This chapter explains in detail how one attains special powers in Yoga.  This is the first text I have read that claims that super-human powers can be achieved through a systematic physical and concentration practice.  It’s like you read that eating a particular fruit at a specific time will help you run a 5-minute mile; wouldn’t you try it?

The basic premise is that by directing awareness to a single topic–a physical object or a concept like space or time–one gains mastery over it.  This results in going beyond physical laws and attaining supernatural powers.  These powers are eventually obstacles in the objective of attaining liberation, but they are available as a byproduct along the journey.

1. देशबन्धश्चित्तस्य धारणा॥ ३.१॥

Dharna(concentration) is holding the mind on a specific object

2. तत्र प्रत्ययैकतानता ध्यानम्॥ ३.२॥

Sole focus on the flow of thoughts that are evoked by holding the chitta on a single object is Dhyana (meditation)

Many translations simply translate it as Constant flow of Dharna is Dhyana. The word used is pratyaya. Pratyaya occurs several times in the Yog Sutra and means that cognitive effect. So the sutra states that while dharna is the focus on the object, dhyana is focusing on the cognitive effects in our chitta themselves (not the object). 

3. तदेवार्थमात्रनिर्भासं स्वरूपशून्यमिव समाधिः॥ ३.३॥

When giving up all forms, one reflects only on its meaning (in dhyana), and the Self drops away, that is Samadhi (integration)

When we concentrate on an object, we are looking at its form (shape, color, size of a physical object, or sound, or spelling of a concept). Then we concentrate on the cognitive image, the colorings it evokes in our mind, that is dhyana. When we continue to concentrate and only focus on its meaning, dropping both the form of the object and the cognitive coloring, that is samadhi.  At this stage, the object has dropped off, and any prior colorings, its current impression on your chitta is the only thing remaining. 

4. त्रयमेकत्र संयमः॥ ३.४॥

These three steps practiced on one object are together called sanyam. (perfect control)

5. तज्जयात् प्रज्ञालोकः॥ ३.५॥

This the way to know the world.

6. तस्य भूमिषु विनियोगः॥ ३.६॥

This can be applied in many fields and stages

7. त्रयम् अन्तरङ्गं पूर्वेभ्यः॥ ३.७॥

These three steps are more internal than the earlier steps

Earlier, we had talked about the five steps of Yama (external rules), Niyama (internal rules), Asana (postures), Pranayama (control of life force), and Pratyahar (withdrawal of senses from external objects).  These were about how we behave with our physical body and senses.  Now we are talking about steps which are more internal to our mind process.

8. तदपि बहिरङ्गं निर्बीजस्य॥ ३.८॥

Even these are external compared to the seedless Samadhi (integration)

As we had read in Chapter 1 on Samadhi (verses 42-51), there are various stages or types of Samadhi.  The final stage is seedless Samadhi in which even the meaning of the object has dropped of and we are absorbed in pure consciousness.

9. As the mastery on samsakaras emerges and the effect of samsakaras decline, we reach the state of stillness (nirodha parinama)

Our mind is filled with latent impressions (samskaras).  As these latent impressions emerge, we create opposing impressions to suppress them.  These controlling impressions are also modifications of our consciousness.  When all such impressions (existing and new ones to control the existing) cease, then we have perfect stillness.

10. व्युत्थाननिरोधसंस्कारयोः अभिभवप्रादुर्भावौ निरोधक्षणचित्तान्वयः निरोधपरिणामः॥ ३.९॥

As the control (nirodh) emerges, and the samskaras (latent impressions) subside, there is a moment of transition where chitta is in stillness, resulting in a state of nirodh (complete stillness)

By constant practice, the mind is established in stillness.  No latent impressions are emerging, and neither are the controlling impressions to still the latent ones.  The only impression is one of stillness.

11. सर्वार्थता एकाग्रतयोः क्षयोदयौ चित्तस्य समाधिपरिणामः॥ ३.११॥

Consciousness gets integrated (samadhi) as multi-pointedness decays and one-pointedness emerges

12. तदा पुनः शान्तोदितौ तुल्यप्रत्ययौ चित्तस्यैकाग्रता परिणामः॥ ३.१२॥

Then again, same thought emerges and recedes in same pattern, rsesulting in one-pointedness.

There is a virtuous self-reinforcing cycle here.  As one concentrates one’s mind, stillness and peace emerge, and as stillness increases, the focus and concentration increase on one essence

13. एतेन भूतेन्द्रियेषु धर्मलक्षणावस्थापरिणामा व्याख्याताः॥ ३.१३॥

In this way (of one-pointed samadhi), we understand the transitions in essence, characteristics, and condition of the elements and our organs

The verse specifically talks about “dharma lakshana avastha”.  Vivekananda and Swami J has translated it as form, timespan, and condition.

