Downloading Your Brain

[Gamer]

Downloading a working model of your brain, all the neurons, down to the synaptic charge, is theoretically possible. Hundreds of billions of neurons can be scanned and mapped in a working model. Most scientists agree on the feasibility of this statement, and it could plausibly happen in the next few decades, maybe sooner. We've already done it with a section of a rat brain. Let's assume for sake of argument all the above is true.

What is exciting about this? When I read about it, my emotions are mixed. On one hand, it's a way to preserve a brain in terms of brain states, and possibly even a mind. That's neat. But on another hand, it's oddly unsatisfying, because I'm unclear as to how this can lead to continuation or transfer of identity. If you could clone your brain into a robot in the next room, once you were aware the deed was done, would you be willing to die as a simple matter of housekeeping? Of course not. Because the robot isn't YOU. It's a copy.

How do we move the locus of perception, the unbroken sense of YOU-ness from an organic substrate to a digital one? Is it a sort of death?
Can we argue that if it's done gradually – like replacing each board on a ship, one by one – it's the same YOU?

These are still philosophical questions. I'm so curious to see where this goes. It may be that locus of perception, the unbroken chain of YOU-ness is overrated, as counter-intuitive as that may sound.

If everyone who submitted to a mind transfer swore by it and said, don't worry, it's fine, it's like blinking – would you do it? Because really, all these proponents are actually clones, waking up for the first time after the transfer. Are they credible witnesses? When you sit down to do the transfer, you are sitting down to die, essentially. Whether a clone goes on or not is irrelevant, you're every bit as dead, from the inside.
Or are you?

Who will dispel these questions? How will we come to think of these issues? Will it matter what WE think? We are getting to the point where we no longer have the luxury of blithely calling The Problem Of Consciousness a perennial imponderable. We are getting down to the wire where we have to figure it out and cast a vote, before it's cast for us.

[James S Saint]

Will it matter what WE think? We are getting to the point where we no longer have the luxury of blithely calling The Problem Of Consciousness a perennial imponderable. We are getting down to the wire where we have to figure it out and cast a vote, before it's cast for us.

No, it doesn't matter. It is already too late. You have no vote.

It can be calculated that at every instant in time, there are over an infinity of replicas of you throughout the infinite universe. And when I say "replica", I mean down to every single atom. And at each of those moments, every one of your replicas are thinking the exact same thing. Such has always been true and mathematically unavoidable. Although I should add that divergence begins immediately as each replica begins to become different and what were close to replicas begin to become exact replicas. So your identical replicas are never in the same place as they were just an instant earlier.

With that in mind, what difference would it make if one of those replicas happened to be sitting beside you, created from you intentionally? Throughout the infinite universe there would also be more than an infinity of you sitting beside your artificial replica. But a replica is a replica. You merely have twice as many now.

The simple, always known fact, is that you are the combination of both your body and your "spirit" (mind/psyche/consciousness/whatever). You are not merely the spirit consciousness of you any more than a government of a nation is the nation. When your spirit abandons the body willingly, it betrays the body just as if the government abandoned the people of its nation (currently being experienced in the USA).

So when your body dies, or your spirit dies, you are left as only half of you and in need of the other half. The fact that there is another you in spirit right beside you doesn't change that fact.

Would you kill one of your dogsled dogs quite freely upon realizing that you have more than you need others just like that one? Socialist utilitarians would .. and do.

[Orbie]

I am not a mathematician, but Could You demonstrate the above both: in philosophic and simple mathematic language?

If You are unable to at the present time, due to such factors as lack of time for it, or some other considerations, there need not be raised the possibility that the idea is without merit.

Thank You, James

[Orbie]

I could fathom the idea, based on probibility functions based on positivist resemblance theory, but not as exact identifiable copies. I could understand that resembling quantitative progressions , as the probability corresponding to a frame of 0~<infinity, would approach near identity, but isn't infinity an open system? If, it were to close, there would be an instant nihilization to absolute zero occurrence, therefore, it would confirm an absolute universal
collapse, into a positive nothingness, with a potential
of another Big Bang. If You are a Creationist, wouldn't this spell bad news?

And a progression of near identity, to total identity, wouldn't/couldn't it be presupposed, that at the critical point almost all copies would/may become indistinguishable ? Thereby defeating it semblance theory?

[Amorphos]

How do we move the locus of perception, the unbroken sense of YOU-ness from an organic substrate to a digital one? Is it a sort of death?

