The widely reported story last week that 1.5 million smart toothbrushes were hacked and used in a DDoS attack is false.
Near as I can tell, a German reporter talking to someone at Fortinet got it wrong, and then everyone else ran with it without reading the German text. It was a hypothetical, which Fortinet eventually confirmed.
Or maybe it was a stock-price hack.
Alan Braggins • February 9, 2024 3:05 PM
The newspaper that ran the original story say Fortinet Switzerland presented it as real, and had the opportunity to correct it before publication.
Via https://cyberplace.social/@GossiTheDog/111895636139647060
Clive Robinson • February 9, 2024 3:29 PM
@ ALL,
We know from past cracks, that some adult toys, have been taken over…
There is also a cartoon around where a woman is holding what is very obviously an electric tooth brush and a shocked retail assistant is captioned as saying,
“No madam we most certainly do nor sell an attachmant for that!!”
So in a way the idea is already out there, all it takes is one enterprising crack and like the Peter Steiner cartoon, published in The New Yorker in 1993 with a black Labrador saying,
“On the Internet, nobody knows you’re a dog”
A new meme about Rabbits for Adults will be born…
Who Knew? • February 9, 2024 5:01 PM
@ Dildo hACKER,
Wow, talk about “in depth” “research”, um, or “mining”, data that is…
hells yeahs, it’s a slimey work, but someone’s gotta do it, someone
once said, right?
holy testical friday • February 9, 2024 5:08 PM
@ dildo hacker,
why not replace SaaS with DoD, dildo on demand?
or IRS – Intercourse Rental Services?
Mexaly • February 10, 2024 12:01 AM
“I say it was a mixmaster, and I say it’s squalid.”
National Lampoon Radio Hour
Jon • February 10, 2024 8:46 AM
It’s a well known fact, that the Internet is a series of tubes… of toothpaste.
John White • February 10, 2024 1:16 PM
This story is likely explained by the fact that Fortinet put out an urgent patch for their notoriously insecure Fortigate servers in the last 48 hours.
Literally trying to push their incompetence out of security news by making up hysterical nonsense
Bernie • February 11, 2024 11:52 AM
I had been considering posting a link to the Ars Technica coverage, but the comments so far have got me thinking along a different path.
– Toothbrushes and DDoS… Can I make one of the D’s stand for Dental?
– IoT hacking and ubiquitous surveillance… Insurance companies monitoring your brushing habits.
Regular readers can connect the dots without me spelling it out.
(If you want that Ars link: https://arstechnica.com/tech-policy/2024/02/viral-news-story-of-botnet-with-3-million-toothbrushes-was-too-good-to-be-true/)
Gert-Jan • February 12, 2024 7:08 AM
Apparently we’re still in an age where compromised internet connected devices is news.
As far as I know, there’s no effective regulation in place to prevent it or intervene quickly.
So this will not only keep happening, I expect an increase. I expect it to happen so often, that it won’t be news worthy anymore.
I think regulation is possible. I don’t just mean in terms of responsibilities (and fines), but also in terms of standards for communications of smart devices.
Standards in communications of smart devices could allow easy identification and thus blocking / filtering in network equipment.
Clive Robinson • February 12, 2024 8:08 AM
@ Gert-Jan, ALL,
Re : It can not be stopped in the direction we are currently heading.
“As far as I know, there’s no effective regulation in place to prevent it or intervene quickly.
So this will not only keep happening, I expect an increase.”
An increase is with little doubt a foregone conclusion.
I keep mentioning that the Software Industry does not learn from history. Even it’s own history easily within living memory.
I also mention that the Software Industry has no useful metrics by which the scientific method can be applied and used to provide safe forward motion.
As with the cartwheel that went from planks of wood nailed together way more than two thousand years ago to the spoke and rim design of the 1800’s actual real development has been both very long and slow, as well as deliberately held back.
Do you blame the artisanal craftsmen or those who try to control benefit to them and their cleaque?
You find exactly the same types of players in the Software Industry, and as long as they are allowed to continue this way the problems will not be solved, in fact as history has repeatedly shown they will get worse untill the harm gets worse a lot worse and body parts get strewn around the countryside untill the point politicians are forced to act.
At which point modern history shows we will get “bad legislation”. We can already see this in place via backdoor taxing. As I’ve mentioned in some parts of the world no matter how qualified you are you are not allowed to practice under law. What this means is “Guild Tests and membership” or direct payment each year to a self serving political authority used to raise money and exert political control. Both create “rice bowl” systems like the equivalent of a Pyramid Franchise / Selling Scheme.
You can see such nonsense already in play in the Indian Academic system requiring “published papers and conference attendance” that are used to paper over a “kick back” system.