14. शान्तोदिताव्यपदेश्यधर्मानुपाती धर्मी॥ ३.१४॥

A common indescribable substrate exists from which every form emerges through transitions

If everything emerges from the same substrate, why are they different? Is it the choice of the emergent, or random coincidence? A choice would place the ownership on the form, and random would give us a more accepting outlook.

15. क्रमान्यत्वं परिणामान्यत्वे हेतुः॥ ३.१५॥

This sequence of transitions varies and results in differentiation in form

Again, the variation in sequence of transitions is a choice or random.

16. परिणामत्रयसंयमाद अतीतानागतज्ञानम्॥ ३.१६॥

By samyam (perfect control) on essence, characteristics, and condition comes knowledge of the past and future.

17. शब्दार्थप्रत्ययानाम् इतरेतराध्यासात् संकरस् तत्प्रविभागसंयमात् सर्वभूतऋतज्ञानम्॥ ३.१७॥

Word, meaning, and our cognition of it get mixed up, and samyam (perfect control) on the distinction of these gives us knowledge of all beings

Swamij.com’s translation of rta is sound which I think is inaccurate.

18. संस्कारसाक्षात्करणात् पूर्वजातिज्ञानम्॥ ३.१८॥

Direct observation of the samskara gives us the knowledge of the earlier birth

As they say, an apple does not fall far from the tree. Observing a person’s samskaras gives us an understanding of the person’s antecedents

19. प्रत्ययस्य परचित्तज्ञानम्॥ ३.१९॥

Focusing on perceptions and thoughts of others, one knows their chitta

This is like the blotter test–a person is shown ink blots and asked to describe them. The description they come up with shows the state of their chitta

20. न च तत् सालम्बनं तस्याविषयीभूतत्वात्॥ ३.२०॥

But not the basis of their chitta, which are not present in the mental thoughts

21. कायरूपसंयमात् तद्ग्राह्यशक्तिस्तम्भे चक्षुःप्रकाशासंप्रयोगेऽन्तर्धानम्॥ ३.२१॥

When a body’s form is observed with perfect control (samyama), one can control its property of “see-ability”; thus, restricting the body’s basis to engage with the light, it becomes invisible to another eye

This describes the process of becoming a black hole!

22. एतेन शब्दाद्यन्तर्धानम् उक्तम्॥ ३.२२॥

In this way, sound and other sense perception of our form can be made to disappear

23. सोपक्रमं निरुपक्रमं च कर्म तत्संयमादपरान्तज्ञानम् अरिष्टेभ्यो वा॥ ३.२३॥

Some actions bear fruit immediately, and some bear fruit slowly, by perfect control (Samyama) on that, and on signs (arisht), one can know the time of death.

24. मैत्र्यादिषु बलानि॥ ३.२४॥

By focusing on friendliness, etc. one gains strengths.

1.33 tells us to have friendliness towards people who are happy, compassion towards people who are unhappy, gladness towards the virtuous, and indifference towards the unvirtuous. By focusing on these attitudes, they gain strength.

25. बलेषु हस्तिबलादीनि॥ ३.२५॥

By focusing on strength one gets strengths of an elephant.

26. प्रवृत्त्यालोकन्यासात् सूक्ष्मव्यवहितविप्रकृष्टज्ञानम्॥ ३.२६॥

By making perfect control (samyama) on light, one can see the remote, hidden and very fine.

27. भुवनज्ञानं सूर्येसंयमात्॥ ३.२७॥

By samyama on sun comes knowledge of the universe

28. चन्द्रे तारव्यूहज्ञानम्॥ ३.२८॥

By samyama on moon comes knowledge of the stars

29. ध्रुवे तद्गतिज्ञानम्॥ ३.२९॥

By samyama on pole star (dhruva tara) comes knowledge of motion of stars

30. नाभिचक्रे कायव्यूहज्ञानम्॥ ३.३०॥

By samyama on the navel, comes knowledge of body constitution

31. कण्ठकूपे क्षुत्पिपासानिवृत्तिः॥ ३.३१॥

By samyama on hollow of throat, comes cessation of hunger and thirst

32. कूर्मनाड्यां स्थैर्यम्॥ ३.३२॥

By samyama on Kurma (nerve) comes stability in the body.

33. मूर्धज्योतिषि सिद्धदर्शनम्॥ ३.३३॥

By samyama on light emanating from the top of the head, one can see the siddh(accomplished)

34. प्रातिभाद्वा सर्वम्॥ ३.३४॥

Or through enlightenment, one gains all this

One way is to focus on one thing at a time, but the other is to attain enlightenment, and then all this is accomplished in one go

35. हृदये चित्तसंवित्॥ ३.३५॥

By samyama on heart, one knows the mind

36. सत्त्वपुरुषयोः शुद्धिसाम्ये कैवल्यम्॥ ३.३६॥

By samyama on a feeling non-separation between pure consciousness (purusa) and the subtlest part of chitta (budhi) attains the knowledge of purusa (the doer).

