Kilogram to be redefined

[John McVey]

At present, the kilogram is internationally defined as the weight of a bar of a platinum-iridium alloy kept safe in a Paris laboratory. Nobody ever liked that too much, and wanted something better. What scientists have alway wanted was something that could be replicated indefinitely without having to measure it physically against either that particular standard or others so measured against it, because the standard as a physical object is susceptible to distortion from the slightest bit of dust and also polishing to get rid of it. That process also allowed errors to creep in and be replicated down through certification chains. To solve the problem, that meant defining the kilogram in terms of universal constants. This is now what is being done. The new standard is going to be that 1 kilogram will be exactly X number of atoms of silicon-28.

In order to ensure extreme consistency with all previous measurements, to calculate that number what is being done now is an international effort to take a hyperpure sample of silicon-28 from Russia, turn it into a single hyperregular crystal in Germany, then have it machined here in Australia to form the world's most perfect sphere ever made. The CSIRO took delivery 15th of June this year. They will then weigh the sphere against the current standard and machine it as needed to get the sphere dead on equal in weight. Once that is done they will then physically count all the atoms in the sphere. A sphere was chosen rather than a cube because it was easiest to do that counting for. Once counted, that number and the process of making the sphere become the new standard, replicable by any lab with suitable equipment.

Sands of time indeed. Fascinating!

JJM

[DragonMaci]

Unless they also redifine how much a gram is they shouldn't be doing that as a kilo is one thousand, so if they do this they should redfine a gram so that a kilogram is still a thousand grams.

[John McVey]

Unless they also redifine how much a gram is they shouldn't be doing that as a kilo is one thousand, so if they do this they should redfine a gram so that a kilogram is still a thousand grams.

The present use of the term kilogram rather than the plain gram is a historical artefact from the time when there were competing standards used by scientists. The whole scientific world has since converged on SI units. In that system the standard base unit of weight is the kilogram, where the gram is a derivative measure defined as 1/1000 of it.

JJM

[Qwertz]

If I understand SI, a gram is actually 1/1000 of a kilogram, rather than a kilogram being 1000 grams. The kg is the base SI unit for mass, so the definition of the gram won't change - 1g will still be 1/1000kg.

I presume they're making spheres because it's easier to measure the volume of a sphere, and the crystal process allows them to know with precision the number of atoms per unit volume. Perhaps Si forms crystals with highly regular and predictable atomic density. That's the only way I can think of how to arrive at the number of atoms in a mass without weighing it. Short of some fanciful atom-counting machine.

The meter used to be a metal rod, too. But they redefined it so that 1m = the distance traveled by light in a vacuum over a time interval equal to 1/299,792,458 of the time it takes for a stationary, ground-state Cs-133 atom at 0K to transition between its two electron spin energy states 9,192,631,770 times. That reduces to about 30 2/3 transitions of the Cs atom per meter, but that's only an approximation. I expect the n in "1kg = n atoms Si-28" will be likewise large and unwieldy, especially since they won't be able to shorten it by expressing n in mol instead of atoms - the mole is mass-dependent.

-Q

[DragonMaci]

Fine, then I am ok with what they are doing since gram will be reset value wise by de facto even if not definition wise. However, I think that in general the metric system is less objective than imperial as imperial has direct reference to something people can easy imagine. For example, an inch is about a thumb, or so I believe, and a foot is just that, a foot.

[DavidOdden]

However, I think that in general the metric system is less objective than imperial as imperial has direct reference to something people can easy imagine. For example, an inch is about a thumb, or so I believe, and a foot is just that, a foot.

A centimeter is about the size of your little fingernail, a meter is about the distance from your hip to the ground. A foot is about 9 inches, i.e. "about, but not quite, a foot". You are confusing objectivity with body-metaphoricality. For ordinary purposes, it doesn't matter if you express your height in meters or feet because there are simple ways to translate, if you're talking to somebody who doesn't know what a "foot" is. Note though that the traditional "foot" is useless as an objective measure because there is no objective standard for determining whether something is 1 foot long or 1.1 feet long except, as is done, to define the foot in terms of the meter. In which case, you not only to start with the meter as the basic unit of measurement, you also have to explicitly define the conversion ratio (.3048, or .30482, or something like that). You can define inches, furlongs, leagues and miles by some standard unit and a conversion number, though for the life of me I can't figure out what the official conversion for a furlong is. There is no problem with having a secondary concept, like a foot which is defined in terms of a more basic concept, but such a concept has to have an objective function. One of the functions of a measurement system is to allow one to measure, and to express significant relationships. The practical applicability of the metric system in terms of the simple volume / mass relationships for water effectively cancels out the intuitive approximation that a thumb is somewhere around an inch and a foot is somewhere around a foot. So there is no sense in which the English system is "more objective" than the metric system, and a real sense in which it's the other way around (the foot has no objective definition of its own).

