Ellen Stuttle

Knowledge vs. Dogma - "Infinitesimal"

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Bob writes:

The square root of -1 is the unit vector turned 90 degrees counter clockwise

That doesn't mean that the square root of a minus number isn't contradictory.

Greg

The theory of complex numbers is as consistent as the theory of real numbers. They can be derived from each other.

Godel proved that the consistency of a theory sufficient to support arithmetic cannot be proven with the system

So far no one has shown in inconsistency within the system of real numbers which is just as consistent as the theory of rational numbers which is just as consistent as the arithmetic of integers. We have no absolute proof of the consistency of arithmetic.

Ba'al Chatzaf

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There is no issue with the theory of complex numbers being consistent. I suspect what is intended in the discussion is whether or not complex numbers in and of themselves have an identifiable matching real world identity and causality related compliment - which they do not. That is not the intention of complex numbers. They are a tool in mathematics allowing ease of computational manipulation in compact form with known properties of how to convert those results back to real world identity and causality related compliments.

Dennis

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Dennis writes:

There is no issue with the theory of complex numbers being consistent. I suspect what is intended in the discussion is whether or not complex numbers in and of themselves have an identifiable matching real world identity and causality related compliment - which they do not. That is not the intention of complex numbers. They are a tool in mathematics allowing ease of computational manipulation in compact form with known properties of how to convert those results back to real world identity and causality related compliments.

Dennis

Thanks for clarifying the point, Dennis. You obviously speak with way more mathematical authority than I could ever have! :laugh: I only know that the square root of minus one (i) literally translates as imaginary and not real. And even though it is a mathematical contradiction, it can nevertheless still be identified.

Humans constantly deal with fantasy by learning how to cancel it out of the equation of reality.

Greg

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Thanks for clarifying the point, Dennis. You obviously speak with way more mathematical authority than I could ever have! :laugh: I only know that the square root of minus one (i) literally translates as imaginary and not real. And even though it is a mathematical contradiction, it can nevertheless still be identified.

Humans constantly deal with fantasy by learning how to cancel it out of the equation of reality.

Greg

Dammit. It is NOT a mathematical contradiction. You simply do not understand it.

The set of real numbers does not contain the root to the equation x^2 + 1 = 0. There complex number system is an extension field of the real number system which contains the roots of x^2 + 1 = 0.

Geometrically the unit length complex number are the set of vectors rooted at the origin with unit length. Ever such unit complex number can be written as cos x + i*sin x for x in the interval [0, 2pi). Every complex number can be written in the form r*z where r is a real number >= 0 and z is a unit length complex number The sums and products of such numbers are easily defined so the complex number system is a field with addition, multiplication, subtract, division (by anything but 0) just like the real number system except product of the complex numbers with real, imaginary parts (0,1) with itself is (-1, 0) so it is a root of

x^2 + 1 = 0.

I simply do not understand where you get the idea there is a contradiction here. It is quite straight forward.

Ba'al Chatzaf.

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There is no issue with the theory of complex numbers being consistent. I suspect what is intended in the discussion is whether or not complex numbers in and of themselves have an identifiable matching real world identity and causality related compliment - which they do not. That is not the intention of complex numbers. They are a tool in mathematics allowing ease of computational manipulation in compact form with known properties of how to convert those results back to real world identity and causality related compliments.

Dennis

Well neither do the real numbers for that matter.

They are a tool in mathematics allowing ease of computational manipulation in compact form with known properties of how to convert those results back to real world identity and causality related compliments.

Once again, one could say the exact same thing about the real number system. Real-world measurement apparatuses never display a decimal to infinite precision.

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Bob writes:

Dammit. It is NOT a mathematical contradiction.

Yes it is.

Mathematics rationally labels the contradictions "imaginary numbers" so as to properly deal with them.

Just as rational people become aware of "imaginary fantasies" so as to properly deal with them.

