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R is the rate of star birth which I have read is about 1...one solar mass born and dies each year. Fp is looking more and more like 1 these days as well....almost all stars we have looked at seem to have planets even binary systems. Ne is something we won’t know IMO until we actually find life. Based on our system it’s less than or equal to .1 not including ALL the moons and such. Fl is odd one for me because to me it should be 1 once Ne is actually known. Because a planet that has life on it IS suitable and one that does NOT is NOT suitable in my mind. We just have not yet learned WHY a certain planet SEEMED suitable but wasn’t...if you get my drift? Fi seems like one in billions based on Earth history....but it’s a big question mark to someday be answered or not. It could remain a mystery for ever IMO. Fc would be 1 in my mind as any or every “intelligent” life form is probably defined as being such by it’s language and technology IMO. L as based on humans...not sure if they want our total life span (over 200,000 yrs already) of just how long we run with technology (only 200 yrs so far)....and as we survive each year, so L increases by 1 each year.
Posts: 1805
Joined: Nov. 8 2010
From: London (living in the Bay Area)
RE: Drake Equation calculator (in reply to Ricardo)
Why is N hard-coded as 1? Maybe they’re out there but just not communicating with us (“Cripes, Fred, we’d better keep away from them — they’re lunatics”).
Also: what’s the threshold for intelligent life? If you count dolphins, N already = 2.
“It has been suggested that brain weight-to-spinal cord weight ratios may provide a rough index of intelligence in vertebrate animals. This ratio in the bottlenosed porpoise average 40:1, as compared to the 50:1 ratio in man.”
Brain-Spinal Cord Ratio in Porpoises: Possible Correlations with Intelligence and Ecology. Psychon. Sci. 6 (11)
Then you’ve got seeing-eye dogs, parrots that can count, tool-using monkeys, crows that use zebra crossings to have cars crack their nuts for them, and all sorts of similar things that 19th century scientists were too obtuse or too bigoted to notice.
So how high an IQ does an alien life-form need to have to count as “intelligent life”? Has anyone answered this yet?
Posts: 14797
Joined: Dec. 14 2004
From: Washington DC
RE: Drake Equation calculator (in reply to Paul Magnussen)
quote:
ORIGINAL: Paul Magnussen
Why is N hard-coded as 1? Maybe they’re out there but just not communicating with us (“Cripes, Fred, we’d better keep away from them — they’re lunatics”).
Also: what’s the threshold for intelligent life? If you count dolphins, N already = 2.
“It has been suggested that brain weight-to-spinal cord weight ratios may provide a rough index of intelligence in vertebrate animals. This ratio in the bottlenosed porpoise average 40:1, as compared to the 50:1 ratio in man.”
Brain-Spinal Cord Ratio in Porpoises: Possible Correlations with Intelligence and Ecology. Psychon. Sci. 6 (11)
Then you’ve got seeing-eye dogs, parrots that can count, tool-using monkeys, crows that use zebra crossings to have cars crack their nuts for them, and all sorts of similar things that 19th century scientist were too obtuse or too bigoted to notice.
So how high an IQ does an alien life-form need to have to count as “intelligent life”? Has anyone answered this yet?
Very good points. N is the final number of civilizations we could possibly communicate with in the galaxy (using a small R value)...so that is not “hard coded” as you say (you have to plug in your own numbers and N changes). What you refer to about intelligence is in relation to Fi (F sub i) fraction of life that evolves what we define as “intelligent” life. The entire exercise here is to find life that we could maybe COMMUNICATE with, and as you point out, there is plenty of life on earth that seems very clever, yet we can’t really communicate properly with them....so it begs the question how could we expect to do something with Alien intelligence if we can’t talk to our pets? Our closest relatives both alive (chimps) and dead (Neanderthal etc) actually COULD communicate with us to some extent via sign language and such. However, I have to draw the line at a proper WRITTEN language, without which there can be no hope of translation and learning.
So when I factor the Fi I am filtering out any creatures that, as smart as they may be, cannot express their thoughts in some abstract symbolic form. While it might be interesting to find such creatures out in the galaxy, (and indeed they increase our Fl fraction) and we might even learn something from them, not a lot is going to get done in terms of advancement and networking. If we find a species that is behind us in development, but we can express with symbols our periodic table of elements for example, then we can bring them up to speed eventually. Conversely if they are more advanced then us, we can learn a lot by comparing their version of the periodic table to ours.