How you get the benefits without the cons is a difficulty that we are going to have to surmount.
The one thing I can say is unrestrained “Guilds and Professional Registration” is most definitely not the way to go, they will only make things worse not better.
bl5q sw5N • February 12, 2024 12:16 PM
@ Clive Robinson @ Gert-Jan
I also mention that the Software Industry has no useful metrics by which the scientific method can be applied and used to provide safe forward motion.
I don’t see how progress will really be made until the question “what is a program ?” has been answered. To paraphrase Michael Spivak’s restatement for mathematics of Aristotle’s characterization of what is a scientific or commensurate universal (cause), you have the right definition when it can be said of any major program that
1. It is trivial to write.
2. It in trivial because the programming elements appearing in it have been properly defined.
Some books on this regard one might want to have on one’s desktop –
Winter • February 12, 2024 1:15 PM
@bl5q sw5N
I don’t see how progress will really be made until the question “what is a program ?” has been answered.
Alan Turing answered that question quite definitively.[1]
We really do know what a program is, anything that can be emulated on a UTM, and we have proof that the “bug problem” is unsolvable.
[1] Turing, A. M. (1937). “On Computable Numbers, with an Application to the Entscheidungsproblem” (PDF). Proceedings of the London Mathematical Society. 2. 42 (1): 230–265. doi:10.1112/plms/s2-42.1.230.
‘http://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf
bl5q sw5N • February 12, 2024 1:41 PM
@ Winter
Alan Turing answered that question quite definitively.
In one sense yes, in another sense no.
The coordinates presentation of linear algebra, i.e. “matrices”, or tensors in differential geometry is in one sense complete. But it does not convey conceptual understanding of itself. One can compute anything but to know what one is talking about, one has to reach the coordinate free (“abstract”) treatment. This provides the right conceptual framework and makes trivial all the opaque calculations of the coordinate based approach.
The situation in computing is similar. We know everything and at the same time nothing.
Winy • February 12, 2024 5:42 PM
@
The situation in computing is similar. We know everything and at the same time nothing.
What has this to do with the question “What is a program?”.
We do know that “Computability” touches at the foundations of mathematics. That is a deep question. But Turing did supply a comprehensive answer to the question you asked. He also proved the impossibility of a general approach to find or prevent all unwanted behavior in general software, aka, bugs.
We can conclude from Turing’s work that the question “What is a program?” has little relevance for progress in software security.
That is no surprise. The question “What is a bridge?” is also of very limited relevance to the design of safe bridges.
Clive Robinson • February 12, 2024 7:59 PM
@ Winy, bl5q sw5N, Winter,
Re : When is a program nolonger a program.
“What has this to do with the question “What is a program?”.”
As far as most people are concerned you have,
Program = data + instructions
What is not clear from this is that there are two types of program,
1, That which acts entirely independently of the data values.
2, That which acts dependently on data values.
The first does not have data dependent branching and is thus more limited and so often seen in the lower levels of the computing stack, “closer to the metal” as in DSP and Embeded systems.
The second is more general purpose and has data dependent branching and can be more complex in function and is found at all levels of the computing stack, however it has a failing of
In a “bag of bits” storage model there is no distinguisher so,
Instructions = data
Data = instructions
This remains true even in a CPU that has seperate memory areas for instructions and data such as a Harvard architecture. Because,
Data can be interpreted as instructions both low and high level.
Which is why back in the 1980’s and earlier BASIC appeared on 8bit computers with very limited memory. The near ultimate form of this was having a stack based system with a language such as Forth. That are still around in PostScript and later PDF files.
As long as you stick to not using data as instructions or not acting on data then you have “full determinism” and behaviour is predictable (we thus tend to think of them as fully defined “state machines” rather than programs even though it is a mistake to do so).
It’s when you have the ability to change behaviour on data values or use data as instructions and instructions as data you start to get a level of indeterminacy to a certain degree and higher levels of complexity along with indeterminate state. This is what the Church-Turing issue or “Halting Problem” is all about.
Now ask the AI question…
It can be argued that at some point a computer program that can change it’s program and data or behaviour can develop beyond it’s self. You can actually see a very limited example of this in Conway’s “Game of Life” where the equivalent of cellular automata with next to no complexity can develop very complex interactional behaviours between the automomata way above the basic automata functionality. This complexity that can only be seen by direct execution or simulation of the automata.
Now if you add two things,
1, Randomization (to data)
2, Fitness function (to instructions)
Then you have a computer system that can evolve it’s behaviour.
Is it,
“Artificially Intelligent?”
Well that rather depends on your definition of “Inteligence”.
