Again about limted stacks (and other limitations)


Hi all, hi Walter and a great new year for all!

Walter, excuse please the late reply. I was away for a couple of days, but your message was indeed very interesting. So I feel that some additional thoughts on the subject might be of some value for a better clarification - or even confusion! ;-) Long message follows..

Nevertheless, one comment: Looking to the market of "scientific" calcs, it seems the big share is not taken by "some device of supreme *mathematical* power" but by a lot of bread and butter calcs, just featuring a more or less complete set of "scientific" operations on top of SQRT. So for most tasks in the real world, "some device of supreme *mathematical* power" seems to be overkill.

Undoubtfully I would also say that still in our days most of the time a scientific calculator is used for just performing quick operations with numbers (other than 0 and 1 ;-)). This number-crunching has been also considered as supreme mathematical power that *had* to be done by mind in times priorly to the dawn of such instruments. Let's keep that in mind for later on.

But on your paragraph above I have to also mention that the idea of the calculator itself as a portable machine that crunches only numbers is outdated. There is no reason to limit the design of such machines to number-crunching; quite the contrary, and even if we consider market shares and the like! There is also a big number of mathematicians or physicists or astronomers out there who would be definitely very glad to be able to solve some partial differential equation and get a result that is not simply 3.7656789 but some formula with all its variables and parameters, or say, to use a small portable machine for doing theoretical research upon the question about some properties of a ring. Why not? The technology is already there and the theoretical fundaments too.

So perhaps the question boils down to asking if it would be possible to attract a reasonable number of the more "theoretical" professionals around for whom the "result" is not 3.7656789 but, say, some formula? I think that this can be achieved. And I think that this is the only consequent continuation of the steps that HP did in the 70s when the company *did* change the way that calculations with numbers were carried out up to that time. (But I also have to admit that it could be only my own steady denial to accept that the visionary times are over - grandpappy you see ;-))

AFAIK the other grandpappies, we simply wish to show up in the real world with a small and decent (understatement!) updated 42S instead of a big fancy student calc loaded with bells and whistles we'll never blow (again ;-))

Well, Walter, it might be true. I notice the same tendencies on myself too. But then... some questions come up!

1) Do we really think that what *we* wish is so important?

2) Do we really think that our (slowly dying out :-D ) generation will return perhaps in some kind of a zombie state and build up the customer group of tomorrow? (It's hard, I know, and I can't get comfortable with the answer to this question too ;-))

3) It could be said that the same wish for "understatement" existed also in the past, when the grand-grandpappies still wanted their slide rules - couldn't it? So, if things *were* changed at those times, and if *we* were the enthousiasts, the very supporters of those changes, what makes us think that the same changes won't happen again? You know, induction is very fundamental! ;-)

IMHO if the 42S would be reissued with an LCD of nowadays resolution, allowing to show some more lines, and supporting some I/O, this will catch 80% of our wishes. Add beveled keys, a (settable) larger stack size, and an extended allowance for CUSTOM or USER functions, and you'll see the forum dance. Hoping to experience this once before I die,

Your words to HP's ears, and I would be only glad to be able to touch such a reissued 42S even just for minutes before I have to face the supreme faschist, as Paul Erdös used to say ;-) In addition I would be even happier to type in, say, some set theory conjecture and follow its logical consequences up to the proof of truth of falsehood, or even of the impossibility of the proof itself! It would be only then that I would say: Burry this machine along with me! ;-)

Addendum: Shouldn't we rather strive for "supreme *mathematical* power" in our brains than in a tool?

This is a very very... dense question, Walter, as it seems to me that the set of answers can only be non-discrete. (You must already have noticed my "basic instincts" ;-)) I think that mathematical power cannot be just the ability to draw roots out of a given number in mind. I also think that the same power cannot be even the ability to solve some given non-linear system of equations in mind. I think that the particular *case* of some given problem must be embedded into the most general possibility of some solution, and then the question arises: What is the main essence of "supreme methematical power"?

Let's remember again that simple number-crunching has also been considered as some kind of skill of even "gift". But is it really a gift of mathematical power? This is where my comment from above comes to play. For me "supreme mathematical power" of mind is the ability to draw the most consequences out of the least premises in their mist general form. It is being able to handle symbols and their logical interdependencies. And that's all! So, it is not as important to find out, say, the solutions of some certain problem by hand, but rather to know/understand what the mathematical logic states about the involved steps. Take for example some formally ill-defined set and all its consequences as being brought into existence by some "insane" assumptions. Well, is it then so important to be able to carry out all logical steps by hand/mind error-free? I think not. I think that the perception of the very fundamental concepts is *the* important thing, and also that the handling of the too many "parameters" of the particular problem should be left to the machine - iff it has the power..