[D'kian]

Not to mention the Imperial system is an arbitrary mishmash of units not related to each other. The Metric system's units are all integrated. For example, all measures of length are multiples or fractions of a meter. But it goes farther. A liter is a cubic decimeter, a kilogram is a liter of water (the units have since been redefined to more constant measurements, as noted above, but the integration remains).

[DragonMaci]

A foot is about 9 inches, i.e. "about, but not quite, a foot".

I thought a foot was 12 inches. That is certainly what I was taught and every conversion chart and dictionary I have looked in said.

You are confusing objectivity with body-metaphoricality.

No, not relly I am talking about objects in general, not just the body or arts of it. The body and its parts are not the only objects. I was merely using body part reference as two examples. That may be semantics, but if you are going to accuse people of things at least get your facts straight first. Also, a few weeks ago I had a good argument presented to me that a form of measurement that is easily referenced, which is true of the imperial system but not the metric system, is more objective. That was what convinced me of what I said.

For ordinary purposes, it doesn't matter if you express your height in meters or feet because there are simple ways to translate, if you're talking to somebody who doesn't know what a "foot" is.

So, you are saying the fact that it is easier for people to imagine 6'1" (my height) than it is for them to imagine 185 metres doesn't matter? I would definately disagree with that.

The imperial system has a dirtect reference to things people can easily imagine, such as a foor or a thumb, but the metric system has things people cannot easily imagine. A metre is defines as how far light travels in a given time (I cannot remember that time). That is both arbitrary and impossible for all but a scientist to imagine. To me such aritrariness seems the exact opposite of objective regardless of whether or not imperial is objective, so if an ything I would say, "and a real sense in which it's the other way around," is wrong in regards to metric at least, even if not about imperial.

Also, if the metric system is to being constantly redifined, that just makes it seem all the more arbitrary.

[softwareNerd]

I thought a foot was 12 inches.

When kids first learn about feet, a foot is about 5 inches -- maybe less.

...it is easier for people to imagine 6'1" (my height) than it is for them to imagine 185 metres doesn't matter?

You mean 185 centi-metres. If you think in metres, imagining 1.85 metres is just as simple, as imagining 6'1". Perhaps the larger number (when expressed in cm) blows "the crow".

Also, if the metric system is to being constantly redifined, that just makes it seem all the more arbitrary.

Do you understand the exact nature of this redefinition? For instance, do you realize that all measuring tapes can stay unchanged after this redefinition?

The base-12 systems are nice because a dozen cookies can be equally distributed among 2 people, 3 people or 4 people. One can probably make a case that as long as very simple measuring and portioning was needed, a base-12 system worked quite well.

However, since we use a base-10 numbering system, as we do more complex calculations, it's just easier to use units of measures where each larger unit is 10 of the smaller unit. Otherwise, we have to know our 144-times tables!

[DragonMaci]

When kids first learn about feet, a foot is about 5 inches -- maybe less.

Maybe that is the way it is done in the US, but we are never taught that here in New Zealand. The first, and only, figure we are taught is 12 inches.

You mean 185 centi-metres.

No, I mean 1.85 metres. My error was not putting in the decimal rather than using the wrong measurement. However, thanks or pointing out that I made an error.

Do you understand the exact nature of this redefinition? For instance, do you realize that all measuring tapes can stay unchanged after this redefinition?

I was talking about in general, not this particular redefinition.

A spelling correction was made.

Edited July 8, 2007 by DragonMaci

[softwareNerd]

Maybe that is the way it is done in the US, but we are never taught that here in New Zealand. The first, and only, figure we are taught is 12 inches.

I was just kidding. David used the term "foot" as in "normal size of a human foot" not "the 1 foot standard of measure". The latter is always 12 inches. The former is little less.

[DragonMaci]

I was just kidding. David used the term "foot" as in "normal size of a human foot" not "the 1 foot standard of measure". The latter is always 12 inches. The former is little less.