Alan Turing kind of upset the apple cart back in the 1940’s and 50’s because he reasoned,
“If God could give man a soul, God could give a machine a soul.”
Which was to many heresy and in earlier times would have caused fairly dire punishment. But Turing went on to further reason that,
“If man was made in Gods likeness, then man could give a soul to a machine.”
Thus the field of AI was born with a question that arises of does,
Soul = instructions + data + random
If true then a lot of theological rice bowls are going to get broken, and “Artificial General Intelligence”(AGI) can exist (if and when we nail a definition down for GI).
Winter • February 13, 2024 1:19 AM
@Clive
Re: Winy
That’s me. I sometimes use a device with overactive spelling correction and very small keys. Should check better before I push submit.
Re: What is a program.
There are many types of programs. But everything that can be run or emulated on a Turing machine is a program. If it cannot be emulated on a Turing machine, it is not a program.
But as a program covers anything that is computable, the question “What a program is”, is irrelevant for how to ensure its correctness.
Clive Robinson • February 13, 2024 6:10 AM
@ Winter,
Re : That’s me – as well.
Yup as you know I’ve suffered from “fat finger syndrome” for years now.
As discussed in another thread it comes of having “big hands” that are not so Doh-gnarled…
(Hopefully that raised a smile this AM 😉
But getting back to the serious side.
“If it cannot be emulated on a Turing machine, it is not a program.”
Turing himself acknowledged that view was both singular and limiting. It’s why he insisted on a Random Number Generator of high quality being included in the computer designs he was involved with.
Even basic simulations go better with random. Have a look through Monte Carlo methods and through Annealing Algorithms to see practical uses of random in a single Turing Machine / CPU system to on average get faster results.
Sometimes it’s not the values you are looking for but the relationship between the numbers. Even Issac Newton knew that the rate of change was more important than absolute values, and sometimes all you need are limits, sometimes the shape of the curve.
Which brings up what Turing’s Engine did not cover, which was multiple engines walking the same tape.
It’s what Conway’s game of life can demonstrate, that very simple automata can demonstrate complex behaviours way beyond their individual capabilities.
This is also demonstrated with the neurones in “Digital Neural Network”(DNN) systems. It’s easy to prove their level of complexity is not even close to that of a Turing Machine, nor can they in any way individually function as such. All they actually do is sum the weighted inputs then use the result in a translation or lookup table.
But even without feedback in operation they can produce results of a complexity beyond that an analysis of an individual neurone can be shown to be capable of (tally and scale have very real limits).
In effect they are like the butterfly in the Fast Fourier Transform, what they are acting on is not the values as encountered on the tape as a Turing Engine does but the spectrum formed by many values simultaneously.
It’s in part why I say that DNNs are in effect “Digital Filters” no different to DSP state machines.
Yet others claim they have “Artificial Intelligence” (something I dispute).
How do you “square that circle?”
As you and I discussed some time ago the “memory” in an LLM is held in the inputs to the neurones at each level. In effect it is the direct equivalent of an input only tape to a state machine, so is in no way Turing capable.
That is a DNN holds data just as data is in the butterflies of an FFT. Yet each successive layer acts as a way to transpose from one domain to another domain.
In the case of the FFT it’s from the ordered time domain to the ordered frequency / spectrum domain or back the other way.
In the case of LLM’s exactly the same thing is happening ordered input from one domain is transformed into another domain and order.
We don’t know with LLMs what that new domain is, or it’s order, that is it is a new spectrum about which we know next to nothing, and that way to many people are giving these spectrums mythical powers.
So to answer the question “no a program does not require a Turing engine to function”.
Also sadly for the AI fans an LLM is certainly not intelligent in any way.
In fact an LLM’s mystique and magic is more due to “rounding errors” on the size of data words and numbers of entries in lookup tables acting on the “random” of noise on the signal input.
So is an FFT a programme?
Arguably not… as it’s base transforms of the butterflies can not do the minimum that is said to be needed to be “Turing Compleat”. Nor does putting them in the layered form make them “Turing Compleat”.
Therefore given the equivalence is an LLM a program?
Again arguably not.
So is an LLM intelligent?
I’ve clearly said I don’t think so by any reasonable definition of “intelligence” and I’ve given reasons why.
Have all those investors in LLMs lost their money?
Arguably yes, but mankind has actually gained for both good or bad which is to be expected of any new technology.
The bad is that LLMs are the next iteration of “Surveillance Technology” that go beyond the aims and objectives of the likes of the Five-Eyes ECHELON. I’ve said they,
“Beguile, Befriend, Bewitch and Betray”
And they do that rather to well. And some self entitled individuals see almost immeasurable personal benefit if they can keep the technology as a cartel or monopoly holding.
