Patent Law Mathematicians:
What assumptions would you need to make in order to be able to describe a mathematical limit of the number of embodiments encompassed by the following claim:
A device comprising: Element "A" coupled to Element "B". pic.twitter.com/wBUoxIK8Ue
— Dennis Crouch (@patentlyo) March 15, 2021
Assumptions:
1. Devices are composed of physical entities, in the limit of infinitesimal function to count as a device, at least two fundamental particles, one read on by “element A” and the other read on by “element B”, are related in physical space-time such that there is an interaction/causation, constituting said “coupling”. Element A and element B may each have any number of additional fundamental particles which may also be coupled. A great many embodiments may be discounted as devices, however, an upper limit requires only causative coupling of two elements.
2. In the next 20 years or so, devices will be composed of matter gathered almost exclusively from the planet Earth, i.e. everything in, on , or in the atmosphere.
3. There are a finite number of fundamental particles, of a finite number of types, which comprise the Earth. Equivalently, there is a finite amount of mass, particle number (lepton number etc.) and other quantities which are conserved even in processes which convert energy into particles and vice versa.
4. There are generally a finite number of ways in which the fundamental particles may be configured to compose particular sub-groups: atoms and molecules, crystals, states of matter etc. which are capable of comprising a device.
5. Taking into account fundamental particles are identical, and embodiments merely translated in space or over time are identical, and many physical systems are functionally equivalent (one random distribution in space-time of gas molecules as a group behave the same as another random distribution in space-time of the same gas molecules – PV = nRT) a great many cases which otherwise would count separately to the total upper limit, may be eliminated as structurally or functionally redundant or degenerate. One cube of amorphous glass although not identical to another cube of amorphous glass it is equivalent. However, to avoid the complexity in the calculation of redundant or degenerate cases, the upper limit may be assumed without counting any cases as redundant or degenerate.
6. IF space-time (or the space-time relationships between groups of particles) is discretized, there are only a finite number of ways to assemble the finite number of possible sub-groups of fundamental particles into devices composed thereof in space time.
IF space time is continuous, there would be technically be an infinite number of ways to assemble the finite number of possible sub-groups of fundamental particles into devices composed thereof in space time, however, as noted above redundancy and degeneracy abound for many physical systems – and hence categories of seeming infinities collapse into single embodiments. The infinite false upper limit can be reigned in by considering that the identity of a device does not, for example, depend upon the particular inconsequential changes (e.g. motions and positions) of its atoms or electrons which might be constantly changing. That said, such collapsing of infinities into categories of equivalents is complex and very possibly untenable, although statistical mechanics, QM, and thermodynamics might provide clues to general approaches.
Conculsion
In a situation where space time is effectively discretized pegging a real corporeal device with a particular configuration of fundamental particles, one could set an upper limit on the kinds and number thereof based on the total mass energy of the Earth, and a lower limit on the possible spacing therebetween (a sort of discretization of space for a corporeal embodiment), and count the finite number of possible ways all the possible sub-portions of all matter of the Earth (in, on, or above) could be arranged into all possible configurations for all devices composed thereof.
In a situation where space-time is not discretized pegging an upper limit requires a consistent and coherent approach to dealing with infinities of physically equivalent devices, and although in theory such might collapse those infinites into a countable set of categories, it is quite possibly unfathomably complex and/or untenable to do so.
As a rough estimate, one could just count all the particles composing the Earth, regardless of type. In other words assume they are all unique – this artificially increases the upper limit but it is still an upper limit. Assume there are no constraints on how they can be configured in a discretized space-time – this also increases the upper limit, calculate all the possible combinations in space-time of all the subsets of all the particles.
A lot of work that simply misses in one important aspect:
The comprising language is open-ended and the point at hand is NOT if there is a physical limit, but whether there is a legal limit.
And if you want to get “physical,” I can counter with the meta-physical and simply invoke the infinite universes of the Multiverse.
