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Reconstructo
 
Reply Mon 19 Apr, 2010 11:55 pm
@ughaibu,
ughaibu;154312 wrote:
There are no negatives in hat problems, there are only smaller or larger numbers than any given number, plus a first number, and a last number of it's a finite hat problem. Numbers are considered to be players, who dont know what colour of hat they're wearing. Ordinarily, the conditions state either that a player can see all hats (other than their own) or only all hats in the positive direction, seeing all hats in the negative direction is another way of stating the algorithmic induction problem.


Oh, I see what you mean. But just to make my point clear, one doesn't need the negative for bi-directionality. All one needs is a spectrum, the natural numbers conceived of as a sequence. And if they are not conceived of as a series (with the exact same interval in between them, which is crucial) they are not numbers in the usual sense. Note that you say they can only see in the positive direction, which means that the game or problem is indeed directional. Even if the hats ignore one directional possibility, they are still arranged bidirectionally, right?

Of course I'm not trying to start an argument. The essence of my point is that a single dimension is always bidirectional, and I think this is just how humans are forced to intuit things. I'm going to look up the algorithmic induction problem. Smile
 
TickTockMan
 
Reply Tue 20 Apr, 2010 12:04 am
@Reconstructo,
Reconstructo;154219 wrote:
I can dig that idea. Here's the paradox for me. Consciousness as a product of biology, and biology as a product of consciousness. I feel like its a moebius strip. What is concept? Could computers have what we refer to "consciousness"?


Yes, this is a paradox.

If one is to buy the package labeled "Biology is a Product of Consciousness," wouldn't one have to by the whole package, that everything (even hard sciences and mathematics) is the product of consciousness, and take the leap to some form of Hyper-Solipsism, where not only is there no brain in a vat, there is no vat. Nor is there even a brain, for that matter. But if there is no brain, what is the agent of consciousness?

At this level even Solipsism would seem to fall apart as there would be no self that could be known or experienced, only a great nothingness (or no thingness, as some Eastern philosophies like to say) which gives rise to the myriad things.

Is consciousness something that has arisen from nothingness then?

This, I think, is where the real mind-bender of the Tao comes into play when it says (and the phrasing may vary depending on your translation, but the idea is the same), "The Tao that can be spoken of is not the Tao." I wonder if this could be extended to say, "nor is the Tao that can be pondered the Tao."

Each answer seems to give rise to more questions, and each answer is immediately suspect and of marginal, if any, use at all.

A Moebius strip is just a fox chasing its own tail, the very definition of insanity: that of doing the same thing over and over and expecting different results.

Perhaps this is why some traditions advocate and teach methods to silence all internal dialog and obliterate the ego and simultaneously all concepts of dualism.

All this said, I would not suggest that I believe any of the above random ramblings.

They're just thoughts that occur to me now and then.

There are other beliefs that are much easier to maintain, and I suspect I've taken your original post way off topic and/or completely missed the point.

Cheers,
The Consciousness known as TickTockMan
 
Reconstructo
 
Reply Tue 20 Apr, 2010 12:14 am
@TickTockMan,
TickTockMan;154333 wrote:
Yes, this is a paradox.

If one is to buy the package labeled "Biology is a Product of Consciousness," wouldn't one have to by the whole package, that everything (even hard sciences and mathematics) is the product of consciousness, and take the leap to some form of Hyper-Solipsism, where not only is there no brain in a vat, there is no vat. Nor is there even a brain, for that matter. But if there is no brain, what is the agent of consciousness?

At this level even Solipsism would seem to fall apart as there would be no self that could be known or experienced, only a great nothingness (or no thingness, as some Eastern philosophies like to say) which gives rise to the myriad things.

Is consciousness something that has arisen from nothingness then?

This, I think, is where the real mind-bender of the Tao comes into play when it says (and the phrasing may vary depending on your translation, but the idea is the same), "The Tao that can be spoken of is not the Tao." I wonder if this could be extended to say, "nor is the Tao that can be pondered the Tao."

Each answer seems to give rise to more questions, and each answer is immediately suspect and of marginal, if any, use at all.

A Moebius strip is just a fox chasing its own tail, the very definition of insanity: that of doing the same thing over and over and expecting different results.

Perhaps this is why some traditions advocate and teach methods to silence all internal dialog and obliterate the ego and simultaneously all concepts of dualism.

All this said, I would not suggest that I believe any of the above random ramblings.

They're just thoughts that occur to me now and then.

There are other beliefs that are much easier to maintain, and I suspect I've taken your original post way off topic and/or completely missed the point.

