I am a historian of science living in Japan. Currently, I am reviewing papers from the early days of quantum mechanics, including those from that period in Japan. At the moment, I am examining Paul Dirac's paper "On the Theory of Quantum Mechanics" from August 1926. The original paper is available for free online in PDF format (https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1926.0133), but when I use OCR, some parts of the text are inevitably read inaccurately. This issue is particularly pronounced with mathematical formulas, which are often not read correctly. I would like to find a text format version of the paper, if one exists. Are such versions available? If so, can they be accessed without using a paid database? If anyone can locate a text-based version of the paper and share it with me, I would greatly appreciate it, as manually inputting each equation is quite tedious.
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1$\begingroup$ You need to understand how such pages are stored so the Pages have already been converted as much as is already possible from the source which is simply a canvas of the source scan so without the paper source you could generally only do worse. You have to clip from the best possible copy (I doubt whether better is publicly available?) see here how I have intentionally faded the canvas on just page 2 so you can see how good the existing OCR text is filetransfer.io/data-package/OenrA2H4#link and the reason the formulae are not attempted is OCR is pants in those remaining equation areas $\endgroup$– K JCommented Sep 16 at 15:00
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$\begingroup$ Compare that with the original repository.lib.fsu.edu/islandora/object/fsu%3A641 $\endgroup$– K JCommented Sep 16 at 15:12
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$\begingroup$ Look into my linked files and you will see a possible solution to cleaning poor OCR. $\endgroup$– K JCommented Sep 16 at 16:03
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$\begingroup$ I found the earlier archived copy from 2006 but it has no OCR ethw.org/w/images/0/06/… $\endgroup$– K JCommented Sep 18 at 17:18
3 Answers
It might be hard to find a text-based version. You can request your librarian to find a high-resolution scan of 600 dpi. However there are a couple of free (or nominal fee) OCR tools which specialize in recognizing advanced mathematics symbolism in texts. See one here: https://mathpix.com/
For example, let us try pg 9 of the low resolution public version, with complex equations 14 and 15 having subscripts and a determinant. One can take a snapshot from the pdf and paste it in MathPix Snip webpage; the pasted image is converted into text. You may have to check for minor transcription errors.
This approach can even be used to translate foreign language scientific texts.
Facile Solutions to the Problems Associated with Chemical Information and Mathematical Symbolism While Using Machine Translation Tools. Journal of Chemical Information and Modeling, 60(7), 3423-3430. Link: https://pubs.acs.org/doi/10.1021/acs.jcim.0c00274
After pasting it in the appropriate box, we get
which can be readily exported to Word to obtain a text based original paper.
These results may evidently be extended to any number of electrons. For $r$ non-interacting electrons with co-ordinates $x_1, y_1, z_1 \ldots, x_r, y_r, z_r$, the symmetrical eigenfunctions are $$ \Sigma_{a_1 \ldots a_r} \psi_{n_1}\left(\alpha_1\right) \psi_{n_3}\left(\alpha_2\right) \ldots \psi_{n_r}\left(\alpha_\tau\right) $$ where $\alpha_1, \alpha_2 \ldots \alpha_r$ are any permutation of the integers $1,2 \ldots r$, while the antisymmetrical ones may be written in the determinantal form
$$ \left|\begin{array}{cccc} \psi_{n_2}(1), & \psi_{n_1}(2) & \ldots & \psi_{n_1}(r) \\ \psi_{n_2}(1), & \psi_{n_2}(2) & \ldots & \psi_{n_2}(r) \\ \cdots & \cdots & \cdots & \cdots \\ \psi_{n_2}(1), & \psi_{n_2}(2) & \ldots & \psi_{n_t}(r) \end{array}\right| $$
Don't forget for check for errors!
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1
The OP Source is a modern (2024 watermarked) medium quality JPEG2000 scan with perfectly good OCR It's base imagery was generated using ABBY OCR in 2017. It would appear to have been proofread. However there are residual flaws in the text, such as below the formula Whenever a p r or W should have the r dropped lower. Whenever a $p_ {r}$ or W ...
There is a prior scanned JSTOR PDF at 600 DPI based on TIFF from 2014 but does not contain the OCR, and thus it is best to use the newer one for the text and possibly the older one for additional contents.
For that reason the text and formula should be considered as separate tasks. Using a combined OCR is often a fail as it tends to concentrate on one or the other as per this poor example.
We can use those higher quality images with any math OCR and export say to Word or Latex or others via many free services.