(I have the better cardinality cards) 🙂
Well, I did a slight pivot from mathematical limit to physical limit, and sometimes I need a break…
You say “the point at hand” (such as it is or could be) is whether there is some “legal limit” on the quoted claim.
What could possibly define consistent and coherent “legal limits” in the context of that overtly broad claim (without brazenly reading into the claim myriad unstated limitations)? The claim is clearly invalid as for all practical purposes it simply claims “A device” and reads on all possible devices as such (no useful working device is absent two discernible elements which are causally coupled), including all those known and all that would qualify as obvious. Furthermore, “number” of embodiments is not any kind of legal concept I am aware of.
So, I do not see how there is any legal point here, specifically with regard to the claim at hand. I submit the only point which could be made is mathematical and/or physical.
As for the Multiverse, I think you may have some jurisdictional issues there.
🙂
BTW: I am interpreting the question as implying a claim which would literally read:
“A device comprising a first element coupled to a second element.”
Rather than a claim which literally replaces “Element A” and “Element B” with specific limitations specifying what Element A and Element B are with any particularity.
Thanks Anon2,
I will note that your interpretation is off.
This is not about merely replacing Element A or Element B.
The open-endedness (and the subsequent tie to other concerns) has to do with SCOPE of the claim – as including or not including those items in addition to ANY literal notion of “A” or “B.”
That’s why the notion of the phrase ‘comprising’ is even in play.
Anon,
You misunderstand my comment. I understand what “comprises” means and what the scope of a claim is.
The point of my previous post is that the hypothetical is posed in a way which leaves the level of specificity of the actual claim to be analyzed ambiguous, such that what kind of claim we are dealing with is not clear.
I could ask you to analyze a claim which reads:
“A device comprising a first element coupled to a second element”
or ask you to analyze a claim which reads:
“A device comprising a harness coupled to a buckle.” or something similar where “harness” or “buckle” is replaced with something just as specific.
In the second example the terms specifying the elements are limiting. In the former case the use of the term “element” itself, is so broad as to include practically anything of which a device may be comprised.
When asking mathematicians or anyone else to determine an upper limit of the number of embodiments a claim covers, the specificity of the language of the claim to be analyzed matters in that determination.
As I stated above my interpretation is that the hypothetical implies the former, i.e. a claim for all intents and purposes to any device.
Ah, I see that you were “having fun” with a different angle — I think I understand now. Thanks.
I wish this blog would post about the continuing weakening of the patent system.
We are now a backwater to China and the EPO. We are reaching a tipping point where there will be a dramatic reduction in patent filings. My guess is that the tipping point will be the new Trade Secret bill that SV is having their minions push to the hollow shell man Biden.
I’d have a clear answer now if math was patentable.
How about if applied math (i.e. engineered items) were patentable?
Do people not know what the scope of enablement means? What is happening is that the CAFC has continued to try and remove the person of ordinary skill from all the analysis. What is enabled to a person of ordinary skill in view of the specification.
All you need is scope of enablement and the reverse doctrine of equivalents to police claim scope. All this stuff from the CAFC is just more judicial activism to try and weaken patents.
The question this post asks about what assumptions one would have to make to count the number of embodiments is not directly answerable.
One would have to make assumptions about how many possible embodiments of element A, element B, and the couplings are possible.
This is pretty much the way of the world. I think more would have to be put in the question for the question to be interesting.
I think that the driver is not merely “A,” “B,” and couplings thereof, as it is the fact that the claim uses an open-ended term of “comprising.”
You might recall my pushing Malcolm (when he attempted his rhetoric of requiring an exacting physical structure as a necessary result of a proper claim). How — exactly — can any structure BE ‘exacting,’ when the claim includes an open-ended parameter?
He never did answer me.
There is no mathematical limit — the number is effectively infinite.