As an example, I was just thinking about the principal possibility of a wave function of the general form EXP(-a*r)*SIN(b*r), where a,b are just parameters and r is the distance from the origin. What general kinds of potentials would give rise to that? My HP49G+ was able to help a lot - even with all its design flaws ;-) The underlying potential - so it said - must be something of the form -1/TAN(X) which is a very mind crushing result considering that the wave function does extend to infinity, and that at the same time the potential goes to infinity at x=pi . The HP49G+ *was* indeed able to generate that kind of irresistible wish to know more... Isn't that great?

And still further on! The very flaws of design of the CAS of that small thingie are a blessing in disguise! Being equiped with ->ALG and similar commands, one can (mis)use the existing "flaws" as the very definitions, for example, for investigating sets themselves! And much more! One can also (mis)use the existing behavior of the CAS in order to examine the CAS (in its very essence) itself. Now, knowing that any CAS can only be intriguingly connected to the universal findings of people like for example Turing or even Cantor, how could we say that dealing *with* and *about* the CAS is not dealing with mathematics itself? This is my question and this is also my hope for that hypothetical portable device of "supreme mathematical power", which I still am sure that I will be able to touch before I face the supreme fasHewchist - you know, the guy that keeps the book of theorems as a secret! ;-)

I know that I often tend to be too... theoretical, too progressive, or perhaps even an ignorant of real existing market needs. I can only repeat that Bill Hewlett thought differently when it came to the decision about the HP35 that started it all, or am I just too mistaken?

If we take into consideration all the above, can any stack or similar limitation be reasonable for what is (hopefully) to come yet? I wish not.

Cheers to all, thanks for all the inspiring thoughts and messages, and have yet another great year - even as a grandpappy! ;-)


Edited: 5 Jan 2008, 5:34 a.m. after one or more responses were posted


3) It could be said that the same wish for "understatement" existed also in the past, when the grand-grandpappies still wanted their slide rules - couldn't it?
There's a difference: The electronic calculator made the slide rule obsolete. An advanced graphing calc won't replace e.g. the TI-30 any time soon for good reasons. Fewer (but sufficiently many) functions mean also better ergonomics if designed carefully. I was quite puzzled about even the simplest operations when getting my 48G.

It seems any improvement results in more copious usage. You even see this when comparing 32S(II) and 35s. For me, the 32SII ist the most useful calculator for this reason. Others have other requirements and therefor make a different choice.

What is the advantage of a slide rule over a modest scientific calc?


Thomas, for a limited time perspective the devices already existing now are not likely to be replaced by some hypothetical super-machine. But limited time perspective is... of course limited. If it's not going to be in 5 years, then it will be in 10, 15, or even 20.

The difference that you refer to, namely replacement of the slide rules by making them obsolete can exactly as well be carried out to the next step: Make calcs, as they are now, also obsolete by providing the means to do mathematics as a superset of just number-crunching. I don't see any difference in the essence of both replacements.

The more "traditional" calculators may be easy in usage - but that word "easy" is not to be taken absolutely. It depends on what the machine is used for. I would be very unhappy having to press 10 keys for just taking a square root, but the same amount of key presses for determining some symmetry group, or for getting the generating function of a sequence would make me more than happy.

As about ergonomy, I don't think that something as complex and with as many interdependend sub-parts like mathematics can ever be absolutely ergonomic in usage and with just some few keys. And this goes much further than personal gusto. Ergonomics is a good consideration for relatively simple systems. But mapping the whole power of such a tight and huge system of meanings (like mathematics) upon human-readable "words", starting with +, -, up to things like "intersection" or "cyclic-decomposition", or whatever you like - and re-mapping that set of words again on a small set of keys... what chanches are for such a thing to be "ergonomic"? And what is ergonomic at all? Is mathematica ergonomic? Or perhaps unix? (Exactly the same problem there.)

I'd find such a system ergonomic enough if it is able to carry out the wished operations, *and* if I am able to code my wishes about such orepations in a language that the system understands. If the language is unambiguous/systematic then I can learn it and live with it, no matter if some key for the SQRT-function is top right or bottom left, or anything else. But I also know that I could sound like a power-lunatic now.. ;-)

Cheers and have a great new year.


P.S.: What is the advantage of some HP41CX over an HP50? ;-)


P.S.: What is the advantage of some HP41CX over an HP50? ;-)

It is smaller! ;)

I think a CAS device should have something like pen input for math symbols. Sketching an integral is way easier than entering a formula with parantheses or using a wysiwyg editor.


