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The Ultimate Atom

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Parmāṅu – the ultimate atom is our topic of discussion today. As it is a big topic, we may have to extend our today’s class.

“O! Finally! I have been waiting for it. No problem in extending the class”, exclaimed Dravya. “So, is it really the ultimate?”

Yes, the ultimate eternal unit of all the observables. It can neither be created nor destroyed and cannot even be transformed to & from something else. It cannot be broken any further.

Basically it means that each parmāṅu was always there and will always be there. And even the total number parmāṅu in the lok also never changes.

Yes. And hence permanent, from that perspective. Moreover, it is a true point, occupying just one space point.

So, it doesn’t have any length, breadth or depth?

Yes, it doesn’t. It is truly infinitesimal having no beginning, end or middle.

So, does it not have shape?

No, it doesn’t. Only pudgal aggregates, spanning over multiple space points, create the notion of shape.

What about its mass?

It is truly massless, i.e. have zero mass, and hence its speed is not limited by the speed of light. In fact, it can travel from one end of the lok to the other end in one samay (smallest unit of time), thus achieving its maximum speed.

But isn’t even light massless?

Not really. Light consists of photons which are not really zero mass equivalent, as they have energy.

So then, how does aggregates composed of parmāṅu get mass?

It is not all aggregates. Only those with infinite parmāṅu, as then zero into infinity becomes some finite quantity. Interestingly, also note that, parmāṅu and other zero mass aggregates are as such of no use to jīv. Hence, if any pudgal is getting used or perceived by us – the jīv – it must have mass.

That’s really interesting.

Coming to motion or movement, parmāṅu is the only thing, ultimately responsible for all dynamism. All but pudgal & jīv are motionless. And jīv also is dynamic only in its worldly existence and that also due to its association with pudgal of karm & other vital functions.

“So basically pudgal is the only one with dynamism – motion or movement”, summarized Gati.

Sort of. More correctly, pudgal is the only substance with inherent dynamism. But that doesn’t mean that it is always dynamic. Let’s dig into it, to understand it further. Dynamism could be classified into two types: 1) Motion and 2) Fusion-Fission

Fusion is combining & Fission is separation of pudgal, right?

Yes, we already talked about this dynamism as differentiator of pudgal, and also that this doesn’t happen always. Motion can be further divided into three types: 1) Vibratory, 2) Rotatory, and 3) Migratory. Even these motions don’t happen always – there are periods of motion & rest interleaved. However, these motions could be either inherent or influenced by external forces. And this self-induced inherent motion is the one which makes pudgal inherently dynamic.

Could this vibratory motion be treated as the reason for say spontaneous release of energy?

Yes – very well thought.

Laws of Motion

Note that, these details of dynamism reveals that even dynamism of pudgal is quantized. All these and more are summarized in the following laws of motion:

  1. A parmāṅu can remain at rest on a single space point for a minimum of one samay (time point) and a maximum of innumerable samay, after which it must do one or more types of the above mentioned motion.
  2. A parmāṅu can remain in motion for a minimum of one samay and a maximum of innumerableth part of an āvalikā (Refer to our discussion on the expanse of time for detail on āvalikā), after which it must come to rest.
  3. Minimum and maximum distances covered by a parmāṅu in one samay are one space unit (space between two adjacent space points) and entire length of lok, respectively. And that defines its minimum and maximum speed.
  4. Parmāṅu moves in a straight line unless acted upon by external forces. This movement is called anushreṅī gati. The movement in one samay is always of this type.
  5. When acted upon by external forces, parmāṅu may change direction and speed, but within the above limits.

Some of these sound like Newton’s laws of motion.

Yes. In fact, these are the governing principles for Newton’s laws of motion.

Principle of Uncertainty

However, even after these definites, there are the following sets of uncertainties about the motion of a parmāṅu, which shows up as the principal of uncertainty:

  1. Exact durations of rest and motion, though minimum and maximum are defined.
  2. Direction & Speed to be taken by the parmāṅu, at the commencement of its motion.
  3. Kind of motion to be taken up by a parmāṅu at rest, i.e. one of vibratory, rotatory or migratory, or any of their combinations.

Eye opener detail with both certainties & uncertainties coded into the signature of parmāṅu. Does that mean that a parmāṅu can do whatever it likes, go wherever it likes?

