hear hear

this is interesting. Units are important to measurement and to definitions

It may not be science but it is the way most scientists think.

Attempting to reduce scientific thinking to "models" under the Pragmatist mantra of "useful" is bad epistemology, with the expected consequences that you repeat in non-answers to posts on Objectivist epistemology. You can't "think about something" that isn't an awareness of it.

You claimed "that scientists 'understand' reality in terms of models and that most of these models are behavioral rather than existential. By this I mean that these models describe how things behave not what things are" and "It may be that the question 'what is it?' is meaningless and the only valid question is 'what does it do?'"

That is not science, it is what some people echo from the conventional bad Kantian philosophy. Repeating conventional, stale bromides is not an answer to Ayn Rand.

You are confusing units of money with the system of numbers for arithmetic. The use of base 10 in number systems (along with others) does not mean there was no need for fractions with different denominators, which does not in turn negate Ayn Rand's point on the early choices for many kinds of units.

Measurement allows us to expand our awareness in conceptual form to the realm beyond our direct perception through the use of a unit we can perceive and are familiar with. Our ten fingers are one such familiar unit, not the only one.

Ayn Rand did not write that all systems of measurement were based on having 10 fingers. It is a fallacy to argue that other systems of measurement not being decimal somehow undermines the origin of the decimal system of numbers. All early units were selected based on what could be easily perceived and duplicated as a standard, such as the "foot". See Klein, The Science of Measurement: A Historical Survey, which shows how complex the evolution of even simple measurements like length based on different local, perceivable standards has been.

The decimal system of numbers did not begin in 1600 and is not "unnatural". Decimal numbers in arithmetic were in fact in common use long before English currency and other physical units were converted. American units of length and other physical units still have not been changed to metric, but the decimal system of numbers have been in continuous use. Base 10 was in fact in used in ancient Greece, Egypt and India long before that, and finger counting and calculating has used before that in primitive societies. Obviously they did not start with that because they needed concepts of smaller numbers first. That does not negate the origins of a special place for 10. There are many scholarly books on this history. It is not correct to say that the decimal system first appeared in 1600 and is "unnatural".

Ayn Rand wrote about concept formation and its purpose in IOE. She referred to what "is supposed" by other specialists about the history of numbers without knowing the details herself. She did not "equivocate" with an unwritten private belief in decimal numbers as somehow "unnatural".

Very interesting posts (read both). I am not sure on the derivation of minos (need to look that up since my prior info on it leads in another direction, but it is not unlikely that one meaning is a spinoff of the other).

I appreciate your pointing out Stevinus to me.

I will add that the earliest measuring systems (Sumerian/Akkadian) had a different method of measuring each type of thing. I include this list (from Wikipedia) for your diversion:


Sexagesimal System S used to count slaves, animals, fish, wooden objects, stone objects, containers.
Sexagesimal System S' used to count dead animals, certain types of beer
Bi-Sexagesimal System B used to count cereal, bread, fish, milk products
Bi-Sexagesimal System B used to count rations
GAN2 System G used to count field measurement
ŠE system Š used to count barley by volume
ŠE system Š' used to count malt by volume
ŠE system Š" used to count wheat by volume
ŠE System Š used to count barley groats
EN System E used to count weight
U4 System U used to count calendrics
DUGb System Db used to count milk by volume
DUGc System Db used to count beer by volume

Jan

The mental metaphor I use is of one of those maps with cutout sections that expand, and then a cutout section of that expanding even further. Newtons Laws are not incorrect, but now they are a cutout-within-a-cutout in relation to quantum mechanics and relativity. They are still correct - but now our 'perceptions' (which, as you point out ewv) are really perceptions of measurements) have them in a broader context.

