Feynman’s Blunder—Part 2

Written by Dr Jerry L Krause

I write this before Feynman’s Blunder—Part 1 has been published.  I do so because at the end of this article I had written:  ‘This article was titled (Feynman’s Blunder—Part 1) because I want to give a reader an opportunity to comment as to what his blunder was.”  For I anticipate (hypothesize) that there will be no comments. feynman photo

For if this proves to be the case, Feynman’s Blunder has more members who are at fault for not correcting his most elementary blunder.  Of course, I recognize that such a conclusion implies that someone actually read Feynman’s Blunder—Part 1 to the end.  However, if a reader of PSI articles did not read this short article to the end, it only confirms that they are part of the problem—uninformed people about what good science is—which PSI is trying to correct.  “The essence of genuine scientific inquiry shall exemplify the sui generis, or the abiding maxim that goodness is indefinable and exists in science only insofar as the pursuit of truth ought to be our abiding goal.”  I send this introduction of this article to John O’Sullivan so there is a witness that I wrote it before Feynman’s Blunder—Part 1 had been published.  For this previous article is an experiment.

“Of course, this is how we manufacture steam out of water—by increasing the temperature; the particles fly apart because of increased motion.”  Feynman has focused his students’ (reader’s in this case) imaginations upon boiling water with which he expects his students are familiar.

“In Fig. 1-2 we have a picture of steam.  This picture of steam fails in one respect:  at ordinary atmospheric pressure there might be only a few molecules in a whole room, and there certainly would not be as many as three in this figure.”  And he continued to empathize this point.  “Most squares this size would size would contain none—but we accidentally have two and a half or three in the picture (just so it would not be completely blank).”

I cannot imagine why Feynman was trying to have his students imagine there are only a few water molecules in a whole room.  For the actual case is that there are so many in the whole room that it is hard to imagine the number of them.

Chemists have a unique unit—mole—and chemists are modelers.  So my chemistry professor had a wooden cube (the model) whose volume was 22.4 liters.  For 22.4 liters, less than one cubic foot, is the volume of 1 mole of a gas at a STP (standard temperature (25oC) and pressure (1 atm.).  And a mole of gas is 6.02 X 1023gas particles (atoms or molecules).  The vapor pressure of water at 25oC is 23.8 mm Hg or 0.0313 atm.  So at 50% relative humidity, the number of water molecules in a cubic foot of air STP and 50 percent relative humidity would be greater than 9 X 1021.  Which is a very big number even though the result of every calculation was rounded well downward to cover for any math errors which I might have made.  And because Feynman used the word—steam—it was not clear to me if he was actually considering a room filled with water molecules at 100oC and 1 atm. pressure or the more conventional room of air which I have assumed.

So, it has been that not only Feynman made this elementary blunder, but also his students who should have known this elementary information from their high school chemistry or physics classes and did not correct (question) what he taught immediately upon hearing it.  And there were others at Caltech who were involved with the students to whom Feynman was lecturing.  And there were two coauthors in addition to Feynman ofThe Feynman Lectures On Physics.  If any of these had seen the blunder and called it to Feynman’s attention, I doubt if the blunder would have ever been published.

And I question: How many people now know how The Feynman Lectures On Physics came about?

In a recent article–http://principia-scientific.org/russian-engineer-invents-revolutionary-new-combustion-engine/–the Russian education of a Russian inventor, Nikolai Shkolnik, is addressed.  “There are big differences between American engineers and those trained in Russia,” said Shkolnik. “American engineers are incredibly effective in what they do, and it usually takes two or three Russian engineers to replace one American. However, Russians have a broader view of things, which has to do with their education; at least in my time it did. They are capable of achieving goals with a minimum of resources.”

The phrase—at least in my time did—caught my attention.  And I wrote a comment to this article, the only one which this previous article has received as this article is being published, which reviewed the rapid change of chemistry and physics education that had already occurred in leading North American universities and institutes of technology when Shkonik graduated, in 1975, from Kiev Polytechnic Institute with a physics major.

In this previous comment I reviewed what authors of physics and chemistry textbooks had written in the prefaces of their textbooks which were published between 1955 and 1964.  And I consider these authors’ comments deserve repeating here because one these authors was Feynman.

In the preface to their 1957 textbook, Physics, J. S. Marshall and E.R. Pounder (McGill University, Montreal) wrote:  “This textbook covers the major branches of physics at a level suitable to the first and second years of a University course.  Sufficient material is included for a two-year course, but it is felt that the book will serve as a text for a one-year introductory course by judicious omission of the more difficult parts. … Calculus is not needed for an understanding of the text.”