I think if there were a conscious process [maybe an unconscious one too] by which the two brains were connected, then you switch off parts of one and switch on equivalent parts of the donor brain, then the consciousness would make utility of the respective function of that part of the brain. If we consider the simile that an augmentation of the brain would get utilised, then we can add augmentations - so to speak, until the complete second brain is being used. Then in much the same way the consciousness kinda moves its seat of perspective, which i would think is the source of its subjective experience. Perhaps this would be a bit ‘alien hand’ like, and i have seen tests where people can be given glasses which make them think they are located at the point of view of the glasses/cameras, and so i would expect that having one optical centre turned off and another turned on, would also result is said change in perspective. so now you just need to see what happens when the old brain is turned off completely!

unless we had the instrumentation which provably shows transferral of consciousness, then the onlooker cannot know if the second brain is a mimic. perhaps even the dweller of the second brain wouldn't know, as its experience would have memories from the old body, ergo it would perhaps think it was the old person from the former brain.
_

[brevel_monkey]

What is exciting about this? When I read about it, my emotions are mixed. On one hand, it's a way to preserve a brain in terms of brain states, and possibly even a mind. That's neat. But on another hand, it's oddly unsatisfying, because I'm unclear as to how this can lead to continuation or transfer of identity. If you could clone your brain into a robot in the next room, once you were aware the deed was done, would you be willing to die as a simple matter of housekeeping? Of course not. Because the robot isn't YOU. It's a copy.

I always felt this would also be a problem if you were using one of those transporter beams on star trek. Even if the same atoms could be 'beamed' somewhere, you'd almost certainly have to be decomposed and then recomposed at the other end, essentially meaning you would die and then be resurrected. A more realistic 'transporter' beam concept is one which takes an exact scan of you, kills you, then rebuilds you using new atoms and molecules at the other side. On this model we could effectively teleport around everywhere, which would be really cool, with the only small caveat being you'd have to die each time.

If everyone who submitted to a mind transfer swore by it and said, don't worry, it's fine, it's like blinking – would you do it?

Not a chance. I can't explain why, I think there is something about the concept which runs so far against my instincts that I would never be persuaded. I would consider myself as being about to die.

I agree that this throws up some really interesting questions about identity. I think it shows that on an instinctual level we (or at least I) associate our identity as being a link between our minds and our bodies, not just purely about whats in our minds.

[James S Saint]

I am not a mathematician, but my cousin is a prof of math at a prestigious institution. Could You demonstrate the above both: in philosophic and mathematic language, and I will try to send her the calculations, , , asking her opinion. Whereas, how would/could You support it philosophically?

If You are unable to at the present time, due to such factors as lack of time for it, or some other considerations, there need not be raised the possibility that the idea is without merit.

Thank You, James

I'm always dubious about having thoughts questioned through a third party. It is hard enough to get the communication straight when talking directly to the person questioning. But I'll give it go. I have posted the math in the religion forum before, though I know not where.

Basically the math begins with the notion that the universe has an infinity-squared number of location points in any and every direction. That is using the real number system such as to allow for every infinitesimal up to an arbitrary 1, and then an infinity of those 1's. That much is merely basic Georg Cantor set ontology applied to euclidean geometry.

In order to do mathematics properly with infinities, one must first select (arbitrarily) a "standard infinity" to be used as reference for all hyperreal math functions. So just for fun, I can declare that "1" means "1 meter". I could validly choose any unit. And that means that the infinite universe has one standard infinity, "infA", of meters in each direction and one standard infinitesimal is then 1 m divided infA. So any given infinite line will have infA² points.

Given that much (which "she" might not like already in that many mathematicians know little of hyperreal mathematics), the infinite universe (as opposed to the fairy tale, pseudo-science limited universe of the BB proponents), we can say that the universe has 3 dimensions, each with infA² location points, yielding an infinite spherical of volume, Vu, of:

Vu = 4/3 π * (infA²/2)³ meters.

But rather than work with that figure, I would rather simplify it a bit because the point of this is the concern of how many of "you" there are, not the precise size of the universe. So let's simplify by accepting for the moment that the infinite universe is actually a cube:

Vu = (infA²)³ meters

And then let's look at another feature of the universe concerning physics and RM:AO.