But the good few have realised yet and that is they are tools to explore the new spectrums in meaning that humans so easily and efficiently acquire yet have difficulty not just in explaining but actually measuring and defining.
Flip the coin, heads some win but most loose, tails some loose but mankind in general benefits…
So back to the balance of,
“Individual Rights v Social Responsibility”
I guess you know where I prefer the balance point on that scale to be 😉
Winter • February 13, 2024 6:48 AM
@Clive
It’s what Conway’s game of life can demonstrate, that very simple automata can demonstrate complex behaviours way beyond their individual capabilities.
Conway’s game of life is Turing Complete, but it has no computational possibilities beyond a UTM.
To get outside Turing’s computability, you can add analogue numbers, ie, numbers with infinite precision, quantum entanglement etc.. However, I have yet to see a physically realizable system that can compute things that cannot be computed by a UTM (with randomness). Maybe quantum computers, but I do not hold my breath.
‘https://en.wikipedia.org/wiki/Hypercomputation
There might be deep connections between computability, mechanics, and the Universe. Seth Lloyd has written about the Universe as a Computer.
Computational capacity of the universe
‘https://arxiv.org/abs/quant-ph/0110141
The universe as quantum computer
‘https://arxiv.org/abs/1312.4455
bl5q sw5N • February 13, 2024 9:51 AM
@ Winter @ Clive Robinson
Turing did supply a comprehensive answer to the question you asked
That’s like saying if we have a numeral notation (e.g. binary) and certain rules for symbolic combinations then we have an answer to the question “what is a number ?”.
One would have to have some idea of what a number is to set up a numeral system, but the numeral system doesn’t explain anything of itself. Likewise Turing machines.
The question “What is a bridge?” is also of very limited relevance to the design of safe bridges.
A definition doesn’t just state a conclusion, as for example (random stab here) “a bridge is a traversable support over an otherwise non-traversable terrain”. That is a conclusion, a statement of what is wanted. The definition of a bridge should state the cause that enables such a thing to be. In grasping this one would certainly be in a position to design safe bridges. Likewise programs. We have in effect conclusions, examples, but no clear statement of underlying cause ie definition.
Spivak illustrates the issue. Classically (19th century) there was Green’s theorem, Stokes’s theorem, Gauss’s theorem, the Divergence theorem. They all had proofs and were thought to indeed be theorems. However they were not really theorems because the real scientific definition involved was not understood. They were special cases of the scientific definition and objects, which is differentiable manifolds and differential forms. The classical theorems are really the same theorem.
piglet • February 13, 2024 12:07 PM
“a German reporter talking to someone at Fortinet got it wrong, and then everyone else ran with it without reading the German text”
Please, bruce, it’s Swiss, not German. and no, the reporter didn’t get it wrong, Fortinet lied.
Winter • February 13, 2024 1:02 PM
@bl5q sw5N
The definition of a bridge should state the cause that enables such a thing to be. In grasping this one would certainly be in a position to design safe bridges.
So, there is such a definition of a bridge? Or a of numbers? Or a chair? Is there anything of which we such a definition?
I would guess, such a definition is impossible. At least, Kant wrote rather a lot of pages showing we could not know the “real” thing (“das Ding an sich”). As no one has shown a counter example, I believe him.
bl5q sw5N • February 13, 2024 1:54 PM
@ Winter
Is there anything of which we such a definition?
Is there anything that exists ? Then it has a definition.
As no one has shown a counter example, I believe him.
As no one knows what he was talking about [1], I don’t believe him.
Winter • February 13, 2024 3:07 PM
@bl5q sw5N
Is there anything that exists ? Then it has a definition.
Can you write it down. If it caybe written down, it is not there.
As no one knows what he was talking about [1], I don’t believe him.
He wrote about your inability to formulate your definition of anything in existence, anything at all, among other things, mostly the philosophy of what can be known.
That seems clear enough.[1]
[1] Kant’s German was indeed opaque. But his ideas were not.
Winter • February 13, 2024 3:08 PM
PS
“If it caybe written down, it is not there.”
->
“If it cannot be written down, it is not there.”
bl5q sw5N • February 13, 2024 3:59 PM
@ Winter
Can you write it down. If it cannot be written down, it is not there.
…
[1] Kant’s German was indeed opaque. But his ideas were not.
The first seems to contradict the second. Taking them together, we get “If it Kant be written down, it is not there.” . That is, Kant is an unreliable guide. 😉
We have to start with our knowing. Everyone really admits they know. Why are you making assertions if you don’t accept that you know ? Knowing involves the “what” (essence in Aristotle/Aquinas) and the judgement that the thing exists (esse).