Several Word Processors like MS Word can themselves segregate the text and the imaged areas from different source types, but need to be tested per case as it not 100% reliable.
Here is Page 1 from a fresh Free OCR web site as the one shown above. https://simpletex.net/ai/latex_ocr
Most Archives will not attempt OCR on formula due to the images threshold problems. Here I have intentionally highlighted an example from Page 2. Where the background scan is at the tipping point and one % either way will be degraded. So am holding at this point for dedicated OCR.
We can then use an online or offline Maths focused OCR to convert that image into a PDF compatible snip for paste into the Word Processor. But all this is very one time specific and not much quicker than selectively typing into a Maths equation editor.
Here I asked CHAT to display that area.
Link to
OOPS spot my OCR (Old Character - Recognition) error dt should be δt
(I am the "old character" :-). easily fixed Link and here for cut and paste !
**
$p_ {r} = -ih \frac {\delta }{\delta q_ {r}} , -W=-ih \frac {\delta }{\delta t} .$
**
<math xmlns="http://www.w3.org/1998/Math/MathML" data-latex="p_ {r} = -ih \frac {\delta }{\delta q_ {r}} , -W=-ih \frac {\delta }{\delta t} .display="block">
<mrow>
<msub data-latex="{}">
<mi data-latex="p">p</mi>
<mrow data-mjx-texclass="ORD">
<mi data-latex="r">r</mi>
</mrow>
</msub>
<mo data-latex="=">=</mo>
<mrow>
<mo data-latex="-">−</mo>
<mrow>
<mi data-latex="i">i</mi>
<mo>⁢</mo>
<mi data-latex="h">h</mi>
<mo>⁢</mo>
<mfrac data-latex="\frac {\delta }{\delta q_ {r}}">
<mi data-latex="\delta ">δ</mi>
<mrow data-latex="\delta q_ {r}">
<mi data-latex="\delta">δ</mi>
<mo>⁢</mo>
<msub data-latex="{}">
<mi data-latex="q">q</mi>
<mrow data-mjx-texclass="ORD">
<mi data-latex="r">r</mi>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
</mrow>
</mrow>
<mo data-latex=",">,</mo>
<mrow>
<mrow>
<mo data-latex="-">−</mo>
<mi data-latex="W">W</mi>
</mrow>
<mo data-latex="=">=</mo>
<mrow>
<mo data-latex="-">−</mo>
<mrow>
<mi data-latex="i">i</mi>
<mo>⁢</mo>
<mi data-latex="h">h</mi>
<mo>⁢</mo>
<mfrac data-latex="\frac {\delta }{\delta t}">
<mi data-latex="\delta ">δ</mi>
<mrow data-latex="\delta t">
<mi data-latex="\delta">δ</mi>
<mo>⁢</mo>
<mi data-latex="t">t</mi>
</mrow>
</mfrac>
</mrow>
</mrow>
</mrow>
<mo data-latex=".">.</mo>
</math>
The "Original" was pre digitization and I defy any OCR to be able to work with those earlier papers. Dirac starts a page as fairly square but the formula ramble sloping all over the place with many strikeouts.
Thus any scanned from the past are always a challenge. I was there in the early days and OCR has not changed much, until now with ροBOTS. (Pun alert: That is pronounced as Rho-bots).
Free Sites that can help Your Mouse pen finger Written text https://webdemo.myscript.com/views/math/index.html
Image to LaTeX (not perfect but depends) https://web.baimiaoapp.com/image-to-latex/en
The example above is good for Latex to MathJax and has lots of useful links
https://saxarona.github.io/mathjax-viewer/?input=p_+%7Br%7D++%3D+-ih++%5Cfrac+%7B%5Cdelta+%7D%7B%5Cdelta+q_+%7Br%7D%7D++%2C+++-W%3D-ih++%5Cfrac+%7B%5Cdelta+%7D%7B%5Cdelta+t%7D++.
https://artofproblemsolving.com/wiki/index.php/LaTeX:Commands
And it depends how you ask question of assistants such as Math GPT which infallibly! remembers where I was yesterday! Worrying or not ? but has a community. You could try asking own questions using right click save my Black orange white thresholder image from above.