Oh, ok, I apologise for not realising. I should of payed more attention to the laughing emoticon. I will make an effort to do so in the future.

[Moebius]

Unless they also redifine how much a gram is they shouldn't be doing that as a kilo is one thousand, so if they do this they should redfine a gram so that a kilogram is still a thousand grams.

Easily solved by anyone who knows how to do simple division.

However, I think that in general the metric system is less objective than imperial as imperial has direct reference to something people can easy imagine. For example, an inch is about a thumb, or so I believe, and a foot is just that, a foot.

A measurement isn't objective. It's arbitrary. One measurement can't be any more objective than another.However, one measurement could be more convenient than another. The fact that the metric system uniformly increases by a factor of 10 makes it much more convenient in almost every instance.

So, you are saying the fact that it is easier for people to imagine 6'1" (my height) than it is for them to imagine 185 metres doesn't matter? I would definately disagree with that.

It isn't any harder for someone to picture 185 centimeters if they grew up with the metric system. In fact it would probably be much harder and wildly inaccurate if they tried to picture a literal "foot" stacked six high (since, you know, everyone has a different sized feet).

[DragonMaci]

The fact that the metric system uniformly increases by a factor of 10 makes it much more convenient in almost every instance.

It is less convient to visualise for most people. For most people a foot or inch is easier to visualise. They are also easier toestimate if you have no means of actually measuring the distance. For myself, neither is easier to viusalise since I can barely visualise at all. Edited July 9, 2007 by DragonMaci

[Moebius]

It is less convient to visualise for most people. For most people a foot or inch is easier to visualise. They are also easier toestimate if you have no means of actually measuring the distance.For myself, neither is easier to viusalise since I can barely visualise at all.

I don't think ANYBODY visualizes a foot as an actual, literal foot. Measurement is learned through experience (plus or minus a person's natural spatial perception capacities), and whether it is easier to measure in terms of feet or meters is determined almost entirely by your experience using them.

And besides, it would probably be exceeding difficult to to measure distances like, say, 200 feet by visualizing 200 of your own actual foot. This would be even harder for things like weight.

[DragonMaci]

I don't think ANYBODY visualizes a foot as an actual, literal foot.

I am sorry I didn't realise i said the word "literal". I thought I hadn't. But you think i did so i must of. Oh, no wait I definately did not.

And besides, it would probably be exceeding difficult to to measure distances like, say, 200 feet by visualizing 200 of your own actual foot..

Easier than visualising its metric equivalent, about 66 metres.

This would be even harder for things like weight

Um, i believe I said distance not weight. Edited July 9, 2007 by DragonMaci

[DavidOdden]

No, not relly I am talking about objects in general, not just the body or arts of it.

But if you're confused about the meaning of "objective", as you evidently are, and think that "objective" means "defined by analogy to an everyday object", then my comment which is about just the body part definitions is still correct. The weak similarity between the physical object "foot" and the homophonous measurement "foot" doesn't make the foot a more objective measure. You have not provided any reason to support your conclusion that the English system of measures is more objective, as you did state. See post #5, "the metric system is less objective than imperial". Objectivity is a concept that relates to reality, not imagination.

So, you are saying the fact that it is easier for people to imagine 6'1" (my height) than it is for them to imagine 185 metres doesn't matter?

I have no idea what that could possibly mean. What do you mean by "imagining" 6'1"? How do you "imagine" a concrete number? Do you really think that you are 185 metres tall (I think we've found the root of your problem). Are you objecting to the fact that the centimeter is a more precise measurement without the use of fractions?

If you're complaining about the fact that when you grow up under the English system, it's difficult to translate when speaking to others who use metric, that's true but irrelevant to the issue of objectivity. Objectivity doesn't mean "facility of use for a particular person". That would be closer to subjectivity.

An objective definition is one that is defined "out there in the world", open for public inspection. The main flaw of the English system is that it is defined in terms of a specific artifact (though now that has been repaired by defining the inch in terms of the meter). You have yet to show how the concept of "objective" is more applicable to one system of measurement vs. another. If you mean that you are personally more familiar with the English system or are more comfortable with it, I don't dispute that and I share the same "Now how do I convert that?" experiences.

The imperial system has a dirtect reference to things people can easily imagine, such as a foor or a thumb, but the metric system has things people cannot easily imagine.