Winter • February 13, 2024 6:23 PM
@bl5q sw5N
We have to start with our knowing. Everyone really admits they know. Why are you making assertions if you don’t accept that you know ?
Yes, indeed. And like Kant wrote, we are unable to know the essence of things.
You claim:
The definition of a bridge should state the cause that enables such a thing to be. In grasping this one would certainly be in a position to design safe bridges.
Then show us this definition. Bridges have been build from times long before Aristotle. Everything there is to know about bridges should be known by now. But I do not know about such a definition. For that matter give us the essential definition of anything that has these marvelous qualities.
I would say that 2 millenia and a few centuries since Aristotle and over half a dozen centuries since Aquinas have resulted in exactly zero such definitions containing the essences of anything. They cannot be formulated by humans, and our best guess is that they are truly incomputable.
If you disagree, it suffices to give just a single definition that contains the essence of something real, say, a chair. As Kant formulated, Das Ding an sich.
Clive Robinson • February 13, 2024 6:53 PM
@ Winter, bl5q sw5N
Re : All definitions are “desired function” dependent.
“And like Kant wrote, we are unable to know the essence of things.”
The “essence” is intrinsic to the thing which is effectively a “black box”.
As an external entity or observer you can see a stimulation going in and a result coming out of the black box.
However you can not fully stimulate the black box so can not see all potential results.
Ergo you can not know the full “essence” of a thing / object / black box.
You can only partially determine output for your “desired function”.
A classic real world example of this was the emissions test from certain vehicles. The “thing” determined it was being tested and adjusted it’s functioning thus output accordingly.
As far as the tester was concerned the “thing” met the required “emissions mask”. And so the tester “assumed” incorrectly what held for the test also held at other times, which was an incorrect assumption as using a different test method showed.
Winter • February 14, 2024 1:14 AM
@Clive
The “essence” is intrinsic to the thing which is effectively a “black box”.
This is even more so for categories of things like “bridges”, or “chairs”.
The fun thing, this is not true for Turing’s definition of a program. A Universal Turing Machine is perfectly transparant, albeit theoretical. It is also comprehensive and captures the mathematical essence of programs.
But that was somehow not the essence @bl5q sw5N intended. So I am at a loss what kind of essence s/he expects or wants.
Clive Robinson • February 14, 2024 5:32 AM
@ Winter, bl5q sw5N,
Re : A soul by any other name…
“But that was somehow not the essence @bl5q sw5N intended. So I am at a loss what kind of essence s/he expects or wants.”
As I noted way above, Turing resoned there was something beyond the state machine that later carried his name. Thus what gave birth to AI was his reasoning in the 1940’s and 50’s that,
“If God could give man a soul, God could give a machine a soul.”
And in turn man must also be able to give a machine a soul.
It is said that,
“The soul is the ineffable spice of life which transcends all.”
Yet others reason whilst we humans are neither mechanical or electronic machines we are nether the less machines, thus everything we are must be due to some form of computation.
Thus,
Soul = program = data + instructions
With the spice comming from,
Evolution = random + fitness functions
And as,
Fitness functions = program…
That just leaves random or perhaps chaos.
Can I prove this conjecture?
Not currently, but nore can it be disproved currently either, and I rather hope it stays not disproved. Why? Well because with it would die “free will” and that is not something I’m willing to cede.
I like to think of a “God at the gambling table” showing yet another human failing… After all we made gods in our likness so why should we deny them the sins of body and mind we know we all posses, it would just take all the fun out of life 😉
Winter • February 14, 2024 6:27 AM
@Clive
Well because with it would die “free will” and that is not something I’m willing to cede.
Given that no one has a good definition of “free will” or actually knows what it is supposed to be, who cares. When asked, most people start with something that comes down to “Randomness”. When pressed, it ends with something outside of the natural universe.
The the question is, “Why does it matter?”. After which we get into the area of a desire for human sacrifice and torture (aka, the desire to punish people).
In the end, the thing is, whether free will exists in the transcendental, metaphysical sense or not does not matter. Even if human behavior were completely deterministic, no entity outside a theoretical God would be able to predict behavior any more than if it were completely random, or Free Will.[1]
And punishment has worked very well for animals that were always considered to have no free will. So it will work with humans too if they have no free will.
So, who cares if we have no “real” Free Will. Humanity will punish people just as happily as they are doing now. And if people want human sacrifice, they will find an excuse, Free Will or not. They are doing it now in the USA, they will continuing doing it later too.
[1] Follows from Turing’s proof of the undecidability of the Halting Problem.