A device comprising: Element “A” coupled to Element “B”
For the vast majority of potential elements, there are an innumerable number of variations of Element A as well as Element B. There are also a vast number of ways certain elements can be “coupled.” The set of those possible combinations is effectively too large to worry about.
although it does suggest that other doctrines (such as full-scope enablement) have some foundational problems
The “full-scope enablement” is a mythical beast — somewhat analogous to one of ordinary skill in the art with the full set of possible prior art spread out before him/her. As long as someone really understands the technology fairly well, applying a decision such as Auto. Techs. Int’l v. BMW to invalidate a claim for failing to enable the full scope of the claimed invention is trivial.
Let’s just contemplate the simple limitation of: “storing a data structure into a data storage device.”
The number of ways a data structure can be formatted is a great many. The number of different types of data storage devices are a great many. There are great many ways as to how data is actually stored in a data storage device. What happens if your specification doesn’t list hard drives, flash drives, and all the different flavors of internal memory available (among a great many other options)? Have you not fully enabled the full scope of the invention?
It seems to me that the doctrine of equivalents and the “full scope” enablement requirement of Auto Tech are somewhat in tension with one another. One says that you can infringe despite not falling within the literal scope of the invention, and the says that the patent is invalid if it doesn’t enable the full scope of the claim. Should the specification enable the full scope of the claim PLUS the equivalents? How is that possible?
I wrote a week or two ago about the traps that the Federal Circuit has been laying — in that instance with regard to how they are treating 112, 6th. This “full scope” enablement requirement is just a different trap — perhaps a more insidious trap. One can actively avoid invoking 112, 6th (although the Federal Circuit is even making that harder), but how does one actively avoid the “full scope” enablement problem without making specifications the size of a phone book (from the 1980s)? Even then, outside of a handful of rare technologies, there is always going to be some enablement that wasn’t fully enabled.
What happens when somebody improves upon a previously-patented device and obtains a patent therefor? Surely, the specification of the original patent didn’t contemplate the improvement but that improvement (as long as the improvement is additive rather than replacing one element with another different element) is encompassed by the scope of the claims of the original patent. Are we going to say that the improvement patent should prima facie invalidate the original patent for failure to meet some “full scope” enablement requirement?
As I also wrote, at its beginning, the Federal Circuit case law evidenced an approach in which the patent laws were construed so as to not excessively burden patent applicants. There was a reasonableness applied to the requirements so as to avoid trapping the unwary — thereby making patent protection more accessible to the unsophisticated. However, the Federal Circuit’s approach has changed over the past decades so as to throw up obstacle after obstacle such that patent law protection is more and more becoming the sport of kings — in which only the most sophisticated and well-heeled can afford to (effectively) dabble in.
It is a sad state of affairs, but that is today’s reality. We rarely see Federal Circuit decisions on damages anymore because so very few trials ever get that far. The Federal Circuit is far more likely to consider decisions in which the judge disposed of the case on 12b6 motions or on motions for summary judgement.
Moreover, when was the last time anybody can remember that a small, unsophisticated party got a substantially large judgment from one of the larger players? What … large companies don’t infringe anymore?
If there are no valid patents, then there can be no infringement
“What happens when somebody improves upon a previously-patented device and obtains a patent therefor? Surely, the specification of the original patent didn’t contemplate the improvement but that improvement (as long as the improvement is additive rather than replacing one element with another different element) is encompassed by the scope of the claims of the original patent. Are we going to say that the improvement patent should prima facie invalidate the original patent for failure to meet some “full scope” enablement requirement?”
Speaking perscriptively, I’m not certain this would be a bad thing. I think it’s a better world where applicants have interests in both the 103 bar being lower and the 103 bar being higher. It seems like that would lead to a better equilibrium for 103.
Ben–the paid blogger–hits at it again.
Improvement patents already are perhaps the best motivation for innovation as when you put a product out then you have to scramble so that someone doesn’t get an improvement that you need to keep your market.