This is simply false. I told you that the foot at the end of the leg is not a foot, a thumb is not an inch long, and in the case of the foot, the actual foot is a lousy approximation of the measurement foot. It is plainly false to fact that a foot is defined as "the length of a man's foot": a foot is defined in terms of the meter, and so whatever problem you have with the concept "meter", it's even worse for the foot because the foot is a meter times some arbitrary number that nobody remembers. Furthermore, if you use your foot as the basis for measuring lumber and sell five thousand "feet" of flooring to a person, you will be committing fraud.

A pint is a totally arbitrary measure. It has no relationship to anything in reality, though you can give it a definition by referring it to some objective measurement system like the liter. A teaspoon is a completely arbitrary measure. Spoons used for tea are not "a teaspoon" in measure. A cup holds between a half a cup and a pint. A foot is not a foot, an inch is not a thumb, a pound is not a (I have no idea what the supposed common object it that defines a "pound"). No rods are actually a rod long. And where in the world is a man's yard only a yard deep? (Maybe central London). The relationship between these units of measurement and common objects is terrible, and worse, highly subjective. People have different size feet, thumbs, spoons and back yards, and to even think that such ill-defined things form a valid basis for "defining" a measurement is to reduce the art of measurement to subjectivism. To be "defined", a measurement must have an objective standard, and "a thumb" is simply not an objective standard.

[DragonMaci]

But if you're confused about the meaning of "objective", as you evidently are, and think that "objective" means "defined by analogy to an everyday object", then my comment which is about just the body part definitions is still correct.

Actually, I don't think it means that. I will admit I accidently implied that I think that, but I don't and never have. I am sorry for accidently misleading you.

Objectivity is a concept that relates to reality, not imagination.

Objectivity doesn't mean "facility of use for a particular person". That would be closer to subjectivity.

Yes, I am quite aware of that. However, I will again admit that I accidently implied otherwise. Again, I am sorry about accidently misleading you.

I have no idea what that could possibly mean. What do you mean by "imagining" 6'1"?

I am sorry, that was bad wording. I meant visualise not imagine. Visualising a cetain measurement is the best that can be done when one does not have a measuring device.

How do you "imagine" a concrete number?

One does not, which is why I was not suggesting one does. I was suggesting visualisation of distance as a substitute when one has no measuring device. Furthermore, people don't measure large distances like 10 kilometres or 10 miles often. Instead they visualise it because it would be impractical to measure that large a distance.

Do you really think that you are 185 metres tall (I think we've found the root of your problem).

If you had of bothered to read one of my above comments you would of seen that I corrected myself to 1.85 metres and me saying that my mistake was accidently forgetting the decimal place. If you don't bother to read corrections you have no grounds to complain about mistakes that people make.

Are you objecting to the fact that the centimeter is a more precise measurement without the use of fractions?

Um, no, far from it. I don't know how you could come to such an illogical conclusion as a result of my addicently leaving out a decimal place. it is quite obvious even before I said it that my error was to forget the decimal place. Either that or I meant centimentres not metres. However, I fail to see how centimetres is more precise that a decimal place. 85 cetmetres is not only the same as .85 metres, it is .85 metres. Since they are exactly the same, how is centimetres any more precise?

you're complaining about the fact that when you grow up under the English system, it's difficult to translate when speaking to others who use metric, that's true but irrelevant to the issue of objectivity.

Actually I grew up with metric and learned imperial reading fantay books and looking in the dictionary to see what measurements like an "inch" and a "foot" were. As, I grew up with metric, so I am more used to that. As for my comfort, I am no more comfortable with either. As I said above, neither is easier for me to visualise due to the fact that I can barely visualise at all. I have nearly no ability to visualise, so I am no better at visualising either. For that reason I have no preference. But that is due to my own limited ability, not the nature of either.

You have yet to show how the concept of "objective" is more applicable to one system of measurement vs. another.

If you mean that you are personally more familiar with the English system or are more comfortable with it, I don't dispute that and I share the same "Now how do I convert that?" experiences.

Well, given that I never intended to convince anyone of it and that I don't care whether or not others agree with me why would I bother?

This is simply false.

No, it isn't. Few people can imagine how far light travels in a given time. Furthermore, that time is, of course, arbitrary.

I told you that the foot at the end of the leg is not a foot, a thumb is not an inch long, and in the case of the foot, the actual foot is a lousy approximation of the measurement foot.