Even current physicists wouldn't argue against the idea that at every point in the universe, there is a electromagnetic potential, "EMF", that might range from an infinitesimal (or merely a Plank unit) up to infinite. And that potential might also be negative, minus an infinitesimal down to minus infinity. We can then mathematically treat that like a line from negative infinity to positive infinity. And using our standard infinity, infA, those potentials throughout the universe at any one moment in time could be within an infA² range (same as points on an infinite line).

So to describe the EMF potential at every point throughout the universe, we must give both the location number and also the potential value at each location, yielding infA² ^((infA²)³) values.

Now let's look at the precise situation for every person. Just as a number to work with, let's say that the average person occupies a volume of 1 cubic meter (over-fed Americans). How many location points are within 1 cubic meter? Each cubic meter has an infA³ number of points, so all in all:

Human Body = infA³ points, each having it's own unique EMF value.

So if Scotty was going to beam you up, he would require infA³ number of memory cells within the transporter so as to keep all of the information concerning you. And of course each of those memory cells must be able to store a number within an infA² range (ain't gunna happen). So to be more practical, he limits the potential value for each point to a range of 10³¹ (keeping Plank in mind). And also, he can't handle an infA³ number of cells, so that gets limited to (10³¹)³.

Each body cube has (10³¹)³ * 10³¹ or 10^124 possible states as a more practical number.

That block of points with their EMF potentials describes you sufficiently to identically recreate you. The question is, how many such blocks might exist throughout the infinite universe that are equal. That is merely a matter of statistics.

How many of those cubes are throughout the infinite (cubic) universe?

Vu / infA³ = (infA²)³ / infA³
Vu = infA³ Human Body size cubes

Now the question is, what is the probability that any two of those are exactly like yours?

The probability that another one is exactly identical is simply 1 / 10^124 and that another randomly generated cube is not identical is
np = 1 - 1 / 10^124

But then we have infA³ cubes so the probability that none of them are identical to yours, is np^infA³ or
Probability of being unique = (1 - 1 / 10^124)^infA³ = 0

So there is actually no possibility that you are totally unique in the infinite universe. So then the next question is, how many of you are there likely to be?

Well, if you have 1 million random numbers that are either 0 or 1, the chances are that half of them (1 million / 2) are 0 and half are 1. And if the numbers could have been 1, 2, or 3, chances are that 1/3 of them (1 million / 3) are each of those numbers. And if the numbers could have been from 1 up to 10^124, then the chances are that 1 million / 10^124 are any particular number chosen .. a pretty small number.

But then if you had infA³ numbers that might be anywhere in a range of 10^124, the chances are that:
infA³ / 10^124 are any one of the 10^124 numbers. And what that means is that the number of you's in the universe at any given time is:

Number of You's = infA³ / 10^124 ≈ infA³

And no matter how accurate you choose to measure yourself, you are still going to have approximately infA³ of you, regardless of your state.

[Amorphos]

^^ IF the physical universe is infinite. As far as I know energy is limited and conserved.

I infinite you then have to ascribe finite values to define its cardinality, an infinite number of red and of blue planets for example. These sets have to be within an encompassing infinity which would necessarily have no cardinality as it contains all and isn't restricted to particulars. this [eternity] infinity would not have boundaries and would fill everything everywhere, if it were carbon or an infinite lump of iron you can see how there would be nothing left. ergo if infinity were physical, there would be nothing else, hence the physical universe is not infinite and that is why it has an amount of energy/mass and not an infinite amount.

[Aussenseite]

It would be only the calculations and logic able to be moved or recalled without hormones that could be transferred or downloaded.

You might have all the memories and experiences, but what sense of weight would they have without the associated hormones and chemicals those hormones react with and to that give those things weight. What would put them in an order that makes up who you are? If we were mere calculators, without emotion, hormones, and sensory input that would be able to apply real value to anything then we wouldn't and couldn't be human. We would have no instinct, no impetus to move thoughts and memories one way or another. We would no longer be us, because we are human and to be human, we need those chemical reactions to become who we are. The chemicals in our brains are directly related to things outside the brain like glands and organs that we have only just begun to understand and may never know or understand fully. I don't believe in the "spirit" or "soul" per se, but we are ever valuing human creatures and without those inputs we would cease to be human.