Jan

While there is no evidence that our consciousness creates or shapes reality it does shape how we interpret our perception of that reality. The act of observing does affect the thing being observed but the classical and quantum physics descriptions of this are quite different. In classical physics observation requires a transfer of information from the thing being observed to the observer. This typically involves a transfer of energy which must influence both participants. This is fairly easy to understand and consistent with conventional logic. However, there are instances involving quantum physics that are far more bizarre. One of these involves the behavior of entangled conjugate pairs of particles. It is known that certain reactions produce particles in pairs and that these particle pairs bear a predictable relationship to one another. PET or Positron Emission Tomography takes advantage of this so the phenomena is demonstrably real. this conjugation can take many different forms. For photons it is polarization and for electrons it is spin. Now the polarization of a photon or the spin of an electron cannot be determined in advance of performing a measurement. There is an equal probability that it will be right or left or up or down as the case may be. However, in the case of conjugate pair particles measurement of one immediately reveals the state of its partner. This occurs independently of the separation of the paired particles. Einstein struggled with this and the EPR paradox describes his concerns. If the standard model of quantum mechanics is correct then prior to measurement the quantum state of a particle can only be described as a spectrum of probabilities. It is the act of measurement that collapses that spectrum to a single point. Well, so far so good. However, the act of measurement also collapses the probability of the particles entangled pair and it does this instantly and regardless of the separation distance between the two particles. It is argued that this implies some form of instantaneous communication between the two particles which is in violation of special relativity. From this Einstein and his associates argued that the standard model is incomplete. Now it is acknowledged that the standard model is incomplete when it comes to gravitation but the EPR paradox suggests that it may be incomplete in other ways as well. The problem is that quantum electrodynamics and quantum chromodynamics are exceptionally precise in predicting the observable behavior of quantum-mechanical events. This is not likely to be coincidental. These theories, which are critical components of the standard model, must bear some close relationship to the underlying reality. I am left with two possibilities; the complexity of reality is infinite which means that no finite theory can ever encompass it, or, the complexity of reality is finite which means, at least in principal, total omniscience is possible. Either way, it's a mighty sobering thought.

"Mental "models" are not reality and not awareness of it." That is precisely the point. Models provide a way to think about something. To the extent that they point a way to gain more information they are useful but they should not be confused with "reality". They may bear a useful relationship to reality but in and of them selves they are, at best, partial analogs of the underlying mechanism that produces what we are able to observe.

smell of course

very interesting

this has been a really fun post. learned some stuff. Thanks guys!

taste and touch

That is all fine and good; and I hate to see you casting your pearls. The fact remains that Base-10 did not come first. Once numbers larger than 2 or 3 were conceptualized - about 5000 BCE; by city-dwellers, not cavemen - many systems were used. You and others attribute bases 60, 16, and 12 to the Babylonians. Britain only decimilized its currency in 1971. Before that it was 12 pence to the shilling and 20 shillings to the pound. Tens had no place in the system. And that "natural" foot was divided into 12, not 10, inches, which themselves were divided by halves down to 16ths and below. The NYSE was on 32nds until the year 2000.

All I noted was that Rand's use of the word "supposed" indicated that she was not intending a literal interpretation of the history of arithmetic, but only offering an easy example. It was technically flawed. That does not change the truth of her assertions.

She did a lot of that, actually, taking "common knowledge" for granted in order to convey her ideas to those who were interested but uninformed. Her stories about the Dollar Sign being the initials US, and of Americans inventing the phrase "to make money" are other examples.

See my comment to dhalling just above.
(https://www.galtsgulchonline.com/post...)

Stevinus was like Copernicus in that he advocated for a system known to others, but not used widely in his own time. 12 pence to the shilling; 20 shillings to the pound. Even though Thomas Jefferson and Alexander Hamilton disagreed on much, they agreed on the need for a decimal currency - but they got the quarter dollar, not the fifth because that was a convenient "two bits" i.e., two Spanish reales. The real was an eighth of a crown or Spanish dollar, not a tenth, of course.

Similarly, the Hindus developed 10s after thousands of years of other counting methods. That Stevinus had to write a book to advocate for decimal arithmetic only underscores how incompletely "Arabic numerals" were integrated into our common conceptualizations of quantity.

Everything real is natural. The Babylonians who followed the Sumerians were pretty good at number theory. They used base-60. Base-10 came later.

The ancient Greeks counted by ones to ten, then by tens to one hundred. But that came thousands of years later.