Yes, but, and this is a big but, it is easier for people to imagine than how far light travels in a given time. Few people can imagine that at all. Most people can get a close approximation of a foot or inch.

a foot is defined in terms of the meter

I have never seen nor heard any such definition before, I have only seen and heard other definitons. In fact the measurement foot was around before the measurement metre was, so i am quite doubtful of your claim. So until you prove it, I see no reason to think you are correct. I don't take what people say on word, especially when I see things to the contrary.

Furthermore, if you use your foot as the basis for measuring lumber and sell five thousand "feet" of flooring to a person, you will be committing fraud.

Ok, now you're just being patronising! There is absoultely no nheed to resort to patronisation! Only a moron would use their foot as opposed to a measuring tape! I would appreciate it if in future if you don't assume I am dumb enough not to use a measuring tape in such a situation!

A pint is a totally arbitrary measure. It has no relationship to anything in reality, though you can give it a definition by referring it to some objective measurement system like the liter.

How many times do I have to say, I am talking about distance only. Besides, a litre is no less abitrary.

A foot is not a foot, an inch is not a thumb

Maybe you missed the word roughly in what I said before. Never once did I use the words literally or exactly. if you don't read all of what is said you have no grounds to complain about what is said since you missed sme of it and so never got the full story.

To be "defined", a measurement must have an objective standard, and "a thumb" is simply not an objective standard.

Oh, and, "the distance light travels in a given time is"? Given that whatever the "given time" of a metre is is abitrary, there is clearly nothing objective about a metre.

[DavidOdden]

I will admit I accidently implied that I think that, but I don't and never have.

You need to learn to use English literally. Think about what you want to say before you say something that reveals a lack of thought, where you have to waste time apologizing for your errors in expression and you have to twist and turn evasively for having mistakenly suggested that there is something "more objective" about the English measurement system. Learn what words mean, and use them correctly. And now, this aspect of the discussion is over, as in finished, ended, terminated.

[DragonMaci]

You need to learn to use English literally. Think about what you want to say before you say something that reveals a lack of thought, where you have to waste time apologizing for your errors in expression and you have to twist and turn evasively for having mistakenly suggested that there is something "more objective" about the English measurement system. Learn what words mean, and use them correctly. And now, this aspect of the discussion is over, as in finished, ended, terminated.

Firstly, I was not evasive. Secondly, I am actually quite good with definitions. However, I am usually not good at thinking what I say through properly unless, a) I am trying to write a story, or I conciously make a lot more effort, which I am not good at remembering to do. In short, it is my application that is flawed, though only becaue of forgetting to properly think through what I say, not because of a lack of knowledge.

Maybe I should treat writing here as if I am writing one of my stories. It is the editing that makes the difference with my story writing. If I do the same here I might do a better job of saying what I mean. I never forget to make the extra effort when editing my stories, so maybe treating this a bit like that will help. I tend to write first drafts that don't get my message across, but my second and subsequent drafts tend to be a lot better. It has certainly helped make this post a lot better than it originally was (I trialed it with this post).

[Qwertz]

The International yard was defined in 1958 as 0.9144 meters, and the International foot as 1/3 an international yard.

The US Survey foot 1200/3937 meters. It is the 'foot' used by US land surveyors, and is about 610nm longer than the International foot.

Prior to 1958, the foot was defined by the inch (12in). Physical exemplars were used to define the inch since about the 12th century. The inch has its origins in the width of a man's thumb, but this definition was displaced when exemplars came into use. Prior to the 12th century, a man's foot (with shoe) was probably used for the foot, but this usage was displaced by physical exemplars when standardized measurements were needed for commerce.

The original definition of the meter, incidentally, was some small, round fraction (1/10,000,000, I think) of the distance from the North Pole to the Equator through Paris. It is to this measure that the metal rod exemplar was made.

-Q

[Capitalism Forever]

I just measured my thumbs and both have a width of exactly 1 inch and 0 thirty-seconds.

[Moebius]

Yes, but, and this is a big but, it is easier for people to imagine than how far light travels in a given time. Few people can imagine that at all. Most people can get a close approximation of a foot or inch.

Most people can just as easily get a close approximation of a centimeter or a meter also. You're just going from approximating one arbitrary length to another. Just because a meter is defined as some arbitrary distance traveled by light, how does that make it any harder to approximate?

