Serious? Anomalies in reporting, replicating, and  discussing the optics of Galileo's telescopes   Jim & Rhoda Morris         Return          Building Precise replicas of Galileo's Telescopes
The last Date 06/03/2007 08:06 PM this page was edited   


Figure courtesy of       

Is the drawing of the lens configuration above  correct? (no)  Did Galileo use  bi-curved  or plano-curved lenses? (yes & no) Does it make any difference?  (Yes?) Why do we ask?

Science is a serious business. It is s not a sport, it is not entertainment.

It  is too  important, too fragile to let lies and mistakes in the data or analysis of the data of any size  to exist  in around or about it. Seemly tiny mistakes  can be  multiplied many times by those who have  an intrinsic mistrust of scientific. They can and do use this mistrust to do  potential harm to the  progress  basic scientific research It is everyone's  responsibility  to  do their best to help keep science as accurate and trustworthy  as possible.

Examining the existing the three objectives lenses  at IMSS attributed to Galileo for three of his telescopes.
The question of whether what  We found  many "incorrectly?" drawn diagrams. We had examples going back to at least to 1812. We noted  examples of bi- curved lenses everywhere in text books on optics, some recent web sites  put together by professors for their students see below. We had made our decisions for the what we felt appropriate to use in our replicas from the data in the  scientific journals  by  (Vasco Ronchi 1923, Greco etal 1992,1993 ).  Their  optical measurements of the lens from IMSS shows relatively  "small" curvature on  the so called "flat side" for  two of the three  lenses. However without these measurements it is easy to see  from casual observations of the lenses that the shallow curves are so shallow that some would have guessed them to be flat. But scientifically  the question that remains is how flat is flat. to help answer this question we made some calculations which is summerized in the figure below.  shown and discussed in the graph below. It looks cluttered because it  packs a lot of information into a small box.


There was no conflict of choice for the IMSS 2428 scope because it was a plano convex objective.  For the IMSS 2427 which we made a replica of also there was a small but real second surface radius. The 2429 which  is the broken objective that has a good chance of being the objective that Galileo used in his discovery of Jupiter's moons etc. has radius of curvature as well. We had chosen to concentrate on the focal length issue where the disagreements were too large for us to be ignore.

Below is a graph showing how much  the curved( flat) side contributes to the total focal length of Galileo's  objective lenses. One can use this graph to get  a feeling of how flat some reviewers feel is flat. (A side note) the slightly curved back surface on th IMSS 2427 helps to reduce the spherical aberration. over a  plano-convex or a symmetrical bi convex lens. Does that mean That Galileo's knew about spherical aberration and made his lenses with the double curves surface to get a better image. We think not.


About one half of approximately  150 people the authors  polled, North of Boston Ma., a high tech area, believed that scientists, because of external and internal  pressure, often misrepresent  data in their published research work. If this is representative of the general population in this country  it is one of the  very serious threats to the acceptance and funding of basic scientific research.
Most of the public apparently do not know that all scientist report investigations in open journals for the world to see  and reproduce their work.   That their papers (are instruction manuals) with all the details made available letting others repeat the work step by step. The whole world  see's and judges  their  work.  If they are wrong  for what ever reason everyone will know it. It is professional suicide for a  scientist to be wrong and if they are everyone will know it.

One of many errors about Galileo's telescope  that keeps popping up again and again

This schism in the public eye was truly a shock for two reasons.
1 st. between the two authors we have accumulate around 70 years experience in basic and applied research at senor levels. We know from first hand observations that one  can easily show that while errors and falsification can happen in scientific work it seldom happens in comparison to the thousands of papers published every year, far less than in any other field.

2 nd.  so many of us have let this error  slip by for over at least two centuries, repeating it again and again.  A gross error for the most important component of the telescope the lenses, which are the  telescope, not just any telescope but one representing the first scientifically important telescope. One that represents an the all time major issue between science an religion. A telescope that is associated with name Galileo that  has 26,800,000 listings on Google. A scientist that seems to hit the top 10 in historical importance on most lists. The telescope one of the most popularly known scientific instrument in the world.