https://math-gpt.org/
https://discord.com/invite/mrkWxFn2t3
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$\begingroup$ You mean, there are services that can read equations from papers for LaTeX? If so, are they all paid services? Also, I'm not very skilled at using these types of apps. $\endgroup$ Commented Sep 17 at 6:39
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$\begingroup$ added a few resources at the end but you can google for different aspects as encountered. $\endgroup$– K JCommented Sep 17 at 12:31
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$\begingroup$ From that scan of handwriting, Mathpix produced: $$ \begin{aligned} & t \mu+x \sqrt{k^2+\mu^2}= \pm \sqrt{z^2-\gamma^2} \quad(t|>| x \mid \\ & \left(t^2-x^2\right) \mu= \pm t \sqrt{2^2-\gamma^2}-x z \quad\left(t^2-x^2\right) \sqrt{k^2+\mu^2}=t_2-x \sqrt{2^2-\gamma^2} \\ & \frac{\gamma^2}{k^2} d \mu=\left(\frac{z}{ \pm \sqrt{2^2-\gamma^2}}-x\right) d z=\frac{d z}{ \pm \sqrt{2^2-\gamma^2}}\left(t_2-\sqrt{2} \sqrt{2^2-\gamma^2}\right) \\ $$ (I cut a few lines to fit it into a comment) $\endgroup$ Commented Sep 18 at 12:45
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$\begingroup$ @NormanGray I dont disagree Mathpix is probably the best this side of the Moon, but that's why it is increasingly a paid for service (WAS totally free when I used it long ago) and many competitive related sites were absorbed or disappeared. Same way that most PDF editors are now disappearing into Apryse's commercial re-badging. If you dont utilise independents then there will not be any for the next job. $\endgroup$– K JCommented Sep 18 at 13:34
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1$\begingroup$ I don't know if they're owned by some larger combine, but as far as I can see Mathpix are an independent (at least currently). They're certainly commercial, but... that seems fair enough, here. $\endgroup$ Commented Sep 18 at 15:27
Answer: use Mathpix.
It's almost that simple: the service is scarily good at turning scanned or written maths into a format which can be exported as LaTeX or a couple of other formats.
It's a freemium service, so you might be able to make some headway with the free tier. I was able to convert the Dirac paper from the PDF to apparently-accurate LaTeX very easily, with no skill involved on my part (I'm fortunate enough to have access to a paid licence, but the free tier is fairly generous, as I recall).
(If the OP wants to contact me out-of-band, I might be able to help further)
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$\begingroup$ Try it on the OP first offered link (it is the pure focus of this question) Both as the extracted pure scanned images (not "with" OCR) and also same page "With the OCR" for a truer comparison. I do expect the two to be different but dont have a MathPix account to determine how different. Note my comment about the one you tried is based on the unseen remainder of such pages where the formula are choppy and disjointed as was Dirac's brain. Brilliant inside but inscrutable to others from the outside. $\endgroup$– K JCommented Sep 18 at 15:05
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$\begingroup$ Do you mean the royalsocietypublishing.org/doi/pdf/10.1098/rspa.1926.0133 link? The PDF from there is the one I converted – I'm not seeing a 'with OCR' version. I just dumped that into Mathpix and got out a LaTeX version of the whole paper, maths and text, which I can latex into a PDF which seems accurate. I'm not sure which 'unseen remainder' you're referring to; we may be talking at cross-purposes. $\endgroup$ Commented Sep 18 at 15:21
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$\begingroup$ Yes I did mean that 1970's one which in my browser is blank pages with watermark !! Only see the images when downloaded ! But was also refering to its predecessor from 1926 which I doubt MathPix could unravel a few pages without heavy handed guidance. the OCR in the OP supplied link is key to a good recognition but did it correct that error on page 2 where I said the
rin the text should be lowered as per the imagery.? It would clearly help if we all were on the same page :-) $\endgroup$– K JCommented Sep 18 at 15:27 -
$\begingroup$ The link that I see in the original question is to royalsocietypublishing.org, which is a link to a scan of the 1926 original; I don't see a 1970s link anywhere. For Eq.2 in that paper, Mathpix produces
p_{r}=-i h \frac{\partial}{\partial q_{r}}...-- is that the subscript ‘r’ the one you're looking for? $\endgroup$ Commented Sep 18 at 15:55 -
$\begingroup$ Ah yes I was looking at other related sources. Here are the supposedly 600dpi cleaner scanned images as PNG The source would have been TIFF but not so easy for me to extract at present So see how those could be done ? filetransfer.io/data-package/gwJIpF5V#link the r is in the incorrect body text not the equation but UNDER it $\endgroup$– K JCommented Sep 18 at 16:49