Jane.
Who wins?
people cannot draw perfect circles, but that doesn’t mean they don’t or cannot exist.
Root two is composed of opposite hemispheres
which rotate in opposite directions - equal
to a zero value existence (plus & minus). As
entity, the opposite hemispheres cancel out.
Root two exist as 4 - 90 degree opposite corner
quadrants, but not as a 360 degree circle.
Root two is Cubic opposites, nothing as circle.
A singularity inflicted scholar has not the
mentality, freedom or guts to know that
academia is a Trojan Horse mind control.
Singularity brotherhood owns your brain,
destroying your ability to think Cubicism.
Evil academia blocks out Time Cube site
and suppresses its discussion and debate.
You are an educated singularity idiot who
can stupidily deny Nature’s Harmonic 4
simultaneous 24 hour days within a single
rotation of Root two, or even make parody of
the Cubic Creation Principle - but your
mental ability to comprehend thegreatest
social and scientific discovery of all human
existence has been lobotomized by the evil
academic singularity bastards hired to
destroy your ability to think opposite. You
cannot comprehend Opposite Creation.
Religous/academic taught singularity is the
reduction of the human mind to android.
The half of Root two seen from
space, cannot exist without
the opposite half not seen…
existing as opposite values.
Root two entity does not exist -
for it is composed of opposite
hemispheres which rotate in
opposite directions - equating
to a zero value existence, and
to nothing as a “singularity”.
You were educated to live an
evil lie - and your heirs will
suffer hell for your stupidity.
The entity you seek is death.
Hi to Wonderer,
The drawing is intended to be a representation of theoretical circle (in blue) whose center is at the origin (intersection) of the vertical and horizontal lines.
The blue line segment is intended to represent the radius of that circle, and the radius should be intersecting the circle at the point (1, 1).
I assumed that everyone would use the Pythagorean Theorem to deduce that the length of the radius squared equals 1 squared + 1 squared, and thus the radius would be square root 2. This in turn means that the length from the origin to where the blue circle intersects the horizontal line is the square root of 2.
Background:
Ladyjane often quotes Colin Leslie Dean at:
gamahucherpress.yellowgum.com/bo … ience4.pdf
(Not working at the current time)
One of the claims in that article is that we can not locate root 2 on the Real line.
I would guess that the overwhelming vast majority of college prep students at one time or another has seen a drawing very similar to what I have displayed above. Surprisingly, when this subject was brought up before no one offered this well known analysis.
Current Matters:
The reason that I have not offered this analysis myself is because there is an underlying fundamental assumption that the Pythagorean Theorem is always valid.
This is not the case.
There are two proofs of the Pythagorean Theorem. One is an “algebraic” theorem attributed to Pythagoras or his students and the other is the Euclidean proof.
Historians tell us that the Pythagorean Theorem was considered of fundamental importance and for Euclid to have a successful mathematical book he needed to come up with a geometric proof of this theorem. He could not devise a proof of this theorem without resorting to the use of the famous parallel postulate. Without this postulate there is no geometric proof of the Pythagorean Theorem.
If we examine the algebraic proof, we need to look at the following figure.
The standard proof states that the area of the large square is (a + b) squared (). The area of the four dark grey triangles is 4(1/2 * ab) () and the area of the light grey square is c squared ()
Multiplying out (a + b) squared is (a squared + 2ab + b squared), and multiplying out 4(1/2 * a*b) is 2ab. Using the fact that the large square is equal to the 4 triangles + the small square we get:
a squared + 2ab + b squared = 2ab + c squared.
Subtracting 2ab from each side we get the famous theorem.
However, statements *, **, *** are all false in non Euclidean geometry. In Riemannian geometry the areas are all greater than Euclidean geometry and in the geometry attributed to Lobachevsky & Bolyai the areas are all less than in Euclidean geometry.
No matter how I look at it, we need to specify the geometry before we can make the claim that we know where root 2 lies on the Real line.
Hi to Xunzian,
I would like to mention that I have read some of your previous posts, and you are one of my favourite posters.
However, I clearly do not understand most of this post.
The following figure is a first stab at understanding your root 2 comments
However, the length of the radius to any of the vertices on the embedded cube is root 3, assuming that we are using an Euclidean metric and the length traversed from the origin on each dimension is 1. This can be normalized to root 2 but I don’t see the point.
I am generally a curious person and would like to know more. Do you have a resource for me to read?
I do know that there are interesting mathematical entities called Quaternions which have a 4 dimensional feel and the operations on them cancel each other out. e.g. i*j = -1.
Anyway I am curious.
Thanks Ed
Ed3, Xunzian’s post is a joke referencing the time cube phenomenon (google it).
On the internet there are always hordes of idiots ready to tell us about how X is all wrong and the X establishment is concealing the truth. Here X = math, but it can also equal physics, medicine, biology, or just about any intellectual endeavor imaginable. It’s so cliche by now.
It makes me wonder – have anything with the typical ingredients of these sort of conspiracy theories ever been proven true?
Ever?
it is a precision issue.
we cannot make a scane number line and point our precisley where root 2 is just as i cannot manually divide 1 by 3.
being able to “point something out on a number line” doesn’t make one difference this way or that.
did you know we cannot precisley locate 1 on a precise numebr line?
did you know we cannot make a precise number line?
put simply, just because we cannot see it does not mean it doesn’t exist.