Even a baby produces hormones and chemicals to cry when it is hungry or cold... what would be the driver to improve? Just to amass more knowledge? To what end? Is knowledge what makes us human, or how we weight each piece of knowledge that makes us us? Do we learn only to feed our ego? And what is ego without the feeling of pride and accomplishment without chemicals? We know that different humans have different chemical and hormonal changes within them that exist outside the brain. Unless you could replicate all of that with all those scenarios and changes within them, I do not believe it would be possible to think like a human brain outside of human sensory input and chemical reactions.

[James S Saint]

^^ IF the physical universe is infinite. As far as I know energy is limited and conserved.

And who told you that energy is limited? Whoever it was, lied (or meant something else).

You might have all the memories and experiences, but what sense of weight would they have without the associated hormones and chemicals those hormones react with and to that give those things weight.

Excellent point. The entire body should be uploaded (not "downloaded") so that the associated mind matches the body and brain that formed it. The same governance does not fit all races of people.

[Gamer]

The mention of hormones is astute. Our "self" is, of course, a culmination of senses and thoughts, moods and existential fabric composed of all the billions of sense inputs and outputs in our bodies, including the chemical stew of dopamine and hormones and a million other things. I suppose the assumption is this stuff could be simulated as well and the exact situation could be reproduced elsewhere. Also, consider that if I take Prozac, I'm still me, so there's, I'd say, wide variance to the neurochemical stew allowed while still maintaining an overall identity or self.

What's strange is we tend to think of our consciousness as pure. Much in the same way a child thinks their native language is self-evident and absolute. Our sense and experience of self is idiosyncratic to human physiology and our evolved way of relating to self and world. There is no pure consciousness, just a human consciousness. We'll find out just how far away we are from pure or absolute consciousness, or if such a thing exists, or if I'm talking complete nonsense.

[Gamer]

I think one possible answer is we allow our brains to grow and augment, and yet the new parts would be inorganic, but function the same way. The organic brain and inorganic sections would reveal what perception and identity is like across both mechanisms. If the brain can continue to grow within the new substrate and create redundancy, and if we can confirm "seat of consciousness" extends to these new areas, we can then slowly migrate most functions, and eventually all functions to the new areas. The difference here is the neurogenesis of the new material, completely integrated with and flowing out of as adjunct, the organic portions. It's a growing brain. What is revealed is what we probably in our hearts know, is that consciousness, and life itself, is a material process that can, in theory, be reverse engineered using inorganic material. But, the key difference in this protocol, is it's not "reverse" engineering. The new consciousness host grows in a very similar way as the old one, rather it's incubated and integrated with organic-hosted consciousness from the onset. Remember, the key here is a non-organic brain, which aside from being more durable and repairable, it can finally act as a server for a more cloud-based consciousness. Only then will we be able to really experiment with the so-called locus of perception, the ghost in the machine, and where exactly that sucker is hiding, or if he exists at all. We can look forward to a deeply philosophical and possibly literary experience. Science will truly blow our minds. We may as a species, suffer a sickness unto death. I think it's crucial that philosophers proactively study this topic. It may only be twenty years out.

[Orbie]

I think that it may prove a useless endeavor to seek an ultimate answer to what 'consciousness' really is, because 'it' can be hypothesized, that it is something, not necessarily some thing. Even if, consciousness predicates a difference from basic animal awareness, even then, it becomes anathema whether it is material, or not. I think , or Inuit may be a better word here, that at the point of realizing the difference, 'it ' may play the same kind of trick that the two slit experiment discovers, as when uncertainty changes the behavior of minute physical particles. At that point, or at some point, the difference does little matter, in in some strange ,odd way, they may then undefinable.

The same with trying to identify a point at which discern ability, in fact plays a part in the identification process. Fairly good descriptions of states at that particular point in time and space, is most that ever can be established, and I do think, this will never ever be cleared entirely, because of uncertainty.

[Orbie]

James:even if, the math is good, however here is the problem: description of such terms as 'unique', 'identical' are merely nominal=signs, with the quanticised concept. There are no concepts of absolute equivalency, since such an absolute has never been demonstrated, on the meta physical level under the molecular level. Atomic descriptions are based on probabilistic certainty, and for that the assumption of identity among atoms, is conceivably necessary. However, it too is only descriptive, as is the language which hypothesized it. It must be so and so, because it acts as such. That metaphysics postulated atomism very early on, seems to me, that
such descriptions have an a-posteriori hierarchy. It is like a very early picture planted in the mind, by the
very langusge, giving rise to the description.