Most of the public apparently do not know that all scientist report investigations in open journals for the world to see  and reproduce their work.   That their papers (are instruction manuals) with all the details made available letting others repeat the work step by step. The whole world  see's and judges  their  work.  If they are wrong  for what ever reason everyone will know it. It is professional suicide for a  scientist to be wrong and if they are everyone will know it. They make very little money in comparison to the years of training and work they put into get their job. The competition  to be right and to be first is fierce. Their only satisfaction they get is to get there first and to be  right.
  • Are the errors in the optics just the tip of an iceberg  of errors in other details of Galileo's telescopes? Yes this has been our experience. It will always be a mystery to us how one can have the overall length of a Galileo telescope be the same as the focal length of the objective e.g. or incorrect description  the focusing arrangement  of the lenses A PhD theses? Most media take liberty with the truths to make science entertaining. Some will even dream up a new creative definitions of science.
  • More fundamentally is this a generic problem affecting all science related literature written by non scientist?
  • How does it affect one of the most important endeavors of the human experience, the progress of basic scientific research?  It materially slows progress down by making it more difficult for the scientist to get acceptance of their findings.


Below is a  fancy picture demonstrating the heart of Galileo's telescope the lenses and how they behave when close to an  object.  For all of its fanciness it is technically  wrong without a legend of supporting data. The lenses in the ray tracing drawing should have been plano-curved,  not bi-curved. The focal lengths are tailored to make the visual affect more pronounced. Nothing is to scale.

Galileo's optical Anomaly?

Example of the anomaly. The figure is more accurate

The bottom  part of the drawing above less the eye  was  originally copied from a 1860 book on Natural Philosophy The top part we did over to correct it.

The figure below shows a modern example. Notice it has the double curve  rather  than plano - curved lenses that Galileo's telescope was supposed to had originally.  The text clearly references this figure as a Galileo Telescope. This figure was copied directly from  a modern web site aimed at  helping students get a grasp of optics and has been  at times one of the first page images from a google images search on the subject.

 Figure courtesy of

05/19/07 A very thoughtful  web site giving a brief discussion of optics of the eye and other instruments. Question how many students per year experience  this information?

If this is not enough evidence click here for more examples of the lens drawings going back 200 years

The real question  about error's arose for us in making the replicas for Griffith observatory and Adler Planetarium was, Is   this error  just the tip of an iceberg of error's in the scientific literature?  Indeed In the process of replicating Galileo's telescopes IMSS 2427 and 2428 other problems reared their ugly heads which we discuss elsewhere on our pages describing the replication projects for  two major museums/planetariums. This optical discrepancy alone  has persisted for at least 200 years  and continues in our modern literature written by professional  teachers of optics and historians of science as we see above and more are found below.

Below we give  several examples for the range of  publications containing the Galileo lens error even a few examples edited by professional historians. We photographed and added these to this webpage.  The data is from  the English speaking world and you will noticed that the  tradition of this error dates back at least 200 years. We have  searched through our library and scanned in samples  of drawings of Galileo's telescope lenses from text books on optics ranging from 2000 to c 1800,  among them  a Encyclopedia going back to 1813. They all illustrate the lenses as either  double convex   and   biconcave  lenses not plano-lenses. Could it be that the artist rendering the drawing took artistic license with the scientist drawing---which more than likely used plano-convex / concave lens---  or was it a scientist that reported the telescope after the double curved telescope was invented and never looked back to what Galileo had used?  could it have been done by an artist who was partial to a symmetrical world?  It would have been refreshing to have had the correct information in the  scientific  literature but as one can see the errors exist there as well.

We also added  a copy of page 50  of  Dr. Albert Van Helden's (an American expert on Galileo) beautiful and very valuable resource on famous early telescopes " the Catalogue of Early Telescopes"   describing Galileo's  leather telescope in some detail. It  shows  a biconvex / concave  diagram  for lenses and  even the diagrams of the lens in their holders are portrayed as   biconvex and biconcave.  They are defined correctly in the text!       

In the appendix of  Dr. Albert Van Helden's fine book ----pages 99 through 111--- The Optical Principals of Telescopes are  a mix.   Fig 9 uses biconvex and biconcave  for the "Optical Layout of the Galilean telescope"  and non of the components are to scale. By remarkable contrast many of the more sophisticated  optical designs further on in the catalog  use a  more accurate  mix of bi-lens  and plano-lenses in the figures again not necessarily to scale.

Click on the thumbnails below to see larger pictures of the tip of the iceberg of errors just  in the optics . Some of the files a quite  large.  

Image from a 371 page 2002 PHD  theses

Title:  Galileo, the telescope and the science of optics in the sixteenth century
Authors:  Dupré, Sven
Issue Date:  2002
Description:  Diss. doct. wijsbegeerte
Appears in Collections: PHD theses (LW)





 Below this image appears on the first page of a google search on images "Galileo telescope" !