Greg

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Since the numbers are imaginary one can image them being either contradictory or not without contradiction beyond the labeling. The numbers must be used rationally and logically; the labels don't matter. I assume--I don't know--real numbers have direct metaphysical referents while imaginary ones spin off the real numbers and as such are purely epistemological constructs. I am thinking of a boomerang with that object only being thought.

--Brant

a layman's view

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Since the numbers are imaginary one can image them being either contradictory or not without contradiction beyond the labeling. The numbers must be used rationally and logically; the labels don't matter. I assume--I don't know--real numbers have direct metaphysical referents while imaginary ones spin off the real numbers and as such are purely epistemological constructs. I am thinking of a boomerang with that object only being thought.

--Brant

a layman's view

"Imaginary" was an ill conceived adjective to describe complex numbers. Is is a misnomer of the same sort as the descriptive phrase applied to the Higgs Boson --- The God Particle!!!!! Jesus H Kryst, I detest journalists.

Or if you will, ALL NUMBERS ARE IMAGINARY, even integers.

Pairs of socks exist in the physical world. The number 2 only exists as a pattern of neurological processes in our heads.

Ba'al Chatzaf

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[...] I loath Metaphysics. For deep down metaphysics I have contumely, low-regard, dislike, detestation, and utter contempt.

Yet on another thread about five hours later the same day you wrote:

My motive would be to find causes and from that cures. Anything is is quack-quack.

What are causes if not "deep down" metaphysics?

Ellen

Initial conditions that lead to subsequent conditions in an (empirically) regular manner. The idea of "necessary connection" between cause tokens and effect tokens has been effectively trashed by Hume. Empirically on can establish connections that happened in the past and use these as provisional markers. There is no absolute guarantee that the connections will -always- hold in the future or in conditions unlike any seen in the past. Cause to Effect is an empirical practical matter no a metaphysical absolute.

The lack of contingency or provisional truth is lacking in metaphysics which is what makes it almost useless for science.

Ba'al Chatzaf

You have a peculiar idea of metaphysics. You've stipulated so limited a meaning you don't recognize metaphysics when you're writing it yourself.

Ellen

I confess to Reality Lite.

1. There is an Out There out there.

2. We can figure out part of it.

3. We will never know all of it.

Ba'al Chatzaf

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"Imaginary" was an ill conceived adjective to describe complex numbers. Is is a misnomer of the same sort as the descriptive phrase applied to the Higgs Boson --- The God Particle!!!!! Jesus H Kryst, I detest journalists.

Was "imaginary numbers" coined by a journalist? There have been plenty of misnomers coined by scientists. Do you detest Fred Hoyle, for instance?

Ellen

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You have a peculiar idea of metaphysics. You've stipulated so limited a meaning you don't recognize metaphysics when you're writing it yourself.

I confess to Reality Lite.

1. There is an Out There out there.

2. We can figure out part of it.

3. We will never know all of it.

Ba'al Chatzaf

Can you figure out which part you can figure out? Or is the difference between what you can and what you can't figure out something you'll never know?

Ellen

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It's really not valuable to say "all numbers are imaginary." The real numbers have real referents, no? Zero (O) is imaginary with zero referents. The invention of the zero ranks with the invention and practical use of the wheel.

--Brant

are we having a real or imaginary discussion?

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It's really not valuable to say "all numbers are imaginary." The real numbers have real referents, no? Zero (O) is imaginary with zero referents. The invention of the zero ranks with the invention and practical use of the wheel.

--Brant

are we having a real or imaginary discussion?

Mathematical abstractions have no existence outside of our heads.

As I have said. I have many pairs of sox in my drawer but the number 2 is not to be found outside of people's brains.

Ba'al Chatzaf

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That's just using conceptual thinking. "Man" is in your head and men or a man is out there. "Desk" is in your head and desks or a desk is out there.

--Brant

there is no "zero" out there

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"Imaginary" was an ill conceived adjective to describe complex numbers. Is is a misnomer of the same sort as the descriptive phrase applied to the Higgs Boson --- The God Particle!!!!! Jesus H Kryst, I detest journalists.

Was "imaginary numbers" coined by a journalist?