Clive Robinson • February 14, 2024 9:25 AM
@ Winter,
Re : Self determination.
“The the question is, “Why does it matter?”. After which we get into the area of a desire for human sacrifice and torture (aka, the desire to punish people).”
As with technology that can be used by a directing mind for good or bad as judged by an observer, it’s about the ability to chose, and for the choice to have meaning.
If our universe was as some believe “created by an entity” they call a deity, then by definition the deity would have to be outside of time.
Further why would an entity create a purposeless universe, which is what a lack of free will would give. That is no matter how many times you run it as an experiment or program the resulting output or terminal state –assuming there is one[1]– would always be the same. More importantly the journey from start to end would always be the same.
So ask yourself how often would you have to watch a TV show episode before you knew everything of importance to the main plot and any sub arcs? Every actors word, look, any errors, or now obvious Chekhov’s guns?
How many times before watching was not just meaningless but some kind of torture?
That’s what lack of free will means
And if there was a creating deity why create just a “Hello Universe” program? Why not something more interesting?
[1] Every time we get a new telescope that lets us see a little further, two things appear to happen,
1.1, What was assumed as a consequence of previous limits becomes challenged.
1.2 What then becomes accepted will with the next telescope become another half truth.
The only fun in it for most of us is watching theoretical physicists burn or fall off of a pedestal into apparent ignominy of the long grass pasture.
Apparently according to less reputable outlets the JWT has proved dark matter is a nonsense, string theory has been debunked, and the big bang if it happened did not happen when we thought it did… Roger Penrose is really sorry, some one hit rock star is now free to sing “it can only get better” just in time for UK elections. And the “string of pearls theory” is now more likely so entropy can go into reverse. All before the vexed question of the multiverse pops up and some one shouts “incoming” and suddenly every room in that infinite hotel is both empty and has a nervous rabbit looking strangely like both a theoretical physicist or a pigeon in it “ducking and covering”… All we need now is Sabine to come and tell us what it really means 😉
bl5q sw5N • February 14, 2024 10:39 PM
@ Winter @ Clive Robinson
Kant wrote, we are unable to know the essence of things
Kant is not talking about essence when he speaks of the “Ding an sich”. He is talking simply about things. He is saying we cannot know things, which amounts to saying that we cannot know at all. This is to be expected as Kant’s starting point is the same as Descartes’s, namely all we have are ideas in the mind. Clearly from that starting point one will never be able to reach outside the mind to actual knowledge of real things (although people have spent 400 years twisting and turning trying to have their cake and eat it.)
But nobody really believes this or acts as if it were so. It’s a false problem. The only cogent starting point is to admit that we are knowers, and then seek to understand how this is possible, what limits we may have in our cognition, what may be known, what implications this brings, etc.
Pursuing that program, it is found that in things there are two, namely the “what” and the “existence”, that is we have knowledge of the thing’s essentia and its esse. The essence is the answer to the question “what is it ?”.
Our answer to the question is complete in the case of mathematics and in the case or artifacts, and generally any production of human endeavor. This is because we know the cause of the thing in these cases. Above I gave examples from mathematics (the general Stokes theorem) and artifacts (my random stab at definition of “bridge”).
In the case of the substances of nature (dog, gold etc.) we know the somewhat of the essence but we have a less perfect knowledge as we are denied knowledge from the point of view of the cause and the “inside”. Natural things are the effects of these causes. We can sometimes and imperfectly reason backwards from the effects to the causes but this is clearly inferior to the kind of knowledge from cause to effect we have in mathematics.
Finally as regards programs, these are artifacts and we should be able to know them completely.
However, we knew planar areas and boundary lines seemingly perfectly and the corresponding Green’s theorem, and also the 3D volumes and bounding surfaces and classical Stokes theorem seemingly perfectly. But nevertheless it turned out that what we knew (seemingly perfectly) were special cases of a higher more universal mathematical object, namely the differentiable manifold. From the point of view of differentiable manifolds, we have a deeper grasp of the classical theorems and see they are really the same theorem with comparatively trivial variations in specific details.
This kind of thing happens all the time in mathematics and is one of the ways mathematics progresses. I don’t see that the situation with programming and the seemingly perfect knowledge of programming the Turing machine provides will not also be eventually seen as a special case of a higher understanding. As was said originally the situation may be like calculations with coordinate matrices giving way to the more universal concepts of vector spaces, linear transformations etc, ie linear algebra. We know our matrix math seemingly perfectly, but that understanding neglects the definition if the real objects involved.
Winter • February 15, 2024 1:06 AM
@bl5q sw5N
Kant is not talking about essence when he speaks of the “Ding an sich”. He is talking simply about things.