Index of /~cass/courses

Telescopes serve much the same purpose as microscopes; both magnify what the user wishes to observe. The difference is that microscopes are supposed to be used to examine small objects that are close to the objective lens, while telescopes are supposed to be used to examine objects that are very far away (in many cases, extra-terrestrial). For historical purposes, we include a diagram of Galileo's telescope here. Courtesy of

ps This is a good site for learning about optics

From the Catalogue Early Telescopes  by A. Van Helden


A good questions often asked in measuring his abilities is  what motivated Galileo to pick the plano spherical stile  and orientation of the lenses  and choosing a negative  eyepiece rather than a positive with its small field of view in his version of  his telescopes?    We submit  figures below as a demonstration of the kind of skill one needs to make the theoretical technical decisions about which lens and its orientation is superior scientifically.

Galileo did not have the benefit of these type of calculations to make this kind of  technical decision but he had a sharp eye knew there was  little time to make his measurements and publish them before some one else did. He more than likely used a lens shape based on the amount of work he had to do to make the lens  acceptable to his viewing needs.

The science  today of studying, choosing  and designing  lens .The figures below are copied from Fundamentals of Optics by F.A. Jenkins & H.E. White 2nd.edition 3rd Impression McGraw-Hill Book Co. N.Y. 1950 pages 126-127.  Click on the thumbnails to make them bigger.------  RETURN

Figure 2
For minimum spherical aberration for parallel light incident on a crown-glass lens, this appears from Fig. 9D to occur at a shape factor of about q = +0.7, not greatly different from the plano- convex lens, for which q = +1.0.

Figure 3

Although the derivation of an equation for spherical aberration from third-order theory is too lengthy to be given here, some of the resulting equations are of interest. For a thin lens we have the reasonably simple formula

Figure 4

very. The basic motive in doing science to begin with. 

The bottom line  in science is that there is no room for research that contains errors, mistakes, or falsehoods.    Accidental mistakes in measurements can and do happen but once found the scientific community expects them to be  reported in a timely fashion with an estimate for the magnitude of the impact on the work using the flawed data.. For those who make a mistakes and don't own up to it when caught, and they are always caught,  are figuratively  burned alive at the stake. It takes years  to become  a senior basic research scientist and their reputation will  be totally destroy overnight when they are caught. The very nature of science is the continual checking and rechecking of prior work looking for a new discovery in the models of how things work. 


There is a a rainbow  in this gray cloud of confusion. We have a 400th anniversary of Galileo's  discoveries  coming up in 2010 where we could emphasize the realities of science.   There is an opportunity to build a bridge of understanding  filling this gap of how science really works. We can  teach  from this Galilean anomaly through our schools and  museums about  business of science and  can bring a real break through in the understanding of science to help reduce or eliminate these harmful schisms in one of the most important endeavors of the human experience that is of the gathering of knowledge of how Nature works so that we can use it for a better life for all of natures creatures.

We suggest  that in the Galileo story there is a classic, simple, straight forward, example of a typical  scientist at  work.  One who just happened to become famous more from an altercation with a powerful, dedicated, religious organization than for his improvement in telescopes and a few weeks of research time using them. From then up to today science  has grown to be one of the most important and powerful things that we do and depend on. Its important that all of us  get it right.

Today the whole story of Galileo is an extraordinary powerful easy to understand example in every detail of science in action them and today.  Most important it is just as relevant to day as it was nearly 400 ago a span of four centuries.



Errors and falsification can happen in scientific work but far less than in any other field, yet surprisingly about one half of approximately  150 people we  polled, North of Boston Ma., believe that scientists, because of external and internal  pressure, often misrepresent  data or just plain lie in their published research work. 

How can this be? What is causing  this schism ? 
Surely this must be a harmful to the funding and progress of basic scientific research.

  1. What about the anomalies in the literature surrounding the optics of Galileo telescopes?

  2. How important are they?

  3. Are these errors just the tip of an iceberg  of errors in other details of Galileo's telescopes?

  4. More fundamentally is this a generic problem affecting all science related literature?

  5. What  is the principal  source of these  errors?

  6. Are these errors intentionally or unintentionally generated?

  7. Who are responsible for replicating them?

  8. Who are responsible for correcting them?

  9. If one is not  committed to doing it right, or at least better, What is the purpose of doing it at all?

  10. Aren't the reporters reporting science poorly just making public  fools of themselves?

  11.  Its easy to check for inaccuracy in reporting scientific issues Using the techniques scientist use to catch errors etc.  in their work.

  12. If half of the public believe scientist lie in the papers and half don't Who is right?

  13. How does it affect one of the most important endeavors of the human experience, the progress of basic scientific research?