At the same time, however, the Greeks did not have a decimal monetary system. Everything was by halves and thirds (and thirds and halves of those). That continued into the 19th century: the German thaler was divided into 12ths. The Spanish dollar was divided into eighths.

The "foot" and "span" etc., speak to the human body as a standard of measurement. Literally, the word for "weight" was also the word for "king" -- mina, minos. "Worth his weight in gold," we still say. Even among the ancient Greeks, the mina was divided into 60 drachma.

(The innovator, Peisistratos, tyrant of Athens, solved a debt crisis by legally redefining the mina to 100 drachmas, thereby reducing the drachmon and allowing debtors to pay the old obligations with the new measure. He was wildly popular with the common folk.)

You miss the point. The Mayans were 8000 years farther long the conceptual trail than the people who invented numbers larger than 3. I just put up a post on "Accounting for Civilization."

Thanks, ewv, but I knew all of that. I have one copy of ITOE that is not marked up. What was Helen Keller's perceptual world before the arrival of Anne Sullivan?

Ayn Rand did not equivocate on her observation that "it is not an accident that man's earliest attempts at measurement ... consisted of relating things to himself -- as for instance ... adopting the decimal system, which is supposed to have its origin in man's ten fingers as units of counting."

She didn't diminish it as "unnatural", she included it as an example of her principle. She didn't use the word "natural" at all. What would it mean for the decimal system to be "natural" versus "unnatural"? All number systems and methods of calculating with them have to be invented; the ideas are not innate just because we have 10 fingers, but neither is conceptual thought "unnatural" to man.

She observed that man's earliest units of measurements were related to himself because measurement allows us to expand our awareness in conceptual form to the realm beyond our direct perception through the use of a unit we can perceive and are familiar with. Our ten fingers are one such familiar unit. The decimal system did in fact originate with the number of fingers we have. There is a large history of finger and toe counting and calculating both in primitive times and in primitive societies found in more modern times. It resulted in counting in 5's, 10's and 20's. Base 10 number systems were used in ancient Egypt, Greece, and India in their progressively more sophisticated numerical records. Babylonia used both 10 and 16 simulataneously.

But there is a big difference between consolidating numbers for mental unit economy with a specific numeral to avoid repetition of smaller units versus the decimal system we have today. That required the conceptualization of the base as opposed to just using it as a device to write numerals, the conceptualization and development of the positional (place) system for both whole numbers and fractions -- including the concept of zero and its use in this context, the open-ended size of exponents for numbers of any magnitude rather than a fixed size with the early distinct symbols for specific groupings, and development of methods of calculation based on rules for using powers of the base.

The mathematical methods used by those early cultures for the kind of arithmetic that we regard as simple was extremely convoluted and complex by today's standards, which is one reason that algebra was slow to develop and geometrical methods were more common in theoretical mathematics. Some cultures used base 12, 16 or 60, which allowed more divisors.

This is why Stevin is credited for today's decimal system as late as about 1600 for his advocacy of the concept of decimal fractions as part of his project to unify and systematize the entire system of measurements with a decimal base. Europeans had already been printing tables of numbers in decimal notation. The first published general theory of positional systems (including the binary system) was by Liebniz about a century later.

But the choice of 10 as the base came from our 10 fingers in the original finger counting.

Mental "models" are not reality and not awareness of it. The subjectivist model mentality leads to all kinds of floating abstractions and nonsense, including reifying abstractions like probability and claims that knowing something changes the thing you know regardless of how you know it. It is bad philosophy, not science.

What you have read is wrong, based on the Copenhagen interpretation with bad philosophy, not science.

An entity pricking you. But you don't know what the entity is yet

Perception means through your sense organs.

Some measurement tools enhance what we can perceive directly, as in seeing through a microscope. Others provide information indirectly, which allows us to infer the existence of things that we cannot perceive, like electrons or electromagnetic waves in the non-visible spectrum, and which we conceptualize with theoretical concepts based on all the evidence that can be accumulated.

The concept of physical reality does not change, we learn more about it and form new concepts for new aspects that are discovered. The referents of a concept are everything it refers to in the present, past and future, known and unknown at the time.

That isn't what I said. A perception is not of yourself, it's of an entity.