He he, yes Marcus! So we wait until skirts with huge pockets come to fashion again? ;-) And in the meantime we can use those trousers with the many extra big pockets that look like going for an expedition. ;-)

But seriously, I can't really think of carrying my calc in my pocket as such a big advantage. I just take some kind of small bag, through it in there, and that's it. It is not something that I can't help, though of course I have to also accept that this is matter of personal gusto.

About CAS and pen for input... your words to HP's ears. Such an input possibility would be a blessing, provided OCR works well. I remember Newton now! ;-)




P.S.: What is the advantage of some HP41CX over an HP50? ;-)

Now you got me since I don't own either of these models nor have I had the opportunity to use them. But, to the best of my knowledge, there is a magnetic card reader available for the 41 while this is most likely not true for the 50G. Well, having a TI-59 with a working set of magnetic cards, one of them from '79 on one hand and a USB memory stick that I had to trash lately due to a defect, I'd say the 41 can't impossibly be obsolete ;-).


Hi Thomas and thanks for your reply!

Well, the HP50 has its memory card with only just a few megabytes more memory than the magnetic cards of the 41 plus the connection to a PC and thus (indirectly) some few terabytes more for storing, but for such little memory differences we can't say that there is any real advantage, can we? ;-)

But still I use that magnetic card reader along with the HP41 and I have a big fun when I have to tinker (again) because of dirt on the read/write heads or wheels that won't transport the medium correctly. So I guess that some kind of "fun factor" is available on the HP41 that the HP50 isn't able of: More tinkering around! ;-)

I mean, what the heck? I still use my cassette deck too and have much fun with band salads in all flavors of Fe/Cr/Me! ;-)

As a side note, and because you referred to your defect calculator, the devices nowadays have a shorter life, but this is something that must be considered separately. We can't say for example that some magnetic card reader of "the old good days" is in general a "better method". It is the fact that our world has perhaps accelerated everything too much, in the sense that life cycles have now a duration of some months - or is it already days? Under this premises *any* device will be of a short life but not because the technology is not better. It is the *usage* of technology that went worse, perhaps also because we trust too much that everything will work fine, and that already in the designing phase of some product. So, we have to compare the two things separately: Some given technology on the one side, and design when using that given technology. With "design" I don't mean only look but much more the whole process of thinking about the requierments, formulating specifications, and so on. No technology will work well if this process is shortened down to milliseconds for catching up with concurrence as soon as possible ;-)




Thomas, for a limited time perspective the devices already existing now are not likely to be replaced by some hypothetical super-machine. But limited time perspective is... of course limited. If it's not going to be in 5 years, then it will be in 10, 15, or even 20.

The difference that you refer to, namely replacement of the slide rules by making them obsolete can exactly as well be carried out to the next step: Make calcs, as they are now, also obsolete by providing the means to do mathematics as a superset of just number-crunching. I don't see any difference in the essence of both replacements.

Anyone who thinks the basic scientific or 4-banger calculator will not be around in 10, 20, 30, 50, or even 100 years is kidding themselves.

There will always be a HUGE market for the basic non-programmable scientific calculator.

There are fundamental reasons why Casio sold their 1 *billionth* calculator last year. Those fundamental reasons will ensure that they continue to sell in massive volumes until some shift in human evolution occurs and we can all suddenly add up better and quicker than a calculator.

The more "traditional" calculators may be easy in usage - but that word "easy" is not to be taken absolutely. It depends on what the machine is used for. I would be very unhappy having to press 10 keys for just taking a square root, but the same amount of key presses for determining some symmetry group, or for getting the generating function of a sequence would make me more than happy.

And that is precisely the reason why all manor of calculators are designed and sold in their hundreds of millions - 4-bangers for the common folk, financials for the money people, graphics for the students, fluoro orange ones for the teeny boppers, scientifics for basic engineering, programmables for the power user, and every manor of calculator for every niche market, like these:



I do think that the 4-banger and its closest number only crunching relatives are already completely outdated for many particular user groups, Dave! While there will (presumably) always be a need for just performing basic arithmetic, like for example in some shop, or anything similar, there *is* also the need of other groups to perform much more operations than basic arithmetic fast and correctly. The fact that the (potential) group of users that works in a more theoretical manner has not been addressed as closely in the past, does not mean that this group doesn't exist.