I have never seen nor heard any such definition before, I have only seen and heard other definitons. In fact the measurement foot was around before the measurement metre was, so i am quite doubtful of your claim. So until you prove it, I see no reason to think you are correct. I don't take what people say on word, especially when I see things to the contrary.

Well sorry to dash it for you but DavidOdden is in fact correct. An inch is defined as 0.3048 metres. From Wikipedia:

International foot

In 1958 the United States and countries of the Commonwealth of Nations defined the length of the international yard to be 0.9144 metres. Consequently, the international foot is defined to be equal to 0.3048 metres (equivalent to 304.8 millimetres).

United States survey foot

The United States survey foot is defined as exactly 1200⁄3937 metres, approximately 0.30480061 m. It is used only in connection with surveys by the U.S. Coast and Geodetic Survey. It is 610 nm greater than the international foot. [2] The U.S. Survey Foot is used by Land Surveyors and other cartographers for the plans and maps they produce. Each state has a law that states which form of the foot is used for surveys within the given state. The difference is particularly noticeable when converting coordinates that are on the State Plane Coordinate System of the given state.

So, there goes every single one of your arguments.

How many times do I have to say, I am talking about distance only. Besides, a litre is no less abitrary.

Actually, you began by talking about the metric system in general. Distance was just one of your examples. This is in fact what you said:

I think that in general the metric system is less objective than imperial as imperial has direct reference to something people can easy imagine. For example, an inch is about a thumb, or so I believe, and a foot is just that, a foot.

All discussions thereafter was regarding this statement. So no, you weren't talking about distance only, because you clearly referred to the metric system "in general". Are you now changing your story?

Oh, and, "the distance light travels in a given time is"? Given that whatever the "given time" of a metre is is abitrary, there is clearly nothing objective about a metre.

You are confusing "arbitrary" with "objective". Something can be both arbitrary AND objective -- they are not mutually exclusive. To be objective, it just has to be based on fact, and exist independently from feelings, interpretations, or prejudices. The speed of light is objective, hence the definition of a meter is objective. Obviously you had no idea what a foot actually was, but since we have established that a foot is defined by a meter, that means a foot is also objective.

Essentially, a foot and a meter is equally arbitrary, as well as equally objective. Your original claim is therefore erroneous.

[DavidOdden]

Something can be both arbitrary AND objective -- they are not mutually exclusive. To be objective, it just has to be based on fact, and exist independently from feelings, interpretations, or prejudices.

...

Essentially, a foot and a meter is equally arbitrary, as well as equally objective.

In fact, neither concept is arbitrary. The meter is based on the cubit, an arm-length measurement, whereby lengths of cloth and rope were measured. The science of measurement has progressed by successively eliminating subjective elements, whence the Royal Artifact approach. The 1-second half-cycle pendulum length and the 1/10,000,000 Earth quadrant length definitions both define the meter in terms of an objective fact while remaining as close to the historical cause of the meter as would be sensible. Subsequent refinements of the definition have worked to retain the original referent, which is clearly not an arbitrary value.

[Ralph Hertle]

The kilogram has been redefined. In science that is major good news.

That means that the Ancient Greek scientific, philosophic, and geometric principles of scientific concept [magnitude to the Ancient Greeks], even-ness, and continuity of principle are the current causal scientific standard.

Interestingly, the methods of manufacturing a sphere permit the precise counting of the number of atoms, and the units of mass, in the kologram object.

The kilogram has survived more accurate than ever.

Science in that sphere has now moved forward and become more precise and more knowable.

To find out how those principles, e.g., even-ness and continuity, are some of the most basic causal principles to the Industrial Revolution read David Pye.

Unfortunately, Dr. Harry Binswanger's destructive criticism of the whole of the geometry of the Ancient Greeks is still the standard of Objectivism, and his lectures on the subject are still being sold by ARI. He says that the straight line, for example, should not be defined by length and even-ness, and that it should be defined by direction from a point and not to a second point. His view requires a direction, however, a direction requires a straight line. Pos hoc ergo propter hoc. The former is demonstably true, and the latter is a definition by a non-essential characteristic. His theories on that topic are demonstrably false or are impossible to demonstrate. A major contradiction exists, and for reasons that I fail to understand the Objectivists are not wanting to confront the issue. ARI should withdraw the CD, or sell it with a warning label.

Support the geometry of the Ancient Greeks and the Industrial Revolution.

Ralph Hertle