To me, just looking at earth, evolution seems sort of like a game where you have to pass a bunch of tests and obstacles in order become viable, with the goal of expansion off of the starting world...and the fantastic distances between the life bearing worlds (relative to the size of life itself) is a “built in” way to protect and nuture all the different life forms that might develop, in order to give them the time to mature. That’s how things look to me, but then again I am just a simple human.
Of course communication with pets could be a thing of the future too:
I forgot to add...that if you want to include dolphins and chimps and such as part of Fi, then obviously your factor Fc must reduce to a much smaller fraction. Since I filter out all those creatures myself, Fc seems like an obvious 1.00 unless the species holds itself back, so something like .5 might be more realistic if this is a normal thing?
Posts: 1805
Joined: Nov. 8 2010
From: London (living in the Bay Area)
RE: Drake Equation calculator (in reply to Ricardo)
quote:
If we find a species that is behind us in development, but we can express with symbols our periodic table of elements for example, then we can bring them up to speed eventually. Conversely if they are more advanced then us, we can learn a lot by comparing their version of the periodic table to ours.
That’s assuming their intelligence functions the way ours does. But it was pointed out long ago that what pass for “aliens” in much Science Fiction (especially on TV) are just people in funny rubber suits, in principle if not in actuality. The first really alien alien in SF is thought to have been Tweel, in Stanley G. Weinbaum’s A Martian Odyssey (1934).
What if there are things out there like Alastair Reynolds’s Pattern Jugglers (Absolution Gap)? More powerful telescopes might show the results of their activity. Could we learn from them? Could they learn from us?
Whatever the answer, though, I think the impact on civilisation of just knowing such things existed would be considerable.
Posts: 4495
Joined: Aug. 9 2006
From: Iran (living in Germany)
RE: Drake Equation calculator (in reply to Ricardo)
I think our main problem is that we see everything from human eyes.
Maybe there are already attempts of communication, and we just can't detect them (or understand them). We imagine that some aliens are (or were) sitting somewhere and sending signals, just like we do. But maybe its something completely different. Like some kind of superluminal communication through micro-wormholes which we can't detect or part of quantum mechanics which we still don't understand.
Maybe other intelligent life forms think differently and their main goal is to NOT communicate with unknowns because of risks.
Maybe they already detected us, but we are so unimportant, so "dumb" that they simply ignored us. Like we would watch a bacteria through a microscope and know it is there, but it doesn't make sense to try and communicate with it. It is too dumb and too simple.
RE: Drake Equation calculator (in reply to Paul Magnussen)
quote:
If you count dolphins
So long, and thanks for all the fish!
_____________________________
"Anything you do can be fixed. What you cannot fix is the perfection of a blank page. What you cannot fix is that pristine, unsullied whiteness of a screen or a page with nothing on it—because there’s nothing there to fix."
RE: Drake Equation calculator (in reply to Ricardo)
The problem for me is patience. Knowing as I do that interstellar time frames and earth geologic time frames are similar, I think we are in for a long, long wait as human beings who have only begun to evaluate our own self consciousness; for about 200 years so far. We have walls of light years to wait for information to reach us, and we've only turned on the transmitter so to speak, in interstellar time, a few milliseconds ago. And concurrently we hold to an understanding of sentience and consciousness that we have set up, and we're very young at evaluating both.
So we have a multiplicity of problems of your own situation and that of our interstellar environment, we have a ling wait ahead. But the Drakes equation can give odds, some rough odds. We're going to have to wait until the radio has been on for 20-30 minutes, interstellar time wise, a few hundred years, before we begin to have enough listening in to evaluate what comes this way. And think, in 35 to 40 years the speeches of Donald Trump and American TV will be passing the same space markers as I Love Lucy and Gilligan's Island are passing right now.
We might make it to Mars and be able to set up better astronomy equipment that much deeper into space and then think about our own consciousness longer. I think we have not conceived yet of what all the possibilities of consciousness are because we are hyper fixated on our own, we may take several hundred more years before we intuit other kinds of consciousness. We have to find out if travel in deep space or continuing the human line in deep space changes our perceptions. Or our ability to perceive.
The performance of the American public in recent elections does not speak well for our ability to recognize alien forms of consciousness.
