Famed Harvard Biologist Gould Dies

http://story.news.yahoo.com/news?tmpl=story&cid=514&ncid=716&e=2&u=/ap/20020520/ap_on_re_us/obit_gould ^ | 5/20/02 | yahoo

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See source for details....

[AndrewC]

OK. So?

From this answer I conclude that you agree with my contention that there are non-physical "things". Furthermore, from your answer in post 922 you admit that these "things" cannot be understood in any meaningful way with physical measurement. So we have non-physical things that are associated with physical things but are unexplainable by these physical things. Are we together here?

[general_re]

Do you always have your tongue in your cheek?

Not always. Sometimes the smile comes with a dagger ;)

[general_re]

1. The figure formed by two lines diverging from a common point.

A good illustration of the limits of general dictionaries in defining mathematical concepts. Consider triangles instead of squares for a moment. Given:

c² = a² + b² - 2abcos(X)

('X' only because I'm not sure everyone can see a theta in their browsers :^) )

What, then, is the value of the given angle 'X' when sides a, b, and c are all zero?

[BMCDA]

It's not defined.

[general_re]

Which should hardly be a surprise, given the nature of the triangle we are describing, don't you think? ;)

IOW, the law of cosines still holds true, even in such a case - it is a law, after all. So to define an angle as "two lines diverging from a common point" is too restrictive - defining it in such a manner implicitly assumes that there is a length involved, when the formal relationship between the sides and angles of a triangle requires no such thing.

[AndrewC]

What, then, is the value of the given angle 'X' when sides a, b, and c are all zero?

BMCDA answered you. I agree.

[AndrewC]

P.S. If you want an illustration go here and set all the sides to zero and click on Angle C. Now put 1,9,1 as the sides and click on Angle C. Same answer. 1,9,1 is not a triangle and neither is 0,0,0.

[general_re]

Same answer. 1,9,1 is not a triangle and neither is 0,0,0.

As much as I hate to use the word on this thread yet again, it is a degenerate triangle. And since, as longshadow has pointed out, the original question never excluded degenerate figures, I have appropriated longshadow's arguments for the unstated remainder. Maybe I can't give you square circles, but I can approximate triangular ones. ;)

[BMCDA]

A length is required.
A line is defined by two points that don't have the same coordinates and for an angle you need at least three points which don't share the same coordinates. These three points form the two diverging lines that comprise an angle (if two points have the same coordinates you have an angle of "0").
So if these points must have different coordinates in order to make sense, you automatically have lenghts that are strictly greater than zero.

[jennyp]

From this answer I conclude that you agree with my contention that there are non-physical "things". Furthermore, from your answer in post 922 you admit that these "things" cannot be understood in any meaningful way with physical measurement. So we have non-physical things that are associated with physical things but are unexplainable by these physical things. Are we together here?

"Associated with physical things"? No! Metaphysically joined at the hip with physical things! Just because it might be practically intractable for someone to analyze a person's thoughts or feelings by mapping their neurons & current potentials, does not mean that the mind is separate from the brain that generates it. So clearly, no we aren't together.

In post 847 I said: "I don't know if "mental terms cannot in principle be replaced by physical terms", but in practice it makes much more sense to deal with the two phenomena on their own terms. And yet it's intuitively obvious that they're two sides of the same coin."

And in post 937 I said: "[The question 'why' is] not physical in a simple sense, yet it is in that it takes a physical person to form the question 'why' in the first place. So I treat the distinction as moot."

"Neutral monism" is the term. (I must remember that.) Here again from the Lewes bio:

In The Physical Basis of Mind [10], which forms the third volume of Problems of Life and Mind, Lewes articulated the classic modern formulation of double aspect theory, dual-aspect monism. In presenting his position, Lewes went well beyond the theories of his predecessors, supplementing the double aspect notion with a view that has come to be called neutral monism. Neutral monism involves the claim that there is only one kind of "stuff" and that mind and body differ only in the arrangement of that stuff or in the perspective from which it is apprehended.

[general_re]

A length is required.

It has a length - zero.

A line is defined by two points that don't have the same coordinates and for an angle you need at least three points which don't share the same coordinates.

Nahh, only if you're interested in defining planes from that. I'm not interested in your planar figures, I'm interested in point-figures. So maybe it's a degenerate angle - whaddaya gonna do? Can't have everything ;)

These three points form the two diverging lines that comprise an angle (if two points have the same coordinates you have an angle of "0").

Or an angle of 2pi radians (360 degrees). Or 4pi radians (720 degrees). Or 6pi radians (1080 degrees). And so forth, on into infinity.

Or, insofar as infinite quantities are usually regarded as undefined, an undefined angle ;)

So if these points must have different coordinates in order to make sense, you automatically have lenghts that are strictly greater than zero.