Cheers,
The Consciousness known as TickTockMan


I think you are well on topic. And I agree with you about the complexities of the mind/matter dualism. I was saying that reality was concept, but if reality is concept, then concept is the wrong word, as it smells of idealism. I think this is what Hegel meant when he said that subject was substance. His idealism was absolute, which I take to mean undiluted. And if all is mind, then all is just as well matter, for "mind" and "matter" depend on one another for contrast. "The tao that can be named." That's like my signature, which is from Hegel. I feel that it it's the same deal. Some hard thinkers really worked on this issue, and realized it was bogus, that the dichotomy itself was a confusion, even if a natural and necessary stage in the development of the philosophical mind.

Well, this is why I'm so into proto-logic. I want to see what kind of glasses I am wearing, or what kind of glasses reality is wearing....Smile

Let's play with this idea. THat reality is a moebius strip. Well, then the actual mobius strip when contemplated would be Realities self-consciousness. Hegel tried to present Reality as Spirit, as being revealed by language. Pretty slick. Of course in German "geist" means mind as much as spirit, or so they say.
 
Deckard
 
Reply Tue 20 Apr, 2010 12:24 am
@Reconstructo,
Hey does the "di" in dimension mean "two"? I guess that would be bimension but maybe the Latin "dis" (apart) traces back through some round about way to the Greek duad. Online Etymology dictionary doesn't seem to support my claim but I don't care. Words like dissect and divide and direction similar to dimension in this respect perhaps.

A trimension or quadrimension or ... would be redundant as they could be just as well and more clearly outlined in terms of dimensions. Did someone say this already?

monomension?


Oh but wait I just thought of something. Buckminster Fullers geometry

That Cartesian way of dividing up things also assumes right angles and perpindicularity. I remember Fuller thought this was a big mistake and rather than dividing space in terms of squares and cubes and hypercubes and...etc. we should be thinking in terms of triangles and tetrahedrons and hypertetrahedrons and...etc.

Fullers point is that squares can be divided into triangles so triangles are more basic. We should not be thinking in terms of rectalinear grids but in term of (what's the word) 60-degree-a-linear frameworks.


So anyway that's my initial response. Now I'll go read what other people have said.
 
Reconstructo
 
Reply Tue 20 Apr, 2010 12:45 am
@Deckard,
Deckard;154344 wrote:
Hey does the "di" in dimension mean "two"? I guess that would be bimension but maybe the Latin "dis" (apart) traces back through some round about way to the Greek duad. Online Etymology dictionary doesn't seem to support my claim but I don't care. Words like dissect and divide similar to dimension perhaps.

I bet you're right. Sounds likely.

---------- Post added 04-20-2010 at 01:46 AM ----------

Deckard;154344 wrote:

A trimension or quadrimension or ... would be redundant as they could be just as well and more clearly outlined in terms of dimensions. Did someone say this already?

I suggest that dimensions times two equals directions. For instance, we live in 3d, and six directions. (Diagonals don't really count.)
 
ughaibu
 
Reply Tue 20 Apr, 2010 12:46 am
@Reconstructo,
Reconstructo;154346 wrote:
I bet you're right. Sounds likely.
You lose your bet: Online Etymology Dictionary
 
Reconstructo
 
Reply Tue 20 Apr, 2010 12:47 am
@Deckard,
Deckard;154344 wrote:

monomension?

A static infinitesimal point? A single digit (1) with no operators to be found. ?

---------- Post added 04-20-2010 at 01:50 AM ----------

ughaibu;154348 wrote:
You lose your bet: Online Etymology Dictionary

Tragic. I will pay i^2(200 dollars) to the authorities.

---------- Post added 04-20-2010 at 01:52 AM ----------

Deckard;154344 wrote:

Oh but wait I just thought of something. Buckminster Fullers geometry

That Cartesian way of dividing up things also assumes right angles and perpindicularity. I remember Fuller thought this was a big mistake and rather than dividing space in terms of squares and cubes and hypercubes and...etc. we should be thinking in terms of triangles and tetrahedrons and hypertetrahedrons and...etc.

Fullers point is that squares can be divided into triangles so triangles are more basic. We should not be thinking in terms of rectalinear grids but in term of (what's the word) 60-degree-a-linear frameworks.

I've heard a bit about that. Even if its better, are we still going to intuit dimensions as bidirectional? I've read something about quaternians (which I think are unrelated), but I don't know if they are an exception. Probably not.
 
Deckard
 
Reply Tue 20 Apr, 2010 12:54 am
@ughaibu,
ughaibu;154348 wrote:
You lose your bet: Online Etymology Dictionary



I win!


note the Greek at the end!