Ben is just constantly just typing from an anti-patent script he got from a non-profit whose focus is to weaken patents.
Right Ben?
No. I am not compensated by any non-profit (or for-profit) organization for my comments.
Frankly, I suspect that your need to believe in paid commentors is derived from a deficiency in perceived self-worth. If some antagonist is being paid for their comments, surely your comments matter and have value as well! This is simply not reality; the comments we share here carry no value to the any patent organization.
That said, it seems like you should have plenty to find self-worth in. You appear to be at the end of a long and reasonably successful career, and you’ve repeatedly claimed to have gone to top schools. You have value as a person, even if your comments here are insignificant and of no renumerative value.
The next time you’re feeling drown, try repeating this mantra in a mirror: “I’m good enough, I’m smart enough, and doggone it, people outside of Patently-o like me.”
Ben, that is pretty funny. Made me laugh.
But, I suspect you are a paid blogger because your comments consistently mirror the positions of the anti-patent judicial activists.
And, as for my “belief” in paid bloggers, well, I have linked to job posting for managing teams of paid bloggers to post anti-patent posts on blogs. I also worked for a law firm a couple of blocks from K Street where we were paid by SV to advocate anti-patent positions for the AIA.
“I’m good enough, I’m smart enough, and doggone it, people outside of Patently-o like me.”
“I have linked to job posting for managing teams of paid bloggers to post anti-patent posts on blogs.”
I would be very obliged if you could repost that link. I don’t think I saw it the first time you posted it.
Even if you can’t, I’d note there is a vast difference between paid bloggers and paid commentors. If you told me that some of the guest bloggers here were being paid, I would not find it to be a ridiculous preposition. There is a vast difference between the impact of words that show up on the front page and the impact of words words that show up under the “show comments” button.
Ben, controlling the narrative on blogs is now part of every PR job.
It is interesting too that the script to try and deflect when people suspect you are a paid blogger is to attack them personally and minimize the effect of paid bloggers.
Ben did both.
Sure – but those tactics are also employed by those simply not wanting to address a point provided (they need not BE paid).
Speaking perscriptively, I’m not certain this would be a bad thing.
Someone comes up with some minor improvement and then the original patent is invalidated — you don’t see anything bad with that?
On the upside, there will certainly be an incentive for copyists to quickly generate improvements. However, how are the original inventors incentivized to continue to innovate and disclose those innovations?
You’ve just spent millions of dollars bring a new technology to market and someone comes along with a trivial improvement (that you didn’t think of and didn’t enable) and now your patent is invalidated. What is the likelihood you’ll spend a comparable amount on your next innovative endeavor?
Personally, I believe the patent system should, by default, favor innovators over copyists. To the extent that a copyist is also an innovator, then they can rights to the follow-on innovation — however, that shouldn’t take away from the rights of the original innovator.
I think it’s a better world where applicants have interests in both the 103 bar being lower and the 103 bar being higher. It seems like that would lead to a better equilibrium for 103.
I think this comment is in need of elaboration. I’m not sure if the full scope of the point you are trying to make is enabled.
“Someone comes up with some minor improvement and then the original patent is invalidated — you don’t see anything bad with that?”
No, I don’t think that’s desirable at all. But if we had a system that didn’t give out patents for “trivial” improvements, it wouldn’t be a problem. A system where patentees could lose their patent due to a follow-on patent is a system which is more likely to have a robust bar for 103.
That’s not to say I don’t recognize any potential cost to such a system. It seems very plausible to me that a superior system could be achieved by reducing the terms of patents with follow-on patents. That way there’d be applicant oriented incentives for a high 103 bar while keeping some degree of reward for every patentee.
But if we had a system that didn’t give out patents for “trivial” improvements, it wouldn’t be a problem.
That raises the interesting question as to what constitutes a “trivial” improvement and what doesn’t? If an improvement is truly “trivial,” wouldn’t it be easy enough to design around or simply just not employ?