The authors discuss the possible reasons behind this schism  from which one can deduce that some how the educational system  must not have  been stressing  some of the  very important components of doing the  science in the process of teaching the science. The knowledge  that covers the issues  of how scientist and scientist really work are key to the success of science and  explain why scientist can't misrepresent  data and get away with it.

We suggest  that in the Galileo story there is a classic, simple, straight forward, example of a typical  scientist at  work.  One who just happened to become famous more from an altercation with a powerful, dedicated, religious organization than for his improvement in telescopes and a few weeks of research time using them. From then up to today science  has grown to be one of the most important and powerful things that we do and depend on. Its important that all of us  get it right.

Today the whole story of Galileo is an extraordinary powerful easy to understand example in every detail of science in action them and today.  Most important it is just as relevant to day as it was nearly 400 ago a span of four centuries.

(There is no ranking with respect to their  relevance. We suggest using Galileo as an example in the discussion.)

  1. What and how scientist (the example "Galileo") make their  discoveries

  2. The debates that follows these discoveries 

  3. The simplicities of Galileo's instruments

  4. The work involved in getting funding

  5. The distortions  by those analyzing his work through the years

  6. The rewards that the average scientist gets

  7. How the scientist are driven to tell the truth about their discoveries

  8. What they do with their discoveries

  9. Why are they driven to make discoveries in how nature works building piece by piece  ,step by step, the tome*  of everything?

  10. That science and scientist  have no cultural, political, business, or religious boundaries.

All these items  are within the grasp of understanding of most everyone of every culture. These are vital pieces of knowledge to make science understandable to everyone. They should be taught to everyone simply because sciences touches everyone and everyone  deserve the truth about how nature is put together.

We have a 400th anniversary of Galileo's  discoveries  coming up in 2010 where we could emphasize these realities of science.   There is an opportunity to build a bridge of understanding  filling this gap of how science really works. We can  teach  from this Galilean anomaly through our schools and  museums about  business of science and  can bring a real break through in the understanding of science to help reduce or eliminate these harmful schisms in one of the most important endeavors of the human experience that is of the gathering of knowledge of how Nature works so that we can use it for a better life for all of natures creatures.

Historic Scientific  Instruments  for Sale


Building Precise replicas of Galileo's Telescopes

Jim & Rhoda Morris      T       Return



Do the errors
in the drawing of the lenses  as noted in all the examples really matter?   yes and no?

 if we worry philosophically about  the ultimate impact it might have on the war against science's  reputation.  Benjamin Franklin  one of  American's famous scientist. He has written (or did he) ? ---

" For the want of a nail, the shoe was lost; for the want of a shoe the horse was lost; and for the want of a horse the rider was lost, being overtaken and slain by the enemy, all for the want of care about a horseshoe nail."

The question becomes  could this be  "another lost  nail issue"  i.e.  be bigger than it might seem?  Don't  errors in general, in science, contribute to schism  thus to a reluctance in funding and acceptance of many of  today's science's  projects?


not much technically in the image that Galileo saw.  Not from an optical performance point of view. It  would have not have significantly altered Galileo's discovery of the moons going around Jupiter.  Using  modern lens design methods, See Figures 2,3, and 4,  one sees that there  is less spherical aberration from the plano-convex lens than the double-convex lens but only by a small almost unnoticeable amount  in Galileo's telescopes.

On the other hand lets talk about science's reputation and the reputation of the writers who write about Galileo scientific work (including us)?  Example;

Yes- It matters
because of  Galileo's  popularity as a scientist. He is often used as a symbol of science and the down side interaction of science with religion, politics, business and people.  We are expected to look up to him for his accurate work with his telescope, one of sciences most  popular and easy instruments to grasp .  However errors  in the literature of  Galileo's work  can and should be  embarrassing for any author (include those writing this discussion) as well as  giving science an undeserved bad name for accuracy (the schism in our culture today).

Yes- It matters to the teachers of science examples  teachers are not knowingly  in the business of teaching something that is wrong. Shouldn't they be  teaching why and how scientist know their discoveries are correct and just how correct the discovery are. What about spending the time laying out the process by which the scientist and their colleagues  achieve confidences in their research results "reliability and accuracy" . (which some say is in short supply in today's world).

Yes- It especially matters
one understands that science's reputation and determination for accuracy is very much their currency of its  legitimacy  yet there is evidence from poles that some who don't share this belief  and cast doubt on  its truthfulness and  strive  to  make it  more difficult to get proper funding for some lines of research. Something we can least afford to lose in the U.S. these days.



So if  it is not the scientist causing most of the errors or misunderstandings where do they come from? Who's is responsible for the schism?  Also what about correcting these sort of errors or stopping them before they are made?  What is their most likely point of origin?