Again anekāntvād in action, both yes & no – apratighāti (not restricted) and pratighāti (restricted). It is not restricted to move, by any other pudgal or jīv as such. It can without any hindrance, penetrate through them, pass through them, occupy & leave a space point occupied by them, without any effect on its rest & motion due to rest of the occupants of the space point. However, its motion & rest are restricted only within the lok (upkārbhāv pratighāti), i.e. it cannot cross the boundaries of lok into alok, as dharmāstikāy (medium of motion) and adharmāstikāy (medium of rest) are absent from alok. Moreover, its motion is restricted & influenced by others in an aggregate, when it is not lone but part of the aggregate (bandhan pariṅām pratighāti). And finally, two self-activated parmāṅu moving at high velocity may cause restrictions in the motions of each other (ati veg pratighāti).

That’s lot of pointers to research into the field of particle physics as well as astronomy, possibly to find the unifying laws of the universe.

Yes indeed, as parmāṅu is the ultimate unifier.

Laws of Fusion

As you are already motivated for further research, it’s right time to talk about the fusion & fission dynamism as well, like we have talked about the motion dynamism. The laws governing fusion in particular are:

  1. A parmāṅu with just one ultimate intensity unit of positive or negative touch never fuses with anything. However note that, parmāṅu inherently keeps changing its intensities of touch, taste, smell, and colour, i.e. the intensities are not permanent. So, it is non-fusable only till it has just one unit of positive or negative touch.

“Can a parmāṅu inherently change its colour, smell, etc, not just their intensities?”, asked Yog.

No it cannot, in its lone state. However, colour etc can be changed by the parmāṅu after its union with others.

  1. Two parmāṅu of same touch (i.e. both positive or both negative) can fuse/combine only if the difference between their corresponding touch intensities is at least two units.
  2. Two parmāṅu of opposite touches (i.e. one positive and one negative) can always combine if each of their intensities is greater than one.

Can two parmāṅu of same touch, one with intensity of one unit and other with three or more units combine?

No. As per the first law, a parmāṅu with just one unit intensity can never combine. Then only, the second and third law comes into picture.

Okay. So second law can be stated as two parmāṅu with same touch can combine only if their touch intensities are X & X + n, or viceversa, where X > 1 and n >= 2.

Yes mathematician smiled the professor. Furthermore, fusion could be of two types: 1) Natural, and 2) Produced by jīv. Natural one can have three possible causes: 1) Fusion due to opposite touch properties – bandh pratyayik, 2) Fusion due to being in same container – bhājan pratyayik, 3) Fusion due to mutation – pariṅām pratyayik.

Do we have laws governing fission also?

Not anything specific. Just that parmāṅu is non-fissionable. And, other aggregate pudgal can fission/separate into as many smaller parts as possible with all possible combinations of parmāṅu in them.

Meaning say a four parmāṅu aggregate can break into two aggregate of 1 & 3 or 2 & 2 parmāṅu, or three aggregates of 1, 1 & 2 parmāṅu, or four aggregates each of 1 parmāṅu.

Perfect. Now, after extensive discussion on dynamism, let’s come back to the four characteristic qualities of pudgal. A parmāṅu would exactly have any one colour out of the five, any one smell out of the two, any one taste out of the five, and exactly two touches each one out of the first two & next two, respectively.

“Yes, as we talked earlier. Specifically, one touch of either cold or hot, and one of either positive or negative”, completed Viṡay.

Perfect. You guys are awesome.

And, various combinations of these four touches form the remaining four touches. But can you tell us the various combinations?

Plentifulness of rukṡ (negative) touch leads to laghu (light) touch. Plentifulness of snigdh (positive) touch leads to guru (heavy) touch. Plentifulness of cold and snigdh touches leads to mridu (soft) touch. Plentifulness of hot and rukṡ touches leads to karkash (hard) touch.

“Are all parmāṅu, of different varieties, or all are identical?”, suddenly questioned Dravya.

Interestingly, parmāṅu just means the ultimate unit, and hence it could be of pudgal (matter & energy), or space, or time, or sensuous qualities, and correspondingly being referred as pudgal parmāṅu (the ultimate atom), kṡetra parmāṅu (the space point), kāl parmāṅu (samay – the time point), bhāv parmāṅu (the indivisible unit aka quantum of intensity of sensuous qualities, viz touch, taste, smell, colour). However, colloquially by parmāṅu we typically refer to the pudgal parmāṅu only, as this is the trigger or reference for the quantization of the other parmāṅu.

How is this (pudgal) parmāṅu, reference for the other parmāṅu?

Because it occupies exactly one space point – no less no more, i.e. kṡetra parmāṅu is quantized as the ultimate unit of space because it is the space exactly occupied by the smallest pudgal – the parmāṅu. However, note that even densely packed pudgal aggregates made up of upto infinite parmāṅu may occupy one space point.

How is that possible? Then, each parmāṅu of that aggregate must occupy less than a space point.