The whole purpose of the calculator, as the phenomenon (has been) started in the past, was focused around the idea that the number is the result. So for example, a civil engineer had to "put in the numbers" in the formula E=m*g*h and calculate the result, say 4.7602. But there is also another group, in which I belong too, and for which the result is not the number but rather the formula itself. When I "calculate", say the period or amplitude of some specific system underlying some given forces, my "result" is not a certain number but some formula that manifests the relation of the participating physical entities to each other. For me some kind of omega=2*pi*alpha/beta *is* the result! Or even finding out if the system behaves periodic at all! Let's keep in mind that the scope of research can cover a vast area of different duties.

Now, with the dawn of the very idea of a CAS on a portable device we (and so I too) have at last the possibility to do more "abstract" research while we sit in the train. Iff we take it as a fact, that there is also a good number of people that had to do that all using pencil and paper (and all the accompanied problems of making mistakes because that %&*$-alpha wasn't carried over ;-)) then I really see an additional *big* group of users that was kind of a bit left out, because... and here it comes! Because we got too tightly stuck to the idea that the calculator calculates numbers. The whole understanding of the meaning of the word "calculate" has been too limited because it *started* all with just numbers.

So, if the huge number of sold devices of some "basic scientific" calculators says something at all, then it says that the corresponding target group has been addressed, and that the market has been *created*. This is the meaning of it, or wasn't it Bill Hewlett himself that insisted on manufacturing the HP35 while all marketing studies clearly said that "there is no market for such a device"? We see something very clearly here: It is not only taking advantage of some already existing market. Much more than this it is *thinking* about markets that do *not* exist yet, and *creating* them.

Specifically for HP, if that company wants to be still top of the tops, it has to work at pioneering realms. It was pioneering realm to create the market for the number crunching device, but it only *was*. It isn't anymore. But this doesn't mean that all pioneer domains ceased to exist. The next step has to be carried out again *outside* the limits of "the generally accepted". The shift of paradigm has been made possible by the very implementation of the CAS on a small portable device - the question is only if some "Bill Hewlett the second" is going to recognize that, and generate the next market. Or else it is going to be somebody else. But it will come one way or another.




This Message was deleted. This empty message preserves the threading when a post with followup(s) is deleted. If all followups have been removed, the original poster may delete this post again to make this placeholder disappear.


Karl, you are not only "probably" but surely right! Me stupid person did use pre-formatting, as I mistakenly thought that it is needed for keeping the format intact. A theorist, you see :-D

OK, I go to that first message roght now, and see if I can remove the unneeded pre-tags that messed it up. Hoping that the next mess will be lower than the previous one! ;-)

Thank you very very much for the hint and for your time and efforts to make my mess more readable!



Hi Nick, welcome back! And a great year for you, too!

Thanks for your response and for your thoughts about a possible future math tool. You are responding to the last post (of Dec. 10th) in this thread.

I agree with you a "device of superior *mathematical* power" (DSMP) as you are defining it now may be a very useful tool for scientists in the areas you mentioned. Personally, I'd enjoy such a little solver, and I'd welcome it definitely if I were a physics student at an university again or a scientist in basic research. But, IIRC, there is an exponential law for applied math stating (in plain words):

For 1e9 people living, 1e8 must calculate, 1e7 go beyond the 4 basic arithmetic operations, 1e6 need also trigonometry, exponential functions and symbolic math (but tend to forget it very fast when out of school), 1e5 may continue to use (apply) this knowledge, 1e4 will continue to do some kind of mathematics in their further life, and maybe 1e3 will be interested in a DSMP as outlined by you.

I'm no marketeer, but it looks like the total market for "scientific" calcs is counted in millions, the total (!) market for serious (or "advanced") scientific calcs contains some e4 up to 1e5 units. Just guessing! But let's just look for the order of magnitude and set 2*pi=10, as my late professor in theoretical physics used to say. - A possible DSMP will have to compete with PC or PDA software, so there may be a request for some hundred DSMPs remaining. Other scientific precision instruments produced in such lots tend to cost some e3 to e4 $, and that's more than even calculator addicted grandpappies are willing (and allowed) to spend for a "single purpose tool" (compared to a PC offering far more applications also for the rest of the family).

Summing up, a DSMP may be a very worthwile challenge. Its users, however, will be counted far easier than even those of advanced scientific calculators as we know them. And I cannot imagine teenagers or housewives doing math with the same unlimited enthusiasm as they chat on the phone, so - sorry - I do not expect the market to explode like for mobile communication ;)

All this shall by no means obstruct you striving for a DSMP, but IMHO the people striving for a better scientific calculator will make a bit more. And for these, a limited stack will be sufficient.

Best regards,



Hi Walter,

and thanks a lot for the very interesting message again!