First if there are few coming from the scientific community, as they claim, what could be an additional source?

To start with----- where do most of us get our daily information about science and scientist. from?

For the most part scientific results are spread through the media in its many forms. The  public's  sole daily source of scientific information including a good dose of the scientist character analysis. is translated evaluated and delivered by a single path way. Click on the figure below to  make the diagram bigger showing the flow of information through the system.


Our  speedy little information person pictured above.  Is a crude outline of the flow of scientific information from scientist  through the guts  of our information person to Politicians, Businessmen,  Religious leaders and  the public. all  of who  use the work of their scientist. This Information Person's  needs a source of nourishment  " is income" which comes from the  business world selling advertising through the media  and in order for the media to stay in business it is absolutely essential to  hold the audience's  attention between the commercials.  Most of the daily business and scientific  world is not  entertaining in the raw so it needs to be spiced up a bit to hold our attention. What can anyone say about  the good or bad taste of the spice added to our science to flavor it?


Scientist have exceptionally good track record for  reliability and accuracy  in their research work but it  is totally invisible to much of the public. We will look into this "hidden" method of achieving this track record further on  this web site where we give a few examples of how this part of science works.

Lets first lets start by taking a fresh look at how and what we are teaching about science, in our schools, museums  and though out the media.  We concentrate well on topics such as the physics of black holes, string theory, the wonders of chemistry, and Einstein's old girl friends. Certainly science or the lack of it is an everyday experience for everyone.  However there seems to be a small but important part missing in our education of science and about the Modus operandi of our scientist. There is to little to nothing taught about  the hidden science  that works behind the scenes, that controls how science is done, the science that scientist take for granted, and it  is hardly ever stressed to the public.  This hidden science that the media finds too boring to talk about, is a topic in what we call "how science works" the so called science of science.

Accuracy is one of the trade mark of  science, a trade mark that   scientist use and depend on it to get funding  for their research especially for large issues that are complicated and hard to understand, by the public and the organization funding the research,  i.e.  global warming, stem cell, and pandemic research are examples.

One of the features  of "how science works" is how scientist gain  truthfulness, accuracy, and  trustworthiness in their business yet are not any more truthful in their personnel lives than  the average persons in his or hers personal life.

Related but not a necessary Why can't we,  Including the authors, do a little better with the  accuracy, especially for on one of natures simplest telescope, two little pieces of glass, three tubes and some glue, and   especially for one of  histories best known telescopes, with an important story  on "how science works" ?

It is one of the clearest case studies in history for how we could do better with gathering and disseminating knowledge. Plus isn't there going to be a "Telescope Year" in or around 2010?  Do we want to carry with us miss information that other wise could be corrected for the up coming celebration? Could we use this opportunity to form a goal to develop such a course teaching  how science really works? Regardless how many illegitimate children Galileo might have had.

The reason we are going to such an extent (on this web page) on accuracy comes from the authors concern for the funding of basic scientific research  in the U.S. Which many of us know is not doing that well in the U.S.

We made  a small study,  a pole of some 150 people,   about 50%   generally miss trust science.  Studies by Dr. Jon Krosnick, Professor of Humanities at Stanford Univ. have found similar results with professional surveys.  In our pole we found  quotes like the following comments below.

  • Scientist  are always waffling and cant make up their minds on most topic.

  • Scientist  are bought and paid for  to support businesses products

  • Scientist are under great pressure to be first and publish before they should and report misleading data.

  • etc. etc. etc...

The major unsolved problem and challenge science has faced and still faces  is the mistrust  of science. The majority of those who aren't  familiar with  how science works  are compelled to mistrust it.   Is there any question that one  has no alternative  but to  mistrust science as one mistrust all other things that are difficult to understand. This mistrust slows  the progress of all science .

Of course this mistrust of science can  and has affected the funding and the acceptance  of basic scientific research in all areas of science some vital to our and our planet's health.

For those who may disagree about trust and science we recommend  they  run a  pole for themselves asking the questions.  on the form similar to the one on this link.

One should ask these questions of  people from as many walks of life as  possible .Caution--Simply listen  to the answers thank those  who have taken the time to answer the questions without  out challenging them.

Some of the examples "How science works"

A few  examples of what we mean when we use the words "How science works" are given below. 