In the preface to his 1955 textbook, College Chemistry 2nd Ed., Linus Pauling wrote:  In the preparation of the second edition of this book an effort has been made to increase the clarity of the presentation of the subject.  [Which had to be an admission that the 1st Ed. lacked clarity]  The first part of the book has been largely revised in such a way that the facts, concepts, and theories of chemistry are introduced more gradually and more systematically than in the first edition.  Some new, rather simple illustrative exercises are given in the text, immediately following the sections that they illustrate.  The exercises at the ends of the chapters have also been considerably revised, with elimination of some of the more difficult ones.”

Then, in the preface to his 1964 textbook, College Chemistry 3rd Ed., Pauling wrote:  “During the last decade the science of chemistry has continued to change.  Descriptive chemistry, the tabulation of the observed physical and chemical properties of substances, is still an important part of chemistry; with each passing decade, however, it becomes possible to correlate these facts in terms of theory in a more and more satisfactory manner.  The theories of greatest value in modern chemistry are the theories of atomic and molecular structure, quantum theory (quantum mechanics), and statistical mechanics.  I believe that the concepts involved in these theories can be learned by the beginning student of chemistry sufficiently well for him to apply them in correlating and understanding the facts of descriptive chemistry.  Moreover, the fundamental experiments upon which these theories are based can be understood by the beginning student.  The theories in their detailed mathematical treatment can then be studied later.”

In the 1961-1962 academic year, the physics department at Caltech, began an educational experiment.  About which Richard Feynman, in his preface of The Feynman Lectures On Physics Vol. I, wrote:  “The special problem we tried to get at with these lectures was to maintain the interest of the very enthusiastic and rather smart students coming out of the high schools and into Caltech.  They have hear a lot about how interesting and exciting physics is—the theory of relativity, quantum mechanics, and other modern ideas.  By the end of two years of our previous course, many would be very discouraged because there were really very few grand, new, modern ideas presented to them.  They were made to study inclined planes, electrostatics, and so forth, and after two years it was quite stultifying.  The problem was whether or not, we could make a course which would save the more advanced and excited student by maintaining his enthusiasm.”

“The question, of course, is how well this experiment has succeeded.  My own point of view—which, however, does not seem to be shared by most of the people who worked with the students—is pessimistic.  I don’t think I did very well by the students.  When I look at the way the majority of the students handled the problems on the examinations, I think that the system is a failure.”

Feynman, the physicist, could not avoid the detailed mathematical treatment which the theories of atomic and molecular structure, quantum theory (quantum mechanics), and statistical mechanics required to ‘understand’, or to ‘explain’, them.  Pauling recognized the importance of these new theories to chemists is that they generally explained much of what chemist already had learned about matter and the changes it undergoes from their experiments.  And it seems that he recognized that these theories also pointed toward phenomena not yet studied.

PSI recently published an article—http://principia-scientific.org/yet-corrections-greenhouse-gas-theory-errors/—which I was credited with writing.  However, I did not write it.  It was a rough draft that some unknown author (UA) had written which I considered deserved to be considered by others.  But such a gem can be easily overlooked.

UA wrote:  “In the present case [greenhouse effect] an obvious and very fundamental question is:  How can matter sometimes absorb radiation incident upon it and sometimes not absorb radiation incident upon it?  Fortunately for me, Albert Einstein [ ] answered this question long ago and Richard Feynman [ ] brought this answer to my attention in a simple way I could grasp.  The fact is that matter always absorbs the radiation it is capable of absorbing according to the usual laws of absorption.  However, Einstein assumed there were two types of emission—spontaneous and induced.  According to absorbed radiation is not always not always converted into sensible or latent heat before it is emitted (strangely termed spontaneous emission) by the matter; instead a portion of the absorbed radiation can be directly emitted (induced emission) from the matter.  From a consideration of Planck’s Distribution Law, Einstein concluded the absorption coefficient of certain wavelengths was equal to induced emission coefficient of radiation having the same wavelength.  That induce emission is a real phenomena is confirmed by the common devices which we call lasers or masers.”  I do not know what UA’s intended references were; but I know that Feynman addressed Einstein’s laws of radiation in The Feynman Lectures On Physics Vol.1, pp 42-8 to 42-10.

And I know that (Vol.1, pp 32-8, 32-9) Feynman taught a scattering theory of radiation by cloud droplets which I have not found being considered by anyone else, including UA.  So, even though it appears that at times Feynman was human like the rest of us and blundered, maybe we should stop ignoring (a blunder) what he maybe did get right.

Feynman’s Blunder Part 1 may be accessed here: http://principia-scientific.org/?s=feynman

Comments (5)

  • Avatar

    Ed Bo


    Good grief! It’s very reasonable — and very clear — what Feynman was arguing; you just missed it completely!

    Feynman was showing what water molecules would look like expanded a billion (10^9) times in length — which means 10^27 (= (10^9)^3) times volumetrically. At this scale, a water molecule would be the size of an apple.

    So at this scale, how close would molecules of gaseous H2O be to each other? You cite that at STP, there are 6.02 x 10^23 molecules of a gas in a volume of 22.4 liters. So blown up by a factor of 10^27 volumetrically, there would be 6.02 x 10^-4 molecules per 22.4-liter volume, or 1 molecule every 1661 instance of this volume.