RNJ
I posit that over time if we manage to become a deep space fairing race we'll shift away from the God paradigm among the humans that leave Earth. In order to move into deep space it's a multi generational commitment; a split away of the main population will have to venture it, and they will be scientists. It's possible our consciousness could develop differently in split off branch that is not fixated on divine paradigm. We tried to explain the wold around us historically by assigning it divine origins, but that is because we are fixed on a planet we could not explain. Now or in the future a space fairing branch of humanity will be surrounded by space, and not the center of space, it most certainly will change the consciousness.
Michio Kaku just published a book in which he says about the same thing. So maybe all that sci-fi was not such bad time spent.
Posts: 3430
Joined: Jan. 20 2004
From: Austin, Texas USA
RE: Drake Equation calculator (in reply to estebanana)
I speculate that God is a product of our evolution as a creature of stratified culture.
Even in huge societies like the USA and China we organize ourselves into a hierarchy with a leader or a set of leaders at the top. Our closest relatives the chimpanzees do the same.
The great majority of my extended family are religious. For some religion is a profound and permeating influence on their daily lives. For others it is more of an intellectual framework. A small minority reject religion. Those who do have grown up in a family environment which also produced deeply religious siblings.
I suspect a genetic component in this phenomenon. My suspicion is fueled by the observation of my own children, born 14 months apart. Almost from birth they displayed quite distinct personalities.
My mother told of lying awake at night listening to her parents. Her mother said to her father, "Pickens says that the people in the town say you are an atheist." Her father replied, "Pickens wouldn't know an atheist if he had one for a neighbor." Pickens was their neighbor. When I was a child Pickens told me at some length of his admiration for my grandfather, who had taught him to read, among other generous acts.
My grandfather died when my mother, the eldest of his children, was 11 years old. My mother told me her father wanted his children to arrive at their own views of religion, not to impose his own. She grew up to be deeply religious. At least one of her brothers was openly atheistic, I suspect the other two of having been the same. Her sister was a deeply religious woman. My mother's younger siblings seem to me to have been too young to have been directly influenced by their father's views, though perhaps stories about him may have had some effect.
In the present youngest generation, at least one is openly atheistic. My religious sister-in-law has lamented the views of at least two of her other 11 grandchildren. All the grandchildren had at least one deeply religious parent, three of them had two such parents, none of the parents showed any visible disinclination to religion.
As I said, I think there is a genetic component of personality that inclines a minority in each generation of my family to reject religion.
Throughout my life I have rejected figures of authority, at times truculently. For quite a while I was my own boss in business. Afterward I participated only in organizations that granted me nearly complete autonomy in positions of leadership. My brother shared the family trait of ambition, but had far smoother relations with his organizational superiors. He rose to a position of international and public prestige. He is also deeply religious.
Among Europeans agnosticism seems to be culturally dominant. Still there are ardently religious people among families with European roots which extend into prehistory. Why should this be, other than an inherent pre-disposition to have a "person" at the apex of society, even if fallible humans consistently disqualify themselves for the post?
Our dominance depends in large part upon our ability to cooperate in vast hierarchies. This must persist if we are to organize the effort required to colonize another planet. What will keep it from occasionally being carried to the logical extreme of monotheism?
I speculate that God is a product of our evolution as a creature of stratified culture.
I agree. However I'm not taking speciation off the table if humans become deep space fairing creatures. And possibly a radical break with the religious paradigms because everything will be different and life will be dependent on sets of empirical values, brain chemistry will change due to being in deep space. I speculate a branching off in human evolution into some sub species of human. After some time of course. In a deep space fair culture there will be generations and generations that will never see Earth, the travel distance will be more than the duration of one lifetime. The arms of the church just ain't that long, and empirical values needed to maintain life support systems will cut out a lot of non essential bullcrap. I speculate the environment of deep space will launch speciation. We'll become our own aliens.
RE: Drake Equation calculator (in reply to Ricardo)
We'll have to wait and see. But monotheism is not the only default setting humans have. I think acceptance of monotheism is highly based on social pressure.
One discouraging tenet of colonial bodies is that they tend to cling to the most base notions of language and religious practice. When cut off from the primary source of a language or practice there is a tendency to place it in a time bubble and not allow it to advance. Purity and ossification become rooted and difficult to break from. So it probably depends on who begins the journey. But again I state that humans penchant for explaining the phenomenology of the world in terms if the Divine stems from not having a modern science to base understanding on. So they invented an hierarchy based on privilege of Divine knowledge. And that is the focus of a shift if a break off branch of humanity happens. The privilege of scaring people into divine compliance is mitigated by the democratization of empirical knowledge.