If they must have different coordinates, you're right. But the question was never defined that way, so I submit that it is a technically correct answer to the question. Or, at least an answer to triangular circles. The relationship between the sides and lengths of a triangle does not specify, a priori, that the lengths must be non-zero - the relationship still holds for triangles of zero length.

And insofar as we can imagine a square as being composed of two right triangles that share a common hypotenuse, I think I can buy you some square circles too. Imagine two degenerate triangles of length 0,0,0 that share a common side to form a degenerate square. Since the angles of our degenerate triangles are undefined, the angles of our new degenrate square must also be undefined. Badda-bing-badda-boom - a degenerate square with length zero, and undefined angles, and now we have our point-square, which is also a point-circle. And we don't even have to worry if those triangles were really right triangles either ;)

Gentlemen, behold the thing that could not exist - I give you...the square circle ;)

[AndrewC]

As much as I hate to use the word on this thread yet again, it is a degenerate triangle.

You can call it Bozo the Clown, but that does not make it Bozo the Clown. It is not a triangle. It is a point, and maybe a point circle, but is not a square nor a triangle. What are the angles for this point? Further are you agreeing with longshadow's argument using unit vectors of length zero?

[PayrollOffice]

A wise man once told me not to bewilder the ignorant. Apparantly Gould was a very rude type. What type was he anyway?

[AndrewC]

Metaphysically joined at the hip with physical things!

This discussion is rapidly becoming senseless. What are your definitions of metaphysically and moot?

[general_re]

It fits the definition of a triangle as long as you're willing to set aside that inconvenient triangle inequality theorem ;), and an equilateral triangle to boot - it has three equal sides of length zero. At least, it satisfies the definition for the purposes of forming a triangle circle. You can calculate the values of the angles yourself, if you like. I think you already did, actually ;)

Equilateral triangles are usually regarded as having three equal angles of 60 degrees. But that is a consequence of having three equal sides of length > 0, not a part of the definition of an equilateral triangle. Obviously, that does not hold true when the lengths are equal to zero.

[AndrewC]

You can calculate the values of the angles yourself, if you like. I think you already did, actually ;)

Yes, that applet did. The result was NaN which means not a number(undefined). The fact that one can play games and define a new geometry is not a secret. But people tend to have agreed upon foundations from which to proceed in debates. So in closing my participation in this greased pig contest I will give a few links to definitions.

Unit Vectors

Unit Vectors:

• Vectors that indicate Direction Only.
• The Length of a Unit Vector is always equal to One.

Triangle -- from Mathworld

Allowable side lengths a, b, and c for a triangle are given by the set of inequalities a > 0, b > 0, c > 0, and , , .

Degenerate --- from Mathworld

A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as the radius approaches 0

[general_re]

Pssst. Go back and look at my post 955 and read the little text again - your definition from Mathworld isn't telling me anything I don't already know....

Go easy, FRiend - as heartlander pointed out, this thread "degenerated" some time ago, so it's all in good fun. No need to get ulcers over triangular circles, I say ;)

[general_re]

IOW, you yourself said that square circles are "foolishness" - don't go getting all serious on me now ;)

[jennyp]

Metaphysically joined at the hip with physical things!

This discussion is rapidly becoming senseless. What are your definitions of metaphysically and moot?

By "metaphysically" I mean pertaining to a thing's essential nature. It's the nature of at least some non-physical entities (we're discussing "mind" and related entities) to be inextricably and fundamentally - "metaphysically" - related to the physical objects that generate them (i.e. the brain). It's a moot point, IOW useless, to try to claim that they're inherently separate entities, even though it makes more sense to analyze the nonphysical mind in very different terms than the physical brain.

If you think that's senseless, then I don't know what to say, except "g'nite".

[AndrewC]

Well, let us see what you have said.

Metaphysically joined at the hip with physical things! = (The essential nature of something is to be) joined at the hip with physical things..

It is the nature of at least some non-physical entities (omitted) to be (superglued, as an essential and necessary part) – “(pertaining to the essential nature)” – related to the physical objects that generate them. It is useless to try to claim that they’re (essential characteristic)ly separate entities, even though it makes more sense to analyze the nonphysical mind in very different terms than the physical brain.

That makes it evident that your mind is metaphysically(in the jennyp sense) closed. You have defined the mind and brain relationship despite acknowledging that even for something as simple as a digital computer one cannot determine purpose from physical measurement. I do note that somehow you have made a weaker statement for the mind in claiming that it makes more sense to “analyze” the mind in different terms than the brain. That is in contrast to -- you won't understand why it happened in any meaningful way by examining the electronic pulses. But then again you might have meant – it is difficult to understand why …

In any case, it is as I suspected, a senseless endeavor to go on. Nothing could sway your mind. I seem to remember making a similar statement to you with respect to miracles. You would never accept anything as a miracle. I believe I presented it as a question which you never answered. One further rhetorical question before I close. Do you know what an emulator is?

I suggest you use naturally or inherently instead of metaphysically, that way you won’t confuse people.