Cosmologically, there are no perfect orbits of

planetary or galactic systems, all of them are slightly elliptical, as if slowly changing orbital patterns would
Give more stability to sustaining the orbit. Now an
absolutely circular motion, would , as energy systems
entropy, due to the decrease of gravity, the system would more likely degrade and entropy, then in a complex elliptical movement.

The absolute is knocked out of the perfectly identical cosmological argument, even on this basis. It is only
The genesis of our language description which gave rise to the idea.

So, on basis, of this argument, it is highly uncertain, that there are in the universe, any two things exactly identical. It may work on a mathematical model, using matrix and probability functions, but, they become privy to the way they were conceived in the first place. For all practical purposes, Newtons formula worked as long as the meta-physics did not require a fine tuning of it, or as long as perception didn't require more exact definition. This came in the form of differentiation of many variables, strangely enough , almost simoltenilusly, by two concurrent thinkers : Newton and Leibnitz, or so they claimed.

[Aussenseite]

The mention of hormones is astute. Our "self" is, of course, a culmination of senses and thoughts, moods and existential fabric composed of all the billions of sense inputs and outputs in our bodies, including the chemical stew of dopamine and hormones and a million other things. I suppose the assumption is this stuff could be simulated as well and the exact situation could be reproduced elsewhere. Also, consider that if I take Prozac, I'm still me, so there's, I'd say, wide variance to the neurochemical stew allowed while still maintaining an overall identity or self.

People who have been on psychotropic drugs that alter the chemical reactions in their brains might argue that they do not feel themselves, and in fact, are not themselves while taking it. They cannot experience things they same way they would if the chemicals were not altering their brains because even just the smallest bump in peaks and valleys in the levels of dopamine, serotonin, hormones and other chemicals cause a wide array of different reactions on their own and in partnership with one another. Right now, the possibilities would be nearly infinite given the number of the humans on the planet and unsurmountable given how very little of the human brain we actually do understand. It is a far more complex a machine than our miniscule minds with their tiny capacity can understand.

The bigger question is. Why would you want to?

Do we really think we are that important to the universe?

[Moreno]

Downloading a working model of your brain, all the neurons, down to the synaptic charge, is theoretically possible. Hundreds of billions of neurons can be scanned and mapped in a working model. Most scientists agree on the feasibility of this statement, and it could plausibly happen in the next few decades, maybe sooner. We've already done it with a section of a rat brain. Let's assume for sake of argument all the above is true.

What is exciting about this? When I read about it, my emotions are mixed. On one hand, it's a way to preserve a brain in terms of brain states, and possibly even a mind. That's neat. But on another hand, it's oddly unsatisfying, because I'm unclear as to how this can lead to continuation or transfer of identity. If you could clone your brain into a robot in the next room, once you were aware the deed was done, would you be willing to die as a simple matter of housekeeping? Of course not. Because the robot isn't YOU. It's a copy.

No, it's as poor as uploading in terms of 'getting to experience stuff later instead of dying before that. Unless one believes in souls and the soul is essentially dragged into the copy. (In a sense I do believe in souls, myself, but very few of the people planning and yearning for these kinds of 'solutions' do, so I wonder what they think is so neat beyond the 'hey, we managed to accomplish something tricky that might have other uses. And those other uses should make one really nervous. Governments + could torture doubles to get information. you could put it in situations and see what it does/would do for use in predicting the behavior of originals. You could replace workers (taken in the broad sense. And likely many other creepy but no doubt 'efficient' instrumental reasonings could be brought to bear on this product)


You're touching on one of the areas where science or technology or corporations are religious in nature and it is obvious. (I think it is happening in many other places, but less out in the open) Here they are trying to do what religion offers or promises in a way their minds are comfortable and are in control and using skills their minds value and have. Underneath this is some of the competition and envy and fears of inadequacy underneath a lot of what gets presented as rational argument and realism.)

[James S Saint]

James:even if, the math is good, however here is the problem: description of such terms as 'unique', 'identical' are merely nominal=signs, with the quanticised concept. There are no concepts of absolute equivalency, since such an absolute has never been demonstrated, on the meta physical level under the molecular level. Atomic descriptions are based on probabilistic certainty, and for that the assumption of identity among atoms, is conceivably necessary. However, it too is only descriptive, as is the language which hypothesized it. It must be so and so, because it acts as such. That metaphysics postulated atomism very early on, seems to me, that
such descriptions have an a-posteriori hierarchy. It is like a very early picture planted in the mind, by the
very langusge, giving rise to the description.