The priest can't hold the same position of power via divine knowledge, so monotheism has less of a chance, maybe, unless the humans who break away are already part of a group that holds divine knowledge and empirical knowledge on the same level. Unlikely they will get into deep space no matter what their cult prophecy says about the mother ship picking them up. It's more likely that the Elon musk types will go forth.
One thing religions did and do well, is to know that humans are not only intellectual creatures, and they will never be satisfied if they would be reduced to that, but that they always seek for a greater purpose than just ourselves. Even many people who don't believe in the old religious stories, feel an unexplainable safety and security in some of these enviroments, and some of the illogical beliefs, because having a carreer, a marriage with kids and all that, is not enough in the deepest levels of our minds. Specially under immense psychological pressure. No matter which time in history and which technological level we are in. Countless books have been written about "how to find happiness, purpose, etc.", but if one of them would have been "the right one", there would be no need for a new book each week. It is the same drive which society is trying to feed with other methods than religion, more or less unsuccessfully. Because you have more and more unhappy, depressed and lost people, because a satisfying replacement is yet to be found for these needs. We are bombarded with attempts of replacements, but these attempts are more or less like drugs to keep that fundamental need suppressed or distract from it.
Science and specially astronomy which lead beyond our little planet, can help to satisfy the same needs for a greater purpose, for moral and unity across country borders, which the basic fundamentals of religions were trying to give in the past, but which are also in trouble today for a vast majority of people, just like the replacement attempts of not religious people and society as a whole. However, it would be wise for future generations to learn from religions some of their wise findings about human nature and to combine more aspects of it with intellectual and scientific findings to have more success for humans as a race. Because humans will never be 100% logical intellectual creatures, specially in difficult circumstances. Even the most atheistic person with an amazing knowledge about science, physics and everything else, might end up finding himself in a situation where he is in desperate need for an illogical answer to his pain to keep moving, because he can not fight the human psyche with bits and bytes.
Once everyone understands that humans sometimes need technically wrong answers in order to be able to move on to find more technically right answers, then we can go forward. And I believe that through this way, more and more technically wrong answers can be replaced with technically right answers and satisfy the needs of future generations.
Current Atheists and their methods are as stupid as religious fundamentalists and their methods.
ORIGINAL: Arash Current Atheists and their methods are as stupid as religious fundamentalists and their methods.
You paint with rather a broad brush.
Although I don't know any personally, there certainly are atheists who are rude, arrogant, condescending and illogical in their attacks upon religion. I read about them, and I have read some of their writings. As a child and youth in the USA I was personally exposed to many fundamentalists with the same character flaws, and there are quite a few here in Texas right now.
But I know atheists who are polite, considerate, thoughtful, and understand that their beliefs are just that, beliefs--perhaps arrived at by careful consideration of evidence, but beliefs all the same.
By the same token I know fundamentalists who are kind hearted, polite, considerate, scientifically or professionally well educated, and who strive to follow what I see as the best precepts of their religion.
But I would agree that there are members of both camps who suffer seriously from the same faults.
RE: Drake Equation calculator (in reply to Ricardo)
Galileo tried to reach a reasoned out co existence with the church. The church arrested him, banned his writings and research for 200 years, held him in detention and only stopped short of torturing him into submission.
I'll take science thanks.
Galileo observed the moons of the gas giants and determined the solar system is not geocentric. Just think where we'd be without the Catholics.
Posts: 3430
Joined: Jan. 20 2004
From: Austin, Texas USA
RE: Drake Equation calculator (in reply to estebanana)
Galileo thought he was relatively safe with a Medici pope. Some say he was trying to repair the Catholic south's reputation for backwardness, compared to the scientifically advancing north of Europe. When the Medici pope died and a reactionary came in, Galileo was out on a limb. He had been officially warned long before by a cardinal not to advocate the heliocentric system. His (mistaken*) theory of the tides relied upon heliocentricity. He described his theory of tides in a letter to Cardinal Orsini, where it was bound to be seen by a lot of people. When the reactionary pope thought he was satirized in the Dialogue Upon the Two Systems, he sic'ed the Holy Office onto Galileo.
Some say that the threat of torture implied by showing the implements to Galileo was an anachronistic formality in Italy. On the other hand, only 80 years before, my ancestor the Lord Chamberlain, Captain of the Guard, Master of the Horse, Lord Lieutenant of Kent, etc. under Mary Tudor, was burning people at the stake--including at least one Bishop-- during the queen's counter-reformation.