You should brush up on your German. It means a “Thing by itself”, not just the “Thing” as we observe it.
You seem to understand “essence” to mean unobservable qualities of things. But you cannot know unobservable qualities.
Winter • February 15, 2024 1:37 AM
@bl5q sw5N
This is to be expected as Kant’s starting point is the same as Descartes’s, namely all we have are ideas in the mind. Clearly from that starting point one will never be able to reach outside the mind to actual knowledge of real things (although people have spent 400 years twisting and turning trying to have their cake and eat it.)
If your starting point is that people can have knowledge of totally unobservable things outside of the physical universe, ie, metaphysics, then indeed Kant and Descartes are wrong.
You will also be unable to prove your point as you cannot prove unobservable facts to other people. Your only recourse is faith. Which end you up in theology.
Two millenniums of history of theology and metaphysics have shown no progress at all. Not a single case of essence or knowledge of a Thing have appeared in these 2+ millenniums of work.
Meanwhile, different theologies have delivered undisputable proofs of the existence of mutually incompatible different Gods.
Metaphysics quest for the essence of things have been futile for thousand of years. Please explain why we, you, can succeed now?
Winter • February 15, 2024 2:04 AM
@bl5q sw5N
This kind of thing happens all the time in mathematics and is one of the ways mathematics progresses.
Mathematics is pure and an artifact of the mind. However, mathematics does not describe the physical universe. Humans look at the physical universe and select the set of mathematical axioms and rules to give an internally consistent description of the physics.
In itself, the mathematics of Newtonian, GR, and Quantum mechanics are incomparable and incompatible. They can be used to describe different, and aspects of the same physical systems. In itself, the mathematics does not describe anything.
bl5q sw5N • February 15, 2024 6:41 AM
@ Winter
brush up on your German
Kant, The Critique of Pure Reason (A273) –
But since the expression “outside us” carries with it an unavoidable ambiguity, since it sometimes signifies something that, as a thing in itself [Ding an sich selbst], exists distinct from us …
A “thing in itself” is then just a thing in the classical sense. Kant only adds the “an sich” to try to distinguish this (unknowable for him) from “things in the mind”.
You seem to understand “essence” to mean unobservable qualities of things. But you cannot know unobservable qualities.
As I said above, the essence answers the question “what is it ?” Knowledge begins in the senses and terminates in the intellect as cognitional identity with the thing. I think everyone would agree that sensing is observing and observing is sensing. The observations ultimately yield information about what kind of thing we have at hand i.e. the essence. The essence itself as such is not sensory and so is unobservable. We don’t see essences floating around. But we know them from what is sensed.
Mathematics is pure and an artifact of the mind. However, mathematics does not describe the physical universe
Mathematics does treat of the real world in terms of its quantitative aspect. Some things, although existing in matter, do not contain matter in their definition. Mathematics is the science that treats of these beings. That’s why when
Humans look at the physical universe and select the set of mathematical axioms and rules
something useful is obtained.
In more detail. What is prior from the point of view of the intellect can be considered without what is posterior without any falsity. Mathematicals, i.e. the quantitative, precede and are prior to natural things (sensory qualities like coloir, weight etc.) existing in matter and motion, for the latter are so related to mathematicals as that they add something to them. Therefore, mathematical investigation can consider the thing from the point of view of its quantity, leaving out of consideration i.e. abstracting from, the matter and motion.
There is a certain freedom in mathematics. The mathematicals in the mind, as quantities, can be combined, divided, square rooted, models made, etc. without reference to actual physical things.
Metaphysics quest for the essence of things have been futile for thousand of years
This is just repeating the Cartesian starting point. You might as well cut to the cjase and say metaphysics is futile. This is simply not so. The key “takeaways” are provided by Aristotle and his subtle correction and extension by Aquinas.
bl5q sw5N • February 15, 2024 11:44 AM
@ Winter
(A273)
That should be A373, the first or A edition of the Critique of Pure Reason, page 373.
https://plato.stanford.edu/entries/kant-transcendental-idealism/
Winter • February 16, 2024 1:56 PM
@bl5q sw5N
But since the expression “outside us” carries with it an unavoidable ambiguity, since it sometimes signifies something that, as a thing in itself [Ding an sich selbst], exists distinct from us …
Here you can find a recent (2015!) article trying to bridge the two sides of this discussion:
‘https://edoc.hu-berlin.de/bitstream/handle/18452/28545/10.1017_S1369415414000284.pdf
However, I rather follow Karl Popper in his interpretation from Conjectures & Refutations beautifully explained in:
‘https://link.springer.com/chapter/10.1007/978-94-015-7704-5_2
Mathematicals, i.e. the quantitative, precede and are prior to natural things
In short, you claim we should go for the essence of things, but the only examples you can give are not “things”, like chairs, but mental ideas, eg, mathematics.