    Most have never seen nor will never, most likely, see through the entertainment media information regards to;

  1.  the most elementary form of a  scientific paper with its guides spelled out for a proper paper

  2.  the steps that have to be taken to validate a new discovery 

  3. the steps in writing  proposal for funding

  4. the number and type of organizations that award funding

  5. What is and how much is the cost of overhead

All these and more  things that are not laboratory work  but have to be done behind the scenes to do the research is seldom or ever taught when teaching science.  These details of the working of science  are at the roots of the success of science. We need to have a fresh look at how and what we are teaching in science, in schools, at museums  and though the media. We most do a much more vigorous job at teaching topic in science  ( Physics, Black holes, string theory, The wonders of chemistry, Einstein's girl friends)  than why  and how it works so well when funded. The authors feel strongly about this issue.

What is the solution to gaining  the  trust that science honestly deserves?  Should we even care about gaining it?

It is absolutely essential  for all of us  to understand the whole issue of why there are very few  errors, mistakes,  falsehoods, or outrageous claims in scientific work  in comparison to errors, mistakes, falsehoods or outrageous claims  in every day life. Again sadly there are few outside the professions of science who know  how and why this is true.

Accuracy is the first and absolute requirement among  scientists.  This can be and often is totally unexpected by the average person. Every day we all encounter errors, mistakes,  falsehoods and  outrageous claims everywhere and in everything we do. There are so many errors, mistakes, falsehoods and  outrageous claims  floating around that most people take  them for granted, even  to the point of ignoring  them, and becoming a perpetual doubting Thomas.

The scientific community works in a system of testable honesty and accuracy that ferrets out errors, mistakes, falsehoods and  outrageous claims.  The system is built on Homo sapiens natural fear of being " wrong". One of the most crushing blows to a scientist is be wrong. Its a very public wrong because their work is out there for everyone to see. Scientist never work alone. as Jules Vern etc. so often portrays them. They work intimately with the ghosts of the past, tested constantly by scientist of today and the future.


The standard process and rules of testing new scientific discoveries or  updating and  replacing existing ones that makes a scientist work one of the bright spots in data reliability.

 Example Scientific paper by Robert Oppenheimer  It is a form all scientist use to describe their work it contains all those things that are important in making the work of a scientist  reliable dependable honest and  trust worthy  independent  of their personal reliability.

  1. What does not work-----A public verbal announce of a discovery with out suitable documentation maybe be exciting but  not acceptable to the scientific community.

  2. What does work---

  3. Everything about the new experiment, ---why it is being done, ----where it fits into the general understanding of the field of investigation -----The methods, instruments, error analysis, of the data  etc. ----has to be published to the public  -----with sufficient  detail so others can replication the discovery.   This is only the  start the journey toward the  acknowledgment of the  new work.

  4. It  has  to be replicated  many times preferable by other laboratories.

  5. Often  scientist can employ other methods and  measurements to cross check the discovery.

  6. When scientist publish their discovery they are required to furnish   textual descriptions, formula, drawing,  etc. written down for all to see and study.

  7. They are required to publish  their methods of gathering their data in detail.

  8. Their analysis of the reliability of their data

  9. The methods of  analysis used to determine the reliability of their data

  10. When all of these things have been completed to most everyone satisfaction it  will be accepted ---- until proven otherwise.

  11. This process may go on for weeks month and years before there is a enough data to check and cross check the new discovery.

  12. This does not delay experiments using this new data to make new discoveries using hardware or paper.

  13. in fact often the  experiment being preformed based on the new discovery  is a way of confirming or trashing the new discovery.

  14. Many times more accurate data will come along and help to  improve and alter  the initial discovery.

  15. Example of a change   to the orginal equation of a very  famous scientist

  16. F=MA    mid 1600's Newton et al.  orginal equation        

  17. F=M0A  c 350 years later Einstein et al. "modernized" Newton's equation  to take into the observation that mass is a function of speed

  18. All things in science are connected by time length and mass

  19. The bottom line is---- each discovery  builds on many other discoveries before it.

  20. Science is a team activity each scientist works on a rather small part of the  big project of understanding of all parts of natural world.  They are very much dependant on other scientist discoveries.

  21. Each discovery will be used to  build other discoveries--- on and on in the steady march  forward to determine how all things in nature fit together giving us the complete story of how  nature works.

Thus honesty in science is at a higher level than most other professions.

One can not ignore or go around errors, mistakes, and especially falsehoods in scientific investigations without being highlighted for all to see. 



This issue  is so important, especially  in today's world where science is again being subjected  to  the Galilean syndrome, that the authors take the opportunity to ask the reader to examine  the full error issue in a more detailed way.


  • Why are there so few errors, mistakes, and falsehoods in the scientific literature?

  • Who finds them?

  • How are they found?

  • What is done about them?