At any rate the Church forced Galileo to recant publicly and put him under house arrest for the rest of his life...where he lived in Florence, again under the protection of the Medici. I believe he was allowed to receive whomever he wished as visitors, and to continue his correspondence with the Academia dei' Lincei and other scientific colleagues.
It took the Church more than three centuries to apologize for its maltreatment of one of the greatest scientists the race has produced.
I favor a version of science without divine intervention. I was just saying to Arash that not all atheists, nor all fundamentalists are a$$holes, like some of each who are now prominent. Some of my religious relatives are among my favorite people. I doubt that they take Genesis literally, but I would not be surprised if they believed in divine guidance of evolution. However they understand that doesn't belong in publicly funded school books or classrooms. They are educated, well read and well traveled, having lived in a variety of places overseas, including Scotland, Portugal, Angola and Saudi Arabia. We are careful not to offend one another.
Some of my other religious relatives need to be told politely to back off, about every 20 years or so.
I condemn wholeheartedly the Republican majority in the Texas legislature, and the Governor and Lieutenant Governor for attempting to impose a fundamentalist regime.
Fortunately we managed to vote the creationists off the School Board, preventing them from putting creationism into the science books, and taking Thomas Jefferson out of the history books.
My conservative and prosperous neighborhood elected the only openly gay member of the City Council, getting rid of a right-wing a$$hole--but on the political map of Texas, Austin is a blue Democrat dot in a sea of Republican red.
My closest friends are mainly agnostic.
RNJ
*Bill O'Reilly, running about three centuries behind the times, criticized Galileo for "not knowing what made waves." O'Reilly was then criticized for not knowing the difference between waves and tides, rather than for being a bloviating pr1ck.
RE: Drake Equation calculator (in reply to estebanana)
quote:
and they will be scientists
A lot of stock has been put into a fairly recent (late 90s I think) poll of members of the National Academy of Science. The results were used widely as proof that scientists almost universally did not believe in God. Indeed, somewhere above 95% were said to have claimed they did not believe in God. However, a closer look at the poll reveals quite a few problems. The main problem is in the questions. The poll used the exact same questions as an older poll designed by James Leuba in the early 20th century. The questions do not stand up to modern scrutiny when it comes to polling methodology. For instance, most of them include several claims at the same time, which is a big no no now, for rather obvious reasons.
Next to that, there have been Gallup polls that do stand up to modern scrutiny when it comes to the methodology and that have yielded results that seemingly contradict the NAS poll. The Gallup poll on evolution for instance showed that the share of scientists that believed evolution was guided by God was roughly equaly to the share of the general population that believe evolution was guided by God (somewhere around 40% if memory serves). Hence the confusion, because if over 95% of scientists are claiming that they don't believe in God, how come 40% of them are saying that they believe evolution is guided by God?
For me, the take-away from most well-designed polls is that scientists do have lower belief rates in most of the "extreme beliefs". Things like young-earth creationism that fly in the face of every piece of available evidence. But when it comes to a more moderate "liberal" understanding of God, scientists don't seem to be any different than the rest of us. Which is why I don't share your belief that a group of scientists that break away from civilization earth would somehow develop more of a knack for atheism. If anything, their awe for the universe would multiply, given all that they would see and discover. How that relates to belief in a God is anyone's guess.
@Arash I would tend to agree, at least when it comes to the more visible figures of atheism today. The focus is on the intellectual discussion around whether the God claim is true or not. And there's a rather strong tendency to treat as fools those who do cling to irrational beliefs (again, among the most visible figures). What is largely ignored is human vulnerability. Most of the main atheist figures seem to just assume that we're all managing pretty well, that life is all in all pretty easy and we don't really need any help. Religions on the other hand say that we're not fairing all that well, that it's a struggle to live a good life and that we could use the help. And the latter view resonates much more with people than the former. Of course, there are many atheists who move on from the mere theoretical discussion and focus on the more important issues of what it means to be human. It goes from the rather pathetic attempt of Auguste Comte to create a godless religion back in the 19th century to effective social groups today. Though it must be said that those social groups today that do provide support, guidance, etc. do not tend to use the "atheist" label and prefer terms such as "humanist" instead. All in all, I don't think it's about needing "wrong answers" to be able to move forward. Rather, it's about asking the right questions. If you're asking how to know whether a God exists or not, then religions don't seem to be a great example to follow. But if you're asking how to create a sense of meaning and community, then they have a lot to offer. The "does God exist" question used to be incredibly important to me. Now it seems rather prosaic, far less interesting than the question of meaning and community.