Also, what may seem trivially today may not seem trivial 5 or 10 years from today when the industry determines that the so-called trivial improvement unlocked great potential. What may start out as important might turn trivial after time — and vice versa. I think an accurate determination of what is “trivial” can only be done in hindsight with a long period of reflection. With that in mind, how do we filter out trivial improvements? There is no non-trivial requirement in the USC. One may think that resides in 103, but 103 talks about obviousness — not triviality. What might be obvious might turn out to be exceedingly important, and what might be nonobvious might turn out to be unimportant. When you think of it, there is likely more motivation to identify important modifications than there is motivation to identify trivial modifications. As such, 103 as it currently is applied appears to be filtering out more important improvements than it is filtering out trivial improvements.
It seems very plausible to me that a superior system could be achieved by reducing the terms of patents with follow-on patents. That way there’d be applicant oriented incentives for a high 103 bar while keeping some degree of reward for every patentee.
Again — what incentive does one have to innovate when what was originally bargained for (i.e., a period of exclusive rights) gets reduced for reasons out of the inventor’s hands?
This would also mean a greater patent term for patents that many people aren’t interested in (and therefore aren’t attempting to improve) over patents for which there is great interest? Giving more exclusivity to less important patents doesn’t seem like a wise policy choice. Here, you are penalizing inventors for having great ideas.
This is the type of approach that people should employ before advocating for certain changes in the US patent system. They should ask how will these changes impact the incentives the US patent system provide to inventors. I know there is a desire to protect the public from US patent system being abused. However, the Founding Fathers thought it important enough to carve out, in the US Constitution, a specific set of rights for inventors. They viewed that incentivizing innovation would be an important driver for the US economic system — and I think they were correct in those views. With that in mind, I think the courts should be very mindful about construing statutes (and/or creating law) in a manner that provides inventors with less incentives.
Personally, I think that the US Patent System is all but dead for individual inventors and small companies. Congress but mostly the Courts have made enforcing patents by these types of entities all but impossible. Big corporations infringe with impunity these days and the Courts bend over backwards to shield them from responsibility.
That.
I didnt realize we were supposed to be mindlessly repeating talking points. I left my script at home, so I will bow out now.
“Personally, I think that the US Patent System is all but dead for individual inventors and small companies. Congress but mostly the Courts have made enforcing patents by these types of entities all but impossible. Big corporations infringe with impunity these days and the Courts bend over backwards to shield them from responsibility.”
Bingo.
Appreciate your thoughts Wandering.
It is a good post. There is no meaning to “enabling the full scope of a claim.”
Enablement should be thought of in terms of a person of ordinary skill and how they would view the claims and then the scope of the claims is easy to understand. It is the scope of enablement for a person of ordinary skill plus the specification.
This is trivial to understand. The CAFC is indeed doing exactly what you say in putting up traps for the unwary, but also what they are doing is creating nebulous cases so that they can on a whim invalidate any claim not just with Alice but with Williamson or Auto. Techs. Int’l.
The judges of the CAFC are not trying to create a workable jurisprudence but finding ways to invalidate any claim they don’t like. I think the only way this is going to change is with the ending of the CAFC. I heard rumors that it might be possible with Trump. Maybe another R will see the CAFC for what it is and abolish the court. I am pretty sure that it is possible to abolish the court and all its precedent. That is the only possible way to get relief.
And again Auto. Techs Int’l makes absolutely no sense—none–when viewed by a person of ordinary skill in the art.
The only meaning is what the POSITA gives it.
Read LizardTech for later arising technologies and reverse doctrine of equivalents.
I’ve posted on here references to engineering books used at MIT that expressly say how functional language should be interpreted. Claims are no different.
Claim scope should be scope of enablement.
All of this is trivial to understand when you take the perspective of the inventors.
It seems like you’d need to assume a new meaning for the word “comprising.”
Perhaps a related interesting question is, what is the cardinality of the set of embodiments encompassed by “A device comprising: Element “A” coupled to Element “B”?