Every discovery made by a scientist is built on all the discoveries preceding it.  An error, mistake, or falsehoods  in the initial work can cause a catastrophe chain reaction to all the work that follows it. Obviously all the scientist who have been racing with each other to be first to  find the great new discovery and who have been mislead by bad data  have wasted their research grant money, their  time, which is very dear to them and the most catastrophic affect, they have  been slowed down by the bad data  and lost the opportunity of being first to a new disco

Can we use this error as a tool for teaching  how Science and scientist work?

We make a suggestions at the end about using this Galilean lens issue to set the record straight about the accuracy of scientific results in today research projects.

Does the error in the drawing of the lenses  as noted above really matter?  Yes for a scientist with Galileo  popularity because he  is often used as a symbol of science.

Galileo's story  is a dramatic interesting  mile post in science.  A subject that constitutes a  famous, simple, straight forward example that most of us can appreciate of every aspects of science. An almost  perfect example   to teach about science and how science works. Its filled with lessons showing how science fits into the larger world of politics, business, and religion in 1600 and today.

Historians  of  science are challenged with who invented or discover  what and when  to see how science moves through history. There is also a preoccupation with the quality of the technologist's thinking. Was the work  just an accident by a run of the mill instrument maker? Others were working at break neck speed  to be first in the new world of science.  Didn't build the first telescopes solely for astronomical use?


There is a bright and useful side to this lenses anomaly.  It gives us a good teaching opportunity to high light  this  very important aspect of science.  giving us a good opportunity to discuss the role of falsehoods and errors in science and  how they can and do come about. It sad that there are some professions of reporting science that are more likely to  embrace such risks of being wrong. See the examples in the literature further on in this web page.

How to keep the record straight A few reasons for why errors in the literature occurs.

  • Out side influences; Because of the Church's position on the nature of Universe Galileo was forced to  modify  his scientific interpretation of his data and conclusions to save his life? 

  • Reporting on Galileo  using secondary sources. in this case  choosing  schematics of  the instrument especially the very heart of  the instrument without checking for the accuracy of the source. This error has been with us hundreds of years 

  • Deliberately changing  historical information to  emphasize an  author needs to gain  more drama for popular consumption.

Some interpreter's judgment of Galileo's skills is keyed to the kind of optics Galileo used for his telescopes. Perhaps some should also be judging the   reporting skills of the  interpreters skills of Galileo's skills.

The dramatic aspects of this error has been  its life time. Its been around for hundreds of years being accepted and repeated over and over again. It suggest extreme caution in using secondary sources in the literature.

The big question is if one can't rely on the reports for  the shape of  two simple  pieces glass,  the most important components of Galileo's  telescope,  for one of the most significant instrument in the history of  science, what can one say about the science of the popular versions of the  history of science ?

So in producing a museum quality replica's of Galileo's telescopes one has be very critical of any literature detailing the  specifications of the telescopes especially of  the lenses, after all they are the telescope. One of the key sources of information which has no language barrier are schematics, drawings, or blue prints. They are a universal vehicle of  communication  in the technical world. They are equivalent to the wiring diagram  of  ones house, computer, brain, or  nervous system.  Drawings  don't have to be  to scale  but one should  expect then to preserve the  relative shape,  location  and interaction of the components along with a clear description of the nature of the drawing, scale etc..

When one looks at the original lenses or photos of the lenses of Galileo's telescope IMSS 2427 one finds that they consist of a plano-convex objective  with a biconcave eye piece. (Note) We believe that original eyepiece of this telescope was a plano-concave eyepiece. See details. here is an example of why the presumed error in the drawings could affect our choice of lenses for the replica and  our  evaluation of Galileo's sense of science forming his choice of lenses.

There is a potential major problem. When one doesn't have access to the originals documents and data. We have go to and rely on the literature, which is generated by a number of sources. They are the profession historians in science, scientist, and the media in all of its forms. There are  tens of thousands of schematics, drawings, or blue prints flooding  the literature on Galileo's lenses. Which source should  we depend on?

Because this issue is so importrant The authors run through our point again. Galileo is a wonderful thrilling story with all of the essence of science, a teacher, a technologist, an entrepreneur, a manufacture of military weapons, a sales person, a basic,  researcher all roll into one at a time when science began to use  the tools of measurement of time, length, mass, calculation and communication to really do science. He confronted one of the most powerful institutions of Europe over a philosophic issue that had meant little to nothing to the average persons or their pocket book.   Here it is nearly 400 years later and the only thing  that has changed is it takes teams of specialist to do what one person did in the 1600's.