According to Wikipedia, Descartes was the first to apply imaginary (imaginaires in French) to numbers.

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Brant writes:Since the numbers are imaginary one can image them being either contradictory or not without contradiction beyond the labeling. The numbers must be used rationally and logically; the labels don't matter. I assume--I don't know--real numbers have direct metaphysical referents while imaginary ones spin off the real numbers and as such are purely epistemological constructs. I am thinking of a boomerang with that object only being thought.

--Brant

a layman's view

You know, Brant...

It just struck me that this discussion possesses a fascinating parallel to truth and lies. Lies are imaginary claims of non reality, and as such are not real. And yet we can know the truth about lies which is real. :smile:

Greg

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I think you're stretching it a little thin, Greg. Anyway, your proposition reads better as "Lies are imaginary claims on reality" or "Lies are claims on imagined reality," etc. You kinda hit/made an obscurely stated double negative.

--Brant

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Brant writes:I think you're stretching it a little thin, Greg. Anyway, your proposition reads better as "Lies are imaginary claims on reality" or "Lies are claims on imagined reality," etc.

It is impossible for a lie to make a claim on reality. Only a liar can claim that a lie is reality. But when a person knows a liar is lying, they know the truth about the lie as well as the liar.

Greg

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Brant writes:

said "claims." I did not say "enforceable claims."

--Brant

That's right. They won't stick. Lies can only prevail over lesser lies.

Greg

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"Imaginary" was an ill conceived adjective to describe complex numbers. Is is a misnomer of the same sort as the descriptive phrase applied to the Higgs Boson --- The God Particle!!!!! Jesus H Kryst, I detest journalists.

Was "imaginary numbers" coined by a journalist?

According to Wikipedia, Descartes was the first to apply imaginary (imaginaires in French) to numbers.

Thanks, Merlin.

And providing the Wikipedia statement:

The term "imaginary" for these quantities was coined by René Descartes in 1637, although he was at pains to stress their imaginary nature[17]

[...] quelquefois seulement imaginaires cest-à-dire que lon peut toujours en imaginer autant que j'ai dit en chaque équation, mais quil ny a quelquefois aucune quantité qui corresponde à celle quon imagine.

([...] sometimes only imaginary, that is one can imagine as many as I said in each equation, but sometimes there exists no quantity that matches that which we imagine.)

However, oh, well.

I meant the question rhetorically as counter-thrust to another of Bob's formulaic-rage replies.

Hence the question if Bob detests Fred Hoyle:

link

Ironically, he [Holyle] coined the the "Big Bang" as a derogatory description of the theory, but the term stuck.

Ellen

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Significant question asked but thus-far unanswered:

You have a peculiar idea of metaphysics. You've stipulated so limited a meaning you don't recognize metaphysics when you're writing it yourself.

I confess to Reality Lite.

1. There is an Out There out there.

2. We can figure out part of it.

3. We will never know all of it.

Ba'al Chatzaf

Can you figure out which part you can figure out? Or is the difference between what you can and what you can't figure out something you'll never know?

Ellen

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Significant question asked but thus-far unanswered:

You have a peculiar idea of metaphysics. You've stipulated so limited a meaning you don't recognize metaphysics when you're writing it yourself.

I confess to Reality Lite.

1. There is an Out There out there.

2. We can figure out part of it.

3. We will never know all of it.

Ba'al Chatzaf

Can you figure out which part you can figure out? Or is the difference between what you can and what you can't figure out something you'll never know?

Ellen

The event horizon for the cosmos we can observer increases in radius by one light year a year. Anything beyond that we must do without. If the light cannot reach us it can not tell us anything.

Ba'al Chatzaf

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And what we see is not necessarily what we need to see; its future usefulness though is possible--usefulness for whatever.

--Brant

and this planet will cease to be habitable long before the next billion years are up as the sun simply gets inexorably hotter--something we don't need to know--in a hundred million years there may still be sharks in the ocean but not a thing recognizably human on land, assuming the land is still habitable at all

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