Let it be said again here, before I write anything else, that the marketing studies of those old times should also suggest Bill Hewlett to abandon his enthusiasm for the HP35. But he insisted, and the results are quite visible today, aren't they? Would we be such "happy grandpappies" today if he wouldn't had dismissed (more or less ;-)) all "No, don't do that" at those times? I can't imagine that.

Not to deny that the group of people that find even delight in working with some "twisted formula" will be very likely magnitudes of order smaller than the group that has to find out how much month is still remaining at the end of the money ;-) But still, if the size of this group is taken *absolutely* and with no relation to the other bigger target groups... couldn't that be big enough for itself? And saying "big" we have to consider, "big" for what?

1) For the immediately connected number of such hypothetical devices surely not as big. Still spectrometer companies sell much less than, say, car companies, and they seem to live quite well too. I can't imagine how Person Elmer could ever close.

2) For the necessary shift of paradigm, however, that generates new markets too, it is exactly that kind of dancing out of line that pushes the limits further, changes the shapes of things, and leads to new ways of working and even perhaps of perception of possibilities.

Especially for the second point, it might seem too "idealistic" at the start, if one always and primarily considers the possible immediate maximum profit for a company that facilitates only the "generally accepted" and just follows the main stream. But still: If we try to think away such general computational devices, like they exist now, we end up in a world of today where for example the mobile phone is not even a wild fantasy, and the associated huge market for it too. In other words, without those "strange guys" who try to somehow gain a general solution of that damned system of equations, we would still stick around with an abacus! ;-) So, it is not only "idealistic" but has also huge "practical" consequences, whatever the word "practical" might mean. It is only that the "practical" monetary exploitation follows in future. It always lags, and thus it needs much of that kind of "foreseeing" a possible future, in which a market that is generated today will be growing then.

A big fat hindrance for this is of course the fact that the world "future" has been crippled down to the next quarter report in companies. ;-) To this view of mine my own feeling of being perhaps somewhat "neglected" or "left out" (as a target group) does contribute very strongly, as I have to always wonder: Where is *my* device?

Yet I don't think that I overestimate the potential of such a hypothetical and "mighty" device that allows me to do even elementary research about some relationship of two algebraic structures. And if we consider the fact that technology advances so rapidly, we perhaps have for the first time the possibility of manufacturing such a device at reasonable costs, that can be used for any calculational purpose, covering all (or at least most) areas of real existing needs, starting at the 4-banger and ending up to who knows what. Here is, as you can see, again that kind of "insisting" when old Bill imore or less sent all marketing studies to Coventry. And he did very well so!

In times in which we do have the results of work of people like Avenard or Parisse, and we do have the chips, and we do have the means, I think that dropping the possibilities like this would be both a shortsighted and onesighted view.

I try to keep such thoughts as general as possible, while I know that my own CAS in mind cannot be anything else than limited! ;-)




Hi Nick,

thanks again for sharing your thoughts. I can follow and agree with most of your statements.

Just one more comment:

Good tools satisfy needs. There was a need for calculating power well before the HP35, and there were desktop instruments covering this. Bill Hewlett's vision was just to have this power in a handheld device, allowing the "computers" to use it wherever they want. Don't get me wrong, this was a great idea! But it was just to concentrate a 9100 to - let's say - 2% of its volume, with all the technological consequences of this, of course. Summing up, the need for calculators in general was well known at that time, Bill Hewlett believed in the need for a handheld calculator - and history gave him right. You have every right to believe in the need for a handheld DSMP.

My experience taught me, however, that well over 99% of people (in an industrial environment at least) have serious difficulties with calculations or abstract thoughts you would call trivial. On this experimental basis I simply cannot imagine a DSMP becoming a breakthrough like the HP35 was, unless mankind would change fundamentally (which happened quite seldom in the last 5000 years so far). But I'd be more than happy if proven wrong by reality.

Any new idea needed at least one person sufficiently convinced and determined (or stubborn) to make it becoming true. Feel free to go ahead. Good luck!


Edited: 5 Jan 2008, 4:41 p.m.


Thanks a lot again for your message, Walter!

Yes, I see too that the domains of usage of a calculator (or any portable thingie called some nice name) are at the moment mainly in fields where the more abstract concepts are really not the important things to do. I just have the feeling that there are also other fields of work that still didn't get any big advantage of such portable machines. The question of course is still if the need is big enough - here I can only guess that it is big enough, though I know too that this could be only my own wishful thinking simply because the idea is tandanizing to me.

Oh well, another grandpappy and his wishes ;-)



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