Galileo mightiest contribution to us all  might just be   to bring all the individual component together in one famous case study  that all can understand just how science works.  Galileo his instruments and his story tells us all about  what science and civilization are all about so that we might cure once and for all the slow downs caused by the Galileo Syndrome.

 what and why
To neglect errors  is never good science and certainly not good for science.  In the case of the lenses neglecting this error distorts our view of what Galileo and the early lens makers knew about optics in the1600's and raises even more strongly the issues of  who invented what and when.   For example  from the professional literature Galileo did not invent the telescope but did invent a more powerful telescope and presumably  used  lenses  essentially  flat on one side. Why?  Why did he use a negative lens as the eyepiece in the first place?. Why didn't he use a plano convex or a double convex lens giving a much larger field of view? What can we learn about Galileo skills by looking at the possible reasons he chose  plano concave ...convex surfaces.  Isn't the use of double curved lenses a different invention by a different inventor?  Are there  sound and  practical reasons and lessons to be learned for his choices? Does the nature of this choice give us an insight  into how  all scientist  make choices  in the process of doing their work? Are these choices intellectual, economic or philosophic?  How did the error in the drawing of Galileo's  lenses get started in the first place, and why has it persisted for hundreds of years? Doesn't it cast more than a shadow of  doubt  over some professions reporting  on the  scientific discoveries as a whole?

The big question; The simple shape of two little pieces of glass, the  lenses, the very essence of the invention of Galileo's telescope.  Can't we  report this information correctly? Don't we  care about getting it right? What does this say about the reporting of the very essence of science, especially basic research, the very human activity for where there are  No Words Powerful Enough To Express its  Importance To Our Past, Present, And Future?  Click here

Summary There is no room for sloppiness in doing science or reporting science.   The most essential tool of scientific research is "accuracy" and  " more accuracy".  When the scientific world present (publishes) their data publicly or in private communications.  The qualification of  data  is just as important as the data. Question such as  how accurate is it and how was it measured is the heart of science. Using this qualification tool is one of the reason science has been so successful.  Each piece of data lays the  ground work for next collection of data etc. etc.. This is true for all or any data used in any science related project.

Conclusion; it is not good practice or science to assume that  drawing for  the shape of the lenses  in a diagrams of  a  optical systems appearing in the text books and papers are the same as the lenses used in the system. Generally for simple optical systems such as a telescope it is traditional for the artist to show all  the lenses as either  double concave or double convex. This  is certainly true  for most  illustrations of the earlier telescopes. The actual lenses used  more than likely  have one side of the lens  flat the other shaped in a concave or convex curve. They are faster and easier to make. So again the reader should be on the alert that the diagrams outlining the optical layout  are neither in scale nor are the lenses shaped as they are in the telescope.

The authors ask the question if one cant rely on the accuracy of  data for the simplest combination of lens in the most celebrated historically significant telescope  how can we rely on  information for today's scientific projects  where our main source of information  is interpreted by  essentially a  poorly scientific educated  media, business, political, religious leaders. Remembering that  There Are No Words Powerful Enough To Express The Importance Of Basic Scientific Research.


Some scientist can be so excited by the future they forget to look back. It looks as if this has happen with the lenses ascribed  to Galileo by many sources in the  literature. This coupled with the  small difference it makes in the performance of his telescopes is why today's  scientist leave it be. But is this a mistake?

But there are two scientist  which say  No!  lets   take issue with this incorrect figure. We had put the incorrect figure on this web page to begin with.   We had copied it from  a 1860 text on natural philosophy. It was pretty.  Then someone  called us on it. We responded that it was just tradition and left it alone just sitting there wrong. After chatting with allot of people about this strange little error and how long it had been in place  We were saddened that, surprising to us, that most people could have cared less because they thought that scientist  were  no more worried about errors in their work than any other profession,  citing examples of contrived errors upon errors by scientist doing research in  evolution, stem cell, and global warming to mention a few. We have asked ourselves whether trying to get the word out about how science works using testable honesty tool. would help science to be more efficient in getting their work out to the public and getting more funding?

We recognize that Galileo was a wonderful example of a scientists being  forced to lie about the conclusion he had made with his telescope. We believe this example could be used as this opportunity to discuss  the issues of honesty in science and make an attempt to set the record straight about honesty in scientific work. Wouldn't be wonderful if politics, business, and religion adopted the same tool? There is something here that is very important. Something that we all could learn from about  science.

Do  schools still teach the George Washington story about the cheery tree he was supposed to have chopped down.  but confessed when caught. 

Galileo is a true story and he was forced by a powerful organization to lie or be burned alive at the stake.

 * tome n. 1. One of the books in a work of several volumes.
2. A book, especially a large or scholarly one

Copy Righted  5/1/2006 Jim & Rhoda Morris

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