But mathematics does not give you knowledge about the material world. It can be used to capture the regularities and “laws” of nature. But mathematics does not tell you which of all the possible worlds in mathematics is actually found in existence.
Popper combines these views by the well known observation that humans (actually, all living things) expect the world to be regular and predictable at some level. They approach the world by supposing some model that they adapt based on experience.
As such, our ideas precede our observations. But these ideas are most often wrong or at most partially correct, so our observations must correct them.
bl5q sw5N • February 23, 2024 12:36 PM
@ Winter
Karl Popper in his interpretation
Skimming through Logic of Scientific Discovery, Conjectures and Refutations, Realism and the Aim of Science, suggests that Popper does accept an external reality, which scientific theories are trying to explain.
(Quotes are from “Realism and the Aim of Science”.)
The task of science, which, I have suggested, is to find satisfactory explanations, can hardly be understood if we are not realists.
For Popper the criterion of “scientific”, in his terminology the solution to the “demarcation problem”, is to be potentially empirically testable or “falsifiable”.
A statement or theory is, according to my criterion, falsifiable if and only if there exists at least one potential falsifier—at least one possible basic statement that conflicts with it logically. It is important not to demand that the basic statement in question be true. The class of basic statements must be characterized in such a way that a basic statement describes a logically possible event of which it is logically possible that it might be observed.
For Popper the extent of knowability of objective reality seems to be a never ending succession of provisional falsifiable models, encompassing more and more observations, and which provide “universal laws” of nature’s “structure”.
Every time we proceed to explain some conjectural law or theory by a new conjectural theory of a higher degree of universality, we are discovering more about the world: we are penetrating deeper into its secrets. And every time we succeed in falsifying a theory of this kind, we make an important new discovery.
…
Only if we require that explanations shall use universal laws of nature (supplemented by initial conditions) can we make progress towards realizing the idea of independent, or non-ad-hoc, explanations.
Elaborating on laws, Popper states they are real and do not arise from objects, rather objects arise from the hidden structure of the world the laws describe.
… we conceive all individual things, and all singular facts, to be subject to these laws. The laws (which in their turn are in need of further explanation) thus explain regularities or similarities of individual things or singular facts or events. And these laws are not inherent in the singular things. (Nor are they Platonic ideas outside the world.) Laws of nature are conceived, rather, as (conjectural) descriptions of the hidden structural properties of nature—of our world itself.
It is clear that the experimental or empirical scientific method has been and will continue to be immensely fruitful in knowledge of the real world.
It uses quantitative (discrete and continuous) measurement of real things. These measured quantities occur as parameters or variables in a mathematical model, which is a combination of variables, structures and equations.
Thus, the real world objects are represented, via their measured quantities, as parts of a (provisional) model structure, and the model is the explanation empirical science offers of the world.
Jacob Klein in his book “Greek Mathematical Thought and the Origin of Algebra” (1934) states the situation very clearly:
… it is impossible, and has always been impossible, to grasp the meaning of what we nowadays call physics independently of its mathematical form: Thence arise the insurmountable difficulties in which discussions of modern physical theories become entangled as soon as physicist or nonphysicists attempt to disregard the mathematical apparatus and to present the results of scientific research in popular form. The intimate connection of the formal mathematical language with the content of mathematical physics stems from the special kind of conceptualization which is a concomitant of modern science and which was of fundamental importance in its formation.
This accounts for what is being said by Popper in his characterizations of universal laws revealing real deep structure and their non-inherence in singular real objects. He is treating the mathematical model, which is purely in the mind, as if it were real.
However, the only element in the model that we know can be “played back” to the real world are the variables representing measured quantities. The rest of the model is purely conceptual. The fact that a chain of models has included more and more variables and accommodates more and more relations between them does not change this. His claim that real objects do not have inherent properties (nature or form in classical terms) that give rise to real observable behaviors and relations is thus not supported.
Popper actually offers separate arguments against the classical account via inherent natures ( and essence or form) of individual things found in Plato and Aristotle. However his statements – e.g. essence is an “animistic” notion – show that he does not actually understand the classical accounts.
Winter • February 24, 2024 1:03 AM
@bl5q sw5N
Skimming through Logic of Scientific Discovery, Conjectures and Refutations, Realism and the Aim of Science, suggests that Popper does accept an external reality, which scientific theories are trying to explain. …
I think we agree 100% on our reading of Popper’s Conjecture and Refutations.
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yet another bruce • February 9, 2024 2:36 PM
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