Cosmologically, there are no perfect orbits of

planetary or galactic systems, all of them are slightly elliptical, as if slowly changing orbital patterns would
Give more stability to sustaining the orbit. Now an
absolutely circular motion, would , as energy systems
entropy, due to the decrease of gravity, the system would more likely degrade and entropy, then in a complex elliptical movement.

The absolute is knocked out of the perfectly identical cosmological argument, even on this basis. It is only
The genesis of our language description which gave rise to the idea.

So, on basis, of this argument, it is highly uncertain, that there are in the universe, any two things exactly identical. It may work on a mathematical model, using matrix and probability functions, but, they become privy to the way they were conceived in the first place. For all practical purposes, Newtons formula worked as long as the meta-physics did not require a fine tuning of it, or as long as perception didn't require more exact definition. This came in the form of differentiation of many variables, strangely enough , almost simoltenilusly, by two concurrent thinkers : Newton and Leibnitz, or so they claimed.

First you say there is no concept of absolutely identical. Then you say that it is highly uncertain that two things are exactly identical. And I don't think the Newton and Leibnitz thing is at all strange.

The existence of absolute equivalency is irrelevant. No two atoms in your body are identical to even themselves one nanosecond later. There is a quantum level of concern below which the differences become irrelevant. If every atom in your body is replaces with another of the same type, even though always slightly different, you would never be able to tell the difference. You would not even be able to scientifically discover the difference.

My calculations were down to the Plank level. You could go down much further than that, but the Plank level is far, far, far below anything measurable by any means.

[Ultimate Philosophy 1001]

It can be calculated that at every instant in time, there are over an infinity of replicas of you throughout the infinite universe. And when I say "replica", I mean down to every single atom. And at each of those moments, every one of your replicas are thinking the exact same thing. Such has always been true and mathematically unavoidable. Although I should add that divergence begins immediately as each replica begins to become different and what were close to replicas begin to become exact replicas. So your identical replicas are never in the same place as they were just an instant earlier.

You have zero evidence of this. At most, you could argue that all of our past selves are simply clones, because they are all points on the timeline and you can't quantify instances of separation on the timeline so they are all infinite amounts. In actuality though it's more like you are a single entity and time warps around you. But you have no evidence of an infinite universe with infinite replicas, that is just a hypothesis you made up, no different than the big bang or "nothing is a bubbling something" or similar made up hypotheses.

[Orbie]

It is true, that one could never tell or discover the difference, but, that there is a difference, is a necessary part of the differentiation in the first place.
Differentiation, or, exclusion, or dis-identification, is the new method of discovery , as such, since the
method has been changed from Descartes on, culminating with Leibnitz/Newton. It is the method it's self which requires the idea of the difference, as a
built in feature, even though not observable. If it is
hypothesized, as You point out, that, there may be a future requirement to descend below the level of Plank measurement, then the differential will be
applied, whether or not, they can actually make an
observable, or even theoretically demonstrated. The demonstration on this level, is as You put it, does not make the difference, on it's equivocal and identifiable

Procedure, or method, however such an assumption is inclusive in it's methodology.

[James S Saint]

To this topic, 100% exactly perfect reproduction is irrelevant.

[Orbie]

Here again, I will not source for other reasons, but to point to the distinctive analytic feature of derivation, as Leibnitz was wont to in his reaction to Descartes' method, re: Pappus, a fellow who distinguished analytic and synthetic derivation of mathematical symbolism.

In particular, and this is referents to my acquisition as purely analytic, as well, so much so that it re-iterates Plato's Phaedo, that the early classical thinkers separated geometry from algebra, which Rennaissance thinkers confounded.

Again, I found this important difference , early on, but later to offer only confusing and differing methods of derivation , r(x), whereas analytics posit
an ideal model, just as Lebnitz has done, drawing or synthesizing algebra out of geometry, drawing calculus out of trigonometry. The fact, that Papus thought that, the classisists drawing algebra out of geometric principles, proved that they were aware of such distinctions, but held it back due to their misgivings of making such pre-determinations useful, necessary, or, understandable, within future, unwarranted assumptions. To my mind this proves the futility of holding the unpredictable and unmeasurable, infinitesimal measurements irrelevant.

[Orbie]

Correction: the dialogue cited above was incorrect, it is the Meno, and not the Phaedo.