Not really. This is possible because of the true point nature of a parmāṅu. Similar to the space occupancy, movements of parmāṅu are always in integral space units per samay. For example, the minimum motion speed of a parmāṅu is one space unit (from one space point to its adjacent space point) in one samay – it can’t be a fraction, as it can’t take more time once it is moving. Hence, samay is the quantization of time due to parmāṅu’s movement. And the intensity of sensuous qualities is anyways quantized by virtue of the parmāṅu, itself. So, by the word parmāṅu, here or otherwise, we typically refer to the pudgal parmāṅu only.

So, are all of these (pudgal) parmāṅu identical to each other?

Yes & No. Yes for their overall characteristics – that’s how they all are pudgal. But no for their specific characteristic values, e.g. they could have different colours, smells, tastes, and touches.

Yes. But including these possibilities, can we conclude that total varieties of parmāṅu are just 200, i.e. 5 colour x 2 smell x 5 taste x (2 x 2 touches) = 200.

High level, yes. But, if you want to go in further detail, intensity of each colour, smell, taste, touch in different parmāṅu varies from one unit to infinite units. Thus, we have infinite varieties of parmāṅu, and hence, depending on the infinite varieties of parmāṅu participating in making an aggregate, we will have infinite varieties of pudgal aggregates. And thus, the material universe comprised of solids, liquids, and gases, atoms and molecules, light and darkness, sounds and shadows, is therefore, infinitely infinite.

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Matter and Energy

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We started with the understanding of science as a branch of philosophy, and after that we have talked about a whole lot of things under philosophy. Lot of new information – many beyond the realm of science, like knowledge, rebirth, … – most of which seemed not directly connected with our today’s science – some seemed to have some connection, like classification of everything, living beings, space, time. And now we shall take up the one, which has the most direct connection with science, or rather is the topic of science. And this, without any doubt, would show science as one of the aspects of philosophy. Any guesses as to what it is about?

“I guess energy, atom, …”, tried Dravya.

Yes, it is about matter & energy – the physical existence – the observable world. And as it is THE topic of science, but from a different perspective, we would like to spend a few sessions on this. The philosophical term for the same is pudgal, the collection of all of which is termed pudgalāstikāy, one of the six fundamental substances of reality.

So, it includes all the sub-atomic particles, elements, compounds, all forms of energies like heat, light, sound, …

Absolutely. And till date, all of you have been knowing all of these from purely science perspective. So, now let’s look at them from the philosophical perspective. And let’s see what more do we get, to further open up doors for deep farther reaching research into science.

“That would be amazing!”, exclaimed Tatva.

The word pudgal is formed of two parts: pud meaning combine / integrate, and gal meaning separate / disintegrate. So, fundamentally anything which undergoes modification through integration and disintegration is pudgal. In the words of modern science, anything which is fusionable and fissionable is pudgal.

Okay. But that is a definition based on when its changing. How do we identify it, if it is not changing?

Exactly, that’s why that is a definition just from one perspective. Depending on the perspective, pudgal can be defined, characterized, classified from many more ways. And to start with, we would look at a few important ones.

But fundamentally all of these would be based on its qualities only, right?

Yes obviously. And not just qualities, it is specific qualities possessed exclusively by pudgal, which distinguishes it from the other five fundamental substances. Now, out of these qualities, some are found in all paryāy (forms & form changes) of pudgal, and some only in some paryāy. The former ones are called characteristic qualities (lakṡaṅ). Pudgal has four such characteristic qualities. Anyone?

“Yes, yes, we already discussed that under the 16 specific qualities: colour, taste, smell, and touch”, quipped Viṡay.

Excellent. So, pudgal can be identified by these as well.

So you mean, every pudgal will have all four of them, or at least one of them?

All four of them.

But how about energy, like sound, heat, … – they don’t have any taste or smell?

Fundamentally, even they have – just that, it is subtle in them. Moreover, as these are the characteristic qualities of pudgal, it is the only observable or mūrt substance out of the six fundamental substances. All others are non-observable aka amūrt. But beware that, pudgal is observable doesn’t mean that we’d be always able to observe it. Observing even the observables is finally limited by our capabilities, not just of our senses but even of our instruments. So in fact, there are many observables aka pudgal, which we won’t be able to observe.

“So, humanly is it not always possible to identify pudgal using even these four characteristic qualities”, questioned Indriya.

Yes. And that’s why, we have various perspectives to look at, so that it at least fits in some. On those lines, let’s explore a very commonly used method (in philosophy) of characterising any substance. It is using the four fold determinants: dravya (substance), kṡetra (location in space), kāl (time), bhāv (qualities), plus the fifth one swabhāv (also at times called guṅ) (behaviour).