37. तस्य पञ्जातयः सिध्दयः॥ ३.३७॥ or ततः शरीरेंद्रियसिद्धिः॥ ३.३७॥

From this omniscience one gets perfect hearing, touch, sight, taste, smell

38. ते समाधौ उपसर्गः व्युत्थाने सिद्धयः॥ ३.३८॥

The emergence of powers is an obstacle in achieving samadhi, though to outside mind they appear as achievements

So while these powers may appear to be special attainments but they are obstacles in the path of ultimate samadhi and attainment.

39. बन्धकारणशैथिल्यात् प्रचारसंवेदनाच्च चित्तस्य परशरीरावेśः॥ ३.३९॥

By relaxing one’s attachment to the body and becoming sensitive to someone else’s chitta, one’s consciousness can enter another’s mind (chitta)

40. उदानजयात् जलपङ्ककण्टकादिष्वसङ्गः उत्क्रान्तिश्च॥ ३.४०॥

By mastering the flow of  upward breath (udana prana), one is unaffected by water, mud, thorns, and other such obstacles by rising above them

41. समनजयात् ज्वलनम्॥ ३.४१॥

By focusing on the flow of lifeforce (prana) through the solar plexus (saman vayu), one kindles inner fire

42. श्रोत्राकाशयोः सम्बन्धसंयमात् दिव्यं श्रोत्रम्॥ ३.४२॥

By samyama on the relationship of space and ear, one gets divine hearing

43.कायाकाशयोः सम्बन्धसंयमात् लघुतूलसमापत्तेः च आकाशगमनम्॥ ३.४३॥

By samyama on the relationship of the body with space and developing samapatti on the lightness of cotton, one can travel through space

44. बहिरकल्पिता वृत्तिः महाविदेहा ततः प्रकाशावरणक्षयः॥ ३.४४॥

When consciousness completely separates from the great bodily disturbances (vrittis), then the covering on light is lifted

45. स्थूलस्वरूपसूक्ष्मान्वयार्थवत्त्वसंयमात् भूतेषु तत्जयः॥ ३.४५॥

By samyama of relation between gross form, essential nature, subtle essence, purpose,  and their interconnectedness, one gets mastery of elements

46. ततोऽणिमादिप्रादुर्भावः कायसम्पत्तद्धर्मानभिघातश्च॥ ३.४६॥

From that (above), the special power to become small is attained as body attains perfection, which is beyond normal natural laws

47. रूपलावण्यबलवज्रसंहननत्वानि कायसम्पत्॥ ३.४७॥

The perfection of the body includes the beauty of form, grace, strength, and durability of a diamond.

48. ग्रहणस्वरूपास्मितान्वयार्थवत्त्वसंयमात् इन्द्रियजयः॥ ३.४८॥

By absorbing your own form, sense of self, pervasive meaning to all objects, one masters the sensory apparatus

49. ततो मनोजवित्वं विकरणभावः प्रधानजयः॥ ३.४९॥

Free from their organs, sense perceive very fast like mind

50. सत्त्वपुरुषान्यताख्यातिमात्रस्य सर्वभावाधिष्ठातृत्वं सर्वज्ञातृत्वं च॥ ३.५०॥

Seeing the difference between sattva (the goodness element of buddhi) and the pure doer, all conditions become known, and omniscience emerges

This concept is similar to the one in the Gita, which involves transcending the tri guna (pure, active, and passive) to a sense of pure action, which is even beyond the three material states.

51. तस्यापि निरोधे सर्वनिरोधान्निर्बीजः समाधिः॥ ३.५१॥

When even this (mastery over prakṛti) is restrained, the seedless samādhi (nirbīja samādhi) arises through the cessation of all mental modifications.

52. स्थानीय उपनिमन्त्रणे सङ्गस्मयाकरणं पुनरनिष्टप्रसङ्गात्॥ ३.५२॥

Even if the higher beings invite, one should not feel pride, else unnecessary suffering will arise

As one gets these supernatural power, if pride arises, then suffering will inevitably follow

53. क्षणतत्क्रमयोः संयमात् विवेकजं ज्ञानम्॥ ३.५३॥

By samyama on the sequence of each moment, one gets discrimination born of knowledge

54. जातिलक्षणदेशैरन्यतानवच्छेदात् तुल्ययोः ततः प्रतिपत्तिः॥ ३.५४॥

This discrimination power allows one to tell apart things which may appear the same due to type (form), time attributes, or place.

55. तदः क्षयात् विवेकख्यातेरधिगमात् कैवल्यम्॥ ३.५५॥

With the destruction of impurity and the rise of discriminative knowledge (viveka-khyāti), liberation (kaivalya) is attained.

56. सत्त्वपुरुषयोः शुद्धिसाम्ये कैवल्यम्॥ ३.५६॥

Once the goodness of nature (sattva of chitta) is purified as pure doer, it is equal to establishing singular awareness (kaivalyam)

{The shloka 3.51 to 3.56 are different in different renditions. I have picked the flow that made sense to me}