Quote:
a Latin prefix meaning "apart," "asunder," "away," "utterly," or having a privative, negative, or reversing force ( see de-, un-2 ); used freely, esp. with these latter senses, as an English formative: disability; disaffirm; disbar; disbelief; discontent; dishearten; dislike; disown.


Use dis- in a Sentence

See images of dis-

Search dis- on the Web

Also, di-.

Origin:
Dis- | Define Dis- at Dictionary.com

---------- Post added 04-20-2010 at 02:28 AM ----------

Reconstructo;154349 wrote:

I've heard a bit about that. Even if its better, are we still going to intuit dimensions as bidirectional? I've read something about quaternians (which I think are unrelated), but I don't know if they are an exception. Probably not.


Shoot, I'm not sure about the quaternions or how it gets to the "quat" which I assume means "4" but suffice to say complex numbers are very powerful. Weirdness of a mension or a few mensions sort of folded up in the square root of -1 perhaps? Gosh but I'm just throwing imaginary darts in the dark.

Regarding the "biderectionality" of Fullers "dimensions".

Hmmm...well...lets we think about the point, the monomension, as the starting point. We are sitting at the point and at this point we can decide how many "mensions" we are going to expand into. And by expanding into I mean developing a latice that incorporates more mensions.

If we decide upon two mensions i.e "dimension" then it will be bidirectional or didirectional, if you will, or rather just plain "directional" (taking account of the fact that Latin "dis" is already hiding in the word "directional")

Okay okay...if we decide upon 3 mensions then we will have trimensions that we can think about trirectionally; if 4 then quadmensions, quadrectionally.

But shucks, we have that Latin "rectus" following us like a spy for the government, pretending not to have an agenda, infiltrating our meetings and spreading its subliminal propaganda. Not sure what to do about rectus. What makes a right angle "right"?

But maybe this is just fun with words words words? No, I think it's worth thinking about a little at least. Yet, at some point we may have to bow to convention, so long as we don't mistaken such conventions for a meaningful traditions? No! If we were really going to break things down and believe in what we are doing we would have to break the language down as well since we are conscious of the etymological baggage that comes with the words we are using.


One last thing to remember, in the most general sense, mensions (measures) need not be spatial nor temporal.

---------- Post added 04-20-2010 at 02:45 AM ----------

Reconstructo;153802 wrote:
Unified quantity can only vary within a dimension.


Is each mension a quality within which quantity can be measured? Spatially that quality might be rightness or leftness, upness or downness but it can also be other qualities...but only quantifiable quantities. Are there qualities that defy quantification? Is something lost in quantification? Can what is lost be recovered by introducing another mension or two or three...So many different qualities to measure eventually we will develop shortcuts that will become ambiguous and our geometry will devolve or evolve into a more or less naive, more or less arbitrary, language like English for example.
 
Reconstructo
 
Reply Tue 20 Apr, 2010 01:56 am
@Deckard,
Deckard;154356 wrote:

I win!


note the Greek at the end!

Dis- | Define Dis- at Dictionary.com

---------- Post added 04-20-2010 at 02:28 AM ----------



Shoot, I'm not sure about the quaternions or how it gets to the "quat" which I assume means "4" but suffice to say complex numbers are very powerful. Weirdness of a mension or a few mensions sort of folded up in the square root of -1 perhaps? Gosh but I'm just throwing imaginary darts in the dark.

Regarding the "biderectionality" of Fullers "dimensions".

Hmmm...well...lets we think about the point, the monomension, as the starting point. We are sitting at the point and at this point we can decide how many "mensions" we are going to expand into. And by expanding into I mean developing a latice that incorporates more mensions.

If we decide upon two mensions i.e "dimension" then it will be bidirectional or didirectional, if you will, or rather just plain "directional" (taking account of the fact that Latin "dis" is already hiding in the word "directional")

Okay okay...if we decide upon 3 mensions then we will have trimensions that we can think about trirectionally; if 4 then quadmensions, quadrectionally.

But shucks, we have that Latin "rectus" following us like a spy for the government, pretending not to have an agenda, infiltrating our meetings and spreading its subliminal propaganda. Not sure what to do about rectus. What makes a right angle "right"?

But maybe this is just fun with words words words? No, I think it's worth thinking about a little at least. Yet, at some point we may have to bow to convention, so long as we don't mistaken such conventions for a meaningful traditions? No! If we were really going to break things down and believe in what we are doing we would have to break the language down as well since we are conscious of the etymological baggage that comes with the words we are using.


One last thing to remember, in the most general sense, mensions (measures) need not be spatial nor temporal.