Yes. I agree that this is really a discrete math problem.
It is only “discrete” as pertains to a first (single) level of infinities.
There are mathematical situations that distinguish on such levels.
I don’t know what you are saying here.
I won’t bother guessing what anon was trying to get at, but I was trying to reference the cardinality of infinite sets.
Infinite sets (such as the set of embodiments within the scope of the claim) can be characterized as having different degrees of something like ‘size’.
I am not clever enough to propose a ‘size’ of the relevant infinite set, but I suspect it is not the smallest size of infinite sets.
Thanks Ben – So, maybe there is no “limit” but this particular infinite set might be smaller than other infinite sets.
Here, for instance, there would seemingly be a larger set of embodiments if the patent only required one of the two express elements.
“there would seemingly be a larger set of embodiments if the patent only required one of the two express elements.”
Except, from what little I understand, infinite set size addition may not work that way. It seems like infinite_size_1+infinite_size_1 = infinite_size_1, but infinite_size_1*infinite_size_1 = infinite_size_2. So perhaps the set of element A + element B is the same size as the set of Element A + Element B + Element C, but the set of Element A modified by adjustment D is bigger.
I am hopelessly out of my depth here, but it seems plausible that it’s something that could be meaningfully analyzed through such techniques.
If you’re looking for keywords to search, I’d start at:
link to en.m.wikipedia.org
Thanks!
See Georg Cantor.
Not all infinite sets have the same cardinality.
Meh. Cardinals get more respect than they deserve.
Both kinds. 🙂
Both kinds?
Baseball and football?
You have to assume (first) that there IS a limit.
Since “comprising” is used, what would be the basis FOR presuming there to be a limit?
Then, I would have to wonder why one is even pursuing the question of having a limit.
This smacks here of an unstated value presumption much like a nose of a camel, should not be allowed to be under the tent so readily.
Thanks Anon., You are right that the “comprising” language of the patent claim suggests that the number of potential embodiments is unlimited. And, I’m not saying that is good or bad, although it does suggest that other doctrines (such as full-scope enablement) have some foundational problems.
I have previously assumed that the number of embodiments is unlimited when someone uses “comprising.” My question here is puzzling into that assumption — is it correct in all situations?
DC
Perhaps it is less that those other doctrines have problems and more as to how certain people attempt to use those doctrines…
As I have pointed out, Random’s “views” necessarily result in such problems.
This is not an indication of a problem with the doctrine as much as it is a problem with the person’s attempted use of the doctrines.
Which is exactly why my post was presented with two prongs.
I have always been troubled by the tension between full scope enablement and the concept that later-developed technology can be covered under the doctrine of equivalents, particularly as it is applied to means-plus-function limitations.
Not sure how one is to provide an enabling disclosure of technology that has not been developed yet.
Perhaps full scope enablement refers only to full *literal* scope.
The normal doctrine of equivalents does not apply to means-plus-function claim limitations, only the more limited version of 112(f).
It is completely (and rightfully) taken for granted that, say, a claim from 2005 that recites: “a processor; and computer readable memory containing instructions that, when executed by the process…” covers a quadcore processor and a 500GB flash drive, even though nobody in 2005 was enabled to make a quadcore processor and a 500GB flash drive.
Could someone please explain why “comprising” must necessarily change the embodiment number “math” question here. If the asserted invention requires also adding C to actually work, what other 112 issues might be raised?
There are other issues as to the number of needed embodiments which seem to me to defy mathematics. Will not the number of embodiments needed in the specification be affected by how many different As and Bs there are, how many such combinations are inoperative for any expressed utility, and how unpredictable are the results of A+B combinations to a POSITA?
“If the asserted invention requires also adding C to actually work”
Careful there Paul — you have (inadvertently?) moved the goal post and added a “required” that is not present in either the “comprising” language or math of number of embodiments language.
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