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"Anything you do can be fixed. What you cannot fix is the perfection of a blank page. What you cannot fix is that pristine, unsullied whiteness of a screen or a page with nothing on it—because there’s nothing there to fix."
I think extrapolating the supposed religious beliefs of the National Academy onto the general population of scientists is potentially a much greater error than confounding claims in poll questions.
Agreed (admittedly I made that very mistake in my previous post as I was just skimming over the issue. Mea culpa). The same researchers (E.J. Larson and L. Witham) posed the same question to a sample of scientists listed in American Men and Women of Science. The results were significantly lower. In the span of a few years they published articles in Nature that were titled "Scientists are still keeping the faith" (AMWS study) and "Leading scientists still reject God" (NAS study). For reference, here are the statements that were used in both of these studies (respondents were asked to mark true or false next to each):
a. I believe in a God in intellectual and effective communication with humankind, i.e., a God to whom one may pray in expectation of receiving an answer. By "answer," I mean more than the subjective, psychological effect of prayer. b. I do not believe in God as defined above. c. I have no definite belief regarding this question.
I'm not sure how anyone can derive any information on the theism or atheism of respondents from that.
_____________________________
"Anything you do can be fixed. What you cannot fix is the perfection of a blank page. What you cannot fix is that pristine, unsullied whiteness of a screen or a page with nothing on it—because there’s nothing there to fix."
Galileo thought he was relatively safe with a Medici pope.
I wonder how many Americans are familiar with the science documentary series The Ascent of Man, by the British mathematician and historian of science Jacob Bronowski?
It was one of the many brilliant programmes made under David Attenborough’s watch as Controller of BBC2. Bronowski’s eminence secured him access to the Vatican archives, and the original documents of Galileo’s trial.
It was BBC2’s second major documentary (after Kenneth Clark’s Civilisation), and I thought it was stunning.
Posts: 3430
Joined: Jan. 20 2004
From: Austin, Texas USA
RE: Drake Equation calculator (in reply to Paul Magnussen)
If anyone should visit Florence, I recommend a visit to the Galileo Museum. It is in the same block of buildings as the world famous Uffizi art gallery. The entrance is at the southeast corner, near the street that runs along the bank of the Arno.
While tickets to the Uffizi must be booked in advance, even then requiring a long wait in line, we went right into the Galileo Museum, even in high tourist season in June.
In several floors it contains a marvelous collection of scientific instruments of the Renaissance. It includes the huge brass armillary sphere, more than six feet tall, that belonged to the Medici, illustrating in motion the very complex geocentric model of the solar system, as well as a number of early astronomical telescopes, which served to refute the highly sophisticated geocentric theory.
The scientists supporting the geocentric theory were not ignorant yokels. Understanding the details required a firm command of the mathematics of the day. Discrepancies from observation were small, compared to the accuracy of the instruments employed. One of the chief arguments in favor of the heliocentric theory was its simplification. In fact the Church authorized use of the heliocentric theory as an "hypothesis" that made calculations much easier. But you couldn't assert "the Earth moves" as fact, without attracting the attention of the Inquisition.
One of the first to come out in support of Galileo was a Roman priest who looked through Galileo's telescope and saw the moons of Jupiter revolving around their planet.
My favorite exhibit at the Museo is an inclined plane, with bells placed at intervals increasing with the square of the distance along the path. A ball rolling down the grooved path rings the bells at equal time intervals, indicating the effect of constant acceleration due to gravity. There is also a brachistochrone, in which a rolling ball travels along an arc in less time than it takes to traverse a shorter straight sloping path connecting the ends of the arc. These objects date from Galileo's lifetime. They illustrate the origins of valid mathematical physics, one of the chief architects of the modern world. There are many other fascinating displays.
On the time scale of history the modernization has occurred with breathtaking speed. My first American ancestor arrived here two years after the trial of Galileo. The transition from medieval technology to the digital age has taken place during the 11 additional generations since then.
The Museo bookshop is another of my favorite haunts. I bought a copy of "The Galileo Affair-a Documentary History" there.
RNJ
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