I agree that mensions don't have to be spatial. For instance, sets aren't spatial, and they are a sort of mension. Monomensions? It does seem that number (sequential) implies di-mension. Either just the Euclidean Line or the Complex plane, or a 3d system. The question remains: do we just naturally think of any spatial dimension as bidirectional...at least when it comes to formalizing it? Or shall I say visualizing it? (Beauty forcing truth?)
Bucky was prob on to something, but then the Pyth theorem is pretty potent. Also it seems that i is used for 90 degree rotations in some significant way in electronics. But I'm a tourist on that issue.

The right angle! Ah yes. Perpendicularity. Does this not connect to the imposition of a number upon the bidirectional number line? The number is singular, is quantity incarnate. The digits are considered as a unity. And we plop them down sequentially by means of these same digits. Reminds me of baby Jesus in the lap of Mary. Unity the son/phallus, and duality is the matrix/mother. The Line would be Time and the number would be eternity.
Our digit for unity is itself the line it has its home on. And zero is recursion incarnate. 1 is written in 1 dimension. 0 in two. 0 is the fulcrum of the negative/positive realms. But I might be having too much fun here..

---------- Post added 04-20-2010 at 02:58 AM ----------

Deckard;154356 wrote:

Is each mension a quality within which quantity can be measured? Spatially that quality might be rightness or leftness, upness or downness but it can also be other qualities...but only quantifiable quantities.

Great questions. What is quantity? It seems like essence and accident. It's essence is that it's a singular object. Its accident would be its position on the mension?

---------- Post added 04-20-2010 at 03:01 AM ----------

Deckard;154356 wrote:
. Are there qualities that defy quantification? Is something lost in quantification?

I think almost everything is lost. But a certain hard core of pure form remains. What are inverse functions, within this context? An inverse is like a binary mirror-image, right? And all the operators have inverses. So this is the 2 thing again, running thru the metamension of dynamics.

I think it's exactly because so much is lost in quantification that so much is also revealed.

---------- Post added 04-20-2010 at 03:04 AM ----------

Deckard;154356 wrote:
..So many different qualities to measure eventually we will develop shortcuts that will become ambiguous and our geometry will devolve or evolve into a more or less naive, more or less arbitrary, language like English for example.

There does seem to be a limit. Perhaps if certain practical purposes are achieved by stacking dimensions, the specialist will toy with them. I lost interest in hyper-spheres, hypercubes, etc. the more I looked at solids. I want to enjoy my geometry. I hear that the mathematica program can solve all sorts of calculus problems, even the rare ones. This is a good, because I only really give a damn about essence...and have no enthusiasm for the complex problems, but only the poetry of the thing. I wouldn't be surprised if they could keep it all rigorous, but perhaps it would lose its "magic", if overcomplicated.
 
TickTockMan
 
Reply Tue 20 Apr, 2010 05:02 pm
@Reconstructo,
Reconstructo;154339 wrote:

Let's play with this idea. THat reality is a moebius strip. Well, then the actual mobius strip when contemplated would be Realities self-consciousness.


I played around with the Moebius strip, tinkered with a few parts, and damned if it didn't turn into Ouroboros.
 
Reconstructo
 
Reply Tue 20 Apr, 2010 05:04 pm
@TickTockMan,
TickTockMan;154632 wrote:
I played around with the Moebius strip, tinkered with a few parts, and damned if it didn't turn into Ouroboros.


A circle is a logarithmic spiral with a zero growth grate. When e dies it becomes a piece of pi.
 
TickTockMan
 
Reply Tue 20 Apr, 2010 05:21 pm
@Reconstructo,
Reconstructo;154634 wrote:
When e dies it becomes a piece of pi.


YouTube - WHAT DO I THINK OF THE PIE?????
 
Deckard
 
Reply Tue 20 Apr, 2010 07:08 pm
@Reconstructo,
Reconstructo;154634 wrote:
A circle is a logarithmic spiral with a zero growth grate. When e dies it becomes a piece of pi.



What's the equation for a spiral? I mean the one that includes e.
 
Reconstructo
 
Reply Tue 20 Apr, 2010 08:00 pm
@Deckard,
Deckard;154687 wrote:
What's the equation for a spiral? I mean the one that includes e.



r = ae^(b*theta)

b would represent the growth rate. if b = 0, then e ^(b*theta) = 1.

and this would leave us with r = a, which is a circle with the radius of a.