Can all substances be characterized using this technique?

Yes. But remember that it is just one of the perspectives of defining. Let’s apply the technique for pudgal. Substantially, i.e. by dravya, pudgal is infinite in number, meaning there are infinite number of different physical entities. Spatially, i.e. by kṡetra, pudgal fills the complete lok (universe). Temporally, i.e. by kāl, pudgal is eternal, i.e. without any beginning and without any end. Qualitatively, i.e. by bhāv, pudgal possesses colour, taste, smell, and touch. Behaviourally, i.e. by swabhāv, pudgal is fusionable and fissionable.

In a way, we have summarized all our (till now) understanding of pudgal in the above five determinants.

Sort of. Additionally, we can talk interactionwise, i.e. about pudgal’s interaction with soul. pudgal is capable of being taken in and transformed by soul in eight forms. Five in form of the five types of bodies, we have already discussed, while discussing variety of living beings.

“You mean: oudārik, vaikriya, āhārak, tejas, kārmaṅ”, confirmed Sharīr.

Yes. The corresponding pudgal vargaṅā (collection) is taken in by soul to transform into the respective body, e.g. oudārik pudgal vargaṅā to form the oudārik body, and so on. And, the remaining three forms are to do with the vital functions of breathing, speech, and thought. All these physiological functions of living beings are possible only by taking in the corresponding pudgal vargaṅā possessing specific properties useful for specific function.

Is it that all pudgal falls into these eight vargaṅā?

No. No. There is a infinite bunch of pudgal which doesn’t interact with soul but only with other pudgal. They don’t fall under these eight. These eight are just an interactionwise understanding of pudgal with soul – so that we know that even these are non-living pudgal, not living things.

“Hmmm. Seems like many angles to understand pudgal, but none seems to completely define it”, Viṡay expressed unsatisfactorily.

Not really true. The four characteristic qualities – colour, smell, taste, touch – completely define pudgal – it is just our incapabilities that we cannot perceive them always. Let’s further categorize them for a better understanding of pudgal.

Ok.

Colour: There are five fundamental colours – black, blue, red, yellow, white.

Meaning all other colours can be formed using these. But why black & white, they are just absence & presence of all colours, right?

Yes from science perspective, but not from inherent colour perspective of pudgal. Smell: good & bad smell. Taste: acrid / spicy, bitter, astringent (kaṡailā), acidic / sour, sweet. Touch: cold, hot, positive, negative, hard, soft, heavy, light.

So, does each pudgal have one category of quality from each of the four, meaning one colour of the five, one smell of the two, one taste of the five, one touch of the eight.

That’s not really a correct question. pudgal is a general term. So, your question is like asking – does each matter has one category of quality from each of the four. And in that case, the answer also would be a general answer – it could have multiple of them. The more specific question would be about the ultimate constituents of pudgal.

“You mean atom, or electron, or may be sub-atomic particles”, added Paryāpti.

Yes – in those lines. But even they are constituted of infinite of parmāṅu – the smallest unit of pudgal. That’s why, even they could have multiple of colours, smells, tastes, and touches.

So, even these sub-atomic particles are not the smallest unit of pudgal?

No way. Think of energy. That is also pudgal. Smallest unit of pudgal has to be the smallest unit of energy also.

“Okay. So, what colour, taste, etc does this so called parmāṅu have?”, continued Viṡay.

If you talk about a parmāṅu, it would exactly have one colour, one smell, one taste, and two touches.

Any one colour, any one smell, any one taste, and any two touches. But why two touches?

Yes, any one colour, any one smell, any one taste, but NOT any two touches. Specifically, one touch of either cold or hot, and one of either positive or negative.

What about then of the other four touches?

They are formed at a grosser level by the various combination of (parmāṅu having) the first four touches.

“So, the various pudgal vargaṅā (collection) we talked about earlier, would possibly also have the other four touches”, questioned Paryāpti.

Possibly yes, but not always. For example, the vargaṅā of each of kārmaṅ body, speech, thought always constitute of only the first four touches. And the remaining five vargaṅā constitute of all the eight touches. With this level of detailing, I hope that we’d understand the intricacies of pudgal better.

“Yes, that’s lot of detailing, and wow, there is actually an ultimate unit of pudgal – the parmāṅu. Can you share more details about it?”, probed Dravya.

Definitely, we would talk about it separately. But before that we shall complete discussing some more perspectives of defining & identifying pudgal, which might be handy when we are unable to perceive its four characteristic qualities.

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