    If we took a large room with a volume of 100 cubic meters (100,000 liters), it would have 4464 instances of this 22.4 liter volume, so there would be about 3 molecules AT THIS SCALE in the room.

    All Feynman was saying was that in the gaseous state, the spacing between molecules is FAR, FAR greater than the size of the molecules, too great to show accurately in a simple drawing.

    No blunder – just a great teacher!

    • Avatar

      Jerry L Krause


      Hi Ed,

      Yes, I understand your point about the fact that Feynman had magnified and magnified the water molecule. And I had submitted a comment to Feynman’s Blunder–Part 1 which still has not been posted because of some glitch.

      But a portion of this comment was:
      “Hi Geoff,
      I consider you are right and my article Feynman’s Blunder-Part 2 should some be published as it had been submitted shortly after Part 1 in case someone like you did answer the challenge. And you will see that no one had before you. You will see when Part 2 is published that I did not expect anyone to even comment because so few of my articles have received any comment.
      However, after submitting Part 2 I saw that what he stated about Fig 2 could be defended because somewhere I read that the approximate spacing between gas molecules, at STP, is about 10 times the diameter of the molecules. Since the distance between the molecules in Fig 2 is much less than 10 times the size of the molecules pictured. But his statement about only few molecules in a room could not be defended by any argument.”

      It could not be defended because he began with a quarter inch cube of water which had been vaporized to ‘steam’ (independent water molecules). This quarter inch cube of water is about 1/20th of a mole of water; which is about 3 X 10^22 molecules of water. And he wrote that the cube of water was heated and its temperature increased until all the molecules separated from each other to form a gas (steam in this case). Which as you say cannot be stable at room temperature but can be if the temperature of the room is 100C or greater. Feynman did not do a great job in accurately defining the conditions of the system upon which he was focusing attention.

      And you wrote: “If we took a large room with a volume of 100 cubic meters (100,000 liters), it would have 4464 instances of this 22.4 liter volume, so there would be about 3 molecules AT THIS SCALE in the room.” What ever the size of the room you want to propose, it must contain about 3 X 10^22 molecules of water unless you insist in proposing the windows and doors of the room were open and all but 3 molecules of water escaped from the room.

      What was Feynman’s purpose when he began to magnify the water molecules? Was it not to help them imagine how tiny atoms and molecules are? As a chemist I sometimes took a graduated cylinder with 18 ml of water in it and then wrote Avogadro’s number with all its zeros across the blackboard to impress upon a students mind how tiny a water molecule had to be if there were that many in the small volume of 18 ml which they could see.

      Have a good day, Jerry

    • Avatar

      Jerry L Krause


      Hi Ed,

      I asked: What was Feynman’s purpose when he began to magnify the water molecules?

      Upon rereading what you wrote, I see you probably consider it was to show them the structure of the water molecule. And you could be right. For I, as a former instructor, I could not understood how this was critical issue at the beginning of a two-year physics course. But he did state what the observed angle was and what the distance between the hydrogen’s nucleus and the oxygen’s nucleus was; except that he did not introduce the fact that an atom has a nucleus (instead he referred to the atoms’ centers), which contains most of the mass of an atom.

      And I only now question his teaching ‘methods’. To me the important issue was, and is, what he factually got wrong. “at ordinary atmospheric pressure there might be only a few molecules in a whole room”.

      Have a good day, Jerry

      • Avatar

        Ed Bo



        I think you are overthinking this. Feynman is simply playing the scale model game, basically asking his students, “if I scale up water molecules to the size of an apple, how many molecules of water in the gaseous state (at standard conditions) would there be in this room?”

        Rescaling objects, both immense and tiny, to standard human dimensions is a common teaching tool. On the US National Mall in Washington DC, there is a model of the solar system, scaled DOWN by a factor of 10 billion in the linear dimension. The key educational point of the model is to give people the proper sense of how far apart the bodies are compared to their size — exactly the same point Feynman is trying to get across about molecules in the gaseous state.

        I started with your molar volume (at STP) of 22.4 liters and scaled it up by a factor of a billion on a side to confirm Feynman’s “3 molecules in a room”. Do you see an error in my math (or in yours)?

  • Avatar

    Jim McGinn


    It’s really unclear what you think Feynman’s blunder is here. Are you suggesting Feyman actually believed there were only two molecules of steam in the whole room? Obviously it couldn’t be that. Is it that he mistakenly assumed steam can exist at the ambient temperatures of the atmosphere? If that is the case then Feynmans blunder is much, much more widespread than you suggest in that all of meteorology and just about everyone else (except me and a handful of people who have been influenced by me) is maintaining this blunder.

    Please be concise and explicit with your response.

    James McGinn

    Like the rest of us, Feynman adopted this blunder from a dude named Isaac Newton:

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