Quote:

Spira mirabilis, Latin for "miraculous spiral", is another name for the logarithmic spiral. Although this curve had already been named by other mathematicians, the specific name ("miraculous" or "marvelous" spiral) was given to this curve by Jacob Bernoulli, because he was fascinated by one of its unique mathematical properties: the size of the spiral increases but its shape is unaltered with each successive curve, a property known as self-similarity. Possibly as a result of this unique property, the spira mirabilis has evolved in nature, appearing in certain growing forms such as nautilus shells and sunflower heads. Jakob Bernoulli wanted such a spiral engraved on his headstone along with the phrase "Eadem mutata resurgo" ("Although changed, I shall arise the same."), but, by error, an Archimedean spiral was placed there instead.[2][3]
I found this out first from Eli Maor in "e : the story of a number." I can't believe they screwed up his tombstone.

More math details here: Logarithmic spiral - Wikipedia, the free encyclopedia

---------- Post added 04-20-2010 at 10:21 PM ----------

I was thinking today about the coordinate plane, the number line, etc., and how these were at least as important as the numbers that danced on them. The matrix. The grid. Of course we need to see them in action, perhaps, to catch their essence, but after that the Cartesian plane when blank has a personality. The C plane is two dimensions, for directions, of course. 2 to the second. Is the Black Painting, in its various forms, an attempt to show the "grid" of Art...a representation of representation? I care what the painter meant, but I also care about what I can squeeze out of their work. That's what's great about art (incl Math), one is working in objects-for-others. Objects that can exist for the eyes or at least the minds of others. But this always requires a matrix, material or imaginary, explicit or implicit. (?) That last line was an assumption, it now seems.
 
Deckard
 
Reply Tue 20 Apr, 2010 10:13 pm
@Reconstructo,
Reconstructo;154695 wrote:
r = ae^(b*theta)

b would represent the growth rate. if b = 0, then e ^(b*theta) = 1.

and this would leave us with r = a, which is a circle with the radius of a.


Hey that's neat. Thanks. With the other equation

theta = ln(r/a)/b

If b= 0 then theta is undefined? But I think this is probably unimportant.
 
ughaibu
 
Reply Tue 20 Apr, 2010 10:28 pm
@TickTockMan,
TickTockMan;154333 wrote:
A Moebius strip is just a fox chasing its own tail, the very definition of insanity: that of doing the same thing over and over and expecting different results.
You might prefer hexaflexagons, they're related to Moebius strip, but do give different "results".
 
Reconstructo
 
Reply Tue 20 Apr, 2010 10:45 pm
@Deckard,
Deckard;154722 wrote:

theta = ln(r/a)/b

If b= 0 then theta is undefined? But I think this is probably unimportant.

I guess it would. I'm guessing that because the constants are arbitrary, one could just make b equal to 1 to neutralize it. My brain doesn't like it defined in terms in theta. Another weakness (or sloth) I must confess is an aversion to "ln" as the symbol for natural log. I know its useful, but the artist in me would prefer to see logs written in exponential form. Or maybe a one character symbol. I find the "dx" notation in calc a little annoying to. I like the deltas.
I was just researching triple integrals in spherical coordinates. Now that's an awesome matrix. That integral sign is a beauty. I also love radians. Something about definite integrals defined in terms of pi. It looks like rho is used for radius in spherical coord. I'm a sucker for greek letters. What amazes me about calculus, which is still quite new me, is that so much information is hidden within the information we already have. From the original equation (static relationship) we can derive a dynamic relationship. From there it's amazingly possible to get the volume of apparently irregular shapes. Of course it's just because these shapes aren't irregular at all, and precisely defined by equations that we can manage this. It's such a mental mastery of space. I'm proud of the humanimals for inventing this thought-tech.Pauls Online Notes : Calculus III - Triple Integrals in Spherical Coordinates
 
ughaibu
 
Reply Tue 20 Apr, 2010 10:57 pm
@Reconstructo,
Addendum to my above post: YouTube - 12 leaf hexaflexagon
 
TickTockMan
 
Reply Wed 21 Apr, 2010 12:14 pm
@ughaibu,
ughaibu;154742 wrote:
Addendum to my above post: YouTube - 12 leaf hexaflexagon


Okay. That's pretty cool.
 
Reconstructo
 
Reply Mon 10 May, 2010 11:29 pm
@Reconstructo,
Well, the number 2 continues to fascinate me. Especially when we consider the bit. I feel that the bit is almost the center of the information age. Yes or no. On or off. 1 or 0. Add them up.

Also the Continuum Hypothesis relies on the number two. Because any member of a set either is or is not a member of a subset within that set. Are you in or out? Are you with us or against us? Can we break it down more than that? Fuzzy logic is an increase of complexity. A spectrum implies a multitude of states. 2 is the minimum plurality. A dimension has two directional possibilities. Left or Right. Up or Down. True or False. Also we all have two parents.
 
 

 
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