Glad somebody got the joke. wipes away tear Ohhh, Time Cube cracks me up every time – speaking of which, wow, Ed3, you managed to make more sense out of the Time Cube stuff than I ever have. There is plenty of insane rambling on the net, some of it is worth responding to, some of it is just so many different kinds of crazy that you can just sit and stare in wonder. LadyJane/Dean’s posts on mathematics tend to be of the latter variety. Talking to them about it generally makes about as much sense as smashing your head up against a wall. But it can be a great joke.
What does it mean to “manually divide” something by something else?
Do you mean compute the decimal expansion? Decimal expansion is only one way to represent a number. And different numbers have finite decimal expansions in different bases. Often, numbers with a terminating expansion in one base have an infinite repeating expansion in another base. For example, 1/3 is written as “0.1” in base 3 expansion, but has the expansion “0.010101…” in base 2. 1/2 is written as the infinite repeating expansion “0.111…,” in base 3, but just as “0.1” in base 2, or “0.5” in base 10.
If you say that you can only “manually divide” when the result has a terminating digit expansion, you have to specify which base you are working in. 1/2 is “manually divisible” in bases 2 and 10, but not in base 3. 1/3 is “manually divisible” in base 3 but not in base 2 or 10.
There’s nothing sacred about the decimal system such that finite decimals correspond to real “manual division” and infinite decimals don’t. The decimal system is just one measuring stick for measuring numbers. Other measuring sticks exist, so to be consistent you should say it’s impossible to divide any number by any other number “manually”.
We only work in base 10 because we have 10 fingers. You don’t want to base math on something that arbitrary do you?
If you give me your attention, I will tell you what I am.
I’m a brilliant math’matician - also something of a ham.
I have tried for numerous degrees, in fact I’ve one of each;
Of course that makes me eminently qualified to teach.
I understand the subject matter thoroughly, it’s true,
And I can’t see why it isn’t all as obvious to you.
Each lecture is a masterpiece, meticulously planned,
Yet everybody tells me that I’m hard to understand,
And I can’t think why.
My diagrams are models of true art, you must agree,
And my handwriting is famous for its legibility.
Take a word like “minimum” (to choose a random word),
{This was performed at a blackboard, and the professor wrote:
////////////////}
For anyone to say he cannot read that, is absurd.
The anecdotes I tell get more amusing every year,
Though frankly, what they go to prove is sometimes less than clear,
And all my explanations are quite lucid, I am sure,
Yet everybody tells me that my lectures are obscure,
And I can’t think why.
Consider, for example, just the force of gravity:
It’s inversely proportional to something - let me see -
It’s r^3 - no, r^2 - no, it’s just r, I’ll bet -
The sign in front is plus - or is it minus, I forget -
Well, anyway, there is a force, of that there is no doubt.
All these formulas are trivial if you only think them out.
Yet students tell me, “I have memorized the whole year through
Ev’rything you’ve told us, but the problems I can’t do.”
And I can’t think why!
Ah, Tom Lehrer. The best jew, like ever.
Has anybody considered that the radius of the circle is ever-changing due to the nature of pi and that root two doesn’t exist, because order in pi doesn’t exist? (except for when I can afford Shari’s a la mode) Therefore, if it has no correlation to the principle, then it hasn’t earned its “right to exist” on the number line, because the number line is actually a bunch of spoiled rich kids who picked on root two in the square root of second grade.
Hi Aporia,
Thanks for the heads up!
Hi Wonderer,
I was going to post on the topology of the Real line, showing that it was metrizable; and pointing out how any Afine transformation (a transformation of the form x’ = ax + b) of the Real line would yield another Real line. This means that 0 and 1 can be any two distinct points; and that we can construct the Natural Numbers and Rational Numbers in a rather straight forward manner. But I like Aporia’s response better.
If you look at Anthem’s post, Aporia’s post, and my post in “Limits” you will get correct and logical answer on your subject matter. I do not care to discuss this matter any longer publically (too many silly responses), but if you PM me I will be happy to go into this subject matter in depth with you.
On Ladyjane:
It is very clear to me that Ladyjane is in large part the Yin to our Yang. This naturally sparked some of the better posts in this forum. Without him we would not have Aporia’s post on Godel’s theorem, and at least a couple of my posts on model theory.
Personally, I learned that there was an alternative axiomization of to ZFC set theory. In addition I cleaned the clock of some guy named Bertrand Russell, in a debate over the Peano axioms. He couldn’t even respond to my post. Imagine that!
In any case it is obvious to me that Ladyjane has been a boom to this site.
i know. i was just saying how in our base system practical uses of root 2 end up being similar to 1/3.
who needs manual when we have the imagination? or it’s lesser cousin “approximation”?
what i’m trying to asy that the root 2 issue is more of a visual problem than anything, much like .3bar. (not to open old wounds)
no not at all. What i was trying to voice is that our measuring sticks don’t have enough notches on them. as a result in the physical world we have to approximate the notch. but just because we cannot find the notch doesn’t mean it doesn’t exist.
Well what if i had only 9 fingers? 
I might have done beter pointing out the fact that these problems arise because of the base system. I took that route in the .999bar argument but it seemed to get me nowhere.
Allow me to needlessly consolidate my position into one simple statement.
You cannot iodentify root 2 on a number line just like you cannot write our infinite 3’s after the decimal in .3bar.
You can’t prove infinity, but you can exercise in futility for a lifetime without anything to show for it.
I wanna challenge ladyjane to a debate where she’s gotta prove that there can be a triangle which isn’t 3 sides and 180 degrees.
Ed3’s diagram does define sqrt(2) on the number line provably and exactly. It is the unique intersection point of the circle and the line he drew. What do you mean by “identify” and how does Ed3’s drawing fall short of it?
I also enjoy watching people sweat when they exercise in futility… 