Patañjali's yogasūtra 1:11 Smṛitiḥ

अनुभूतविषयासंप्रमोषः स्मृतिः 

anubhūtaviṣayāsaṃpramoṣaḥ smṛitiḥ

अनुभूत विषय असंप्रमोषः स्मृतिः 

Memory is not allowing a subject which has been experienced to escape [from the mind]. 

अनुभूत - experienced; past participle from anu+√bhū i.e. that which follows [a] happening 

विषय - subject, matter, object, topic; masc. noun

असंप्रमोषः - not allowing to be carried off; masc. noun from a+sam+pra+√muṣ (1P) 

स्मृतिः - memory, remembrance; fem noun

Memory, then, is the retention of experiences in the mind. These are retained in a potential state, as impressions (saṃskāra). It is when these impressions are converted from their potential state into an active mental process that it is considered a citta-vṛitti (modification/activity of the mind).

The process by which this activation takes place is complex and not fully explicable.  But to understand it, think back to the number times have you said in frustration - "Oh, his name is on the tip of my tongue ... I can see his face but I can't remember his name!"  That is the memory in the potential state. And when it suddenly 'comes back to you' (chamkaa!!) right then or maybe after a night's sleep, or a few days later, even after you've stopped trying consciously to remember - that is when it has  become an active 'memory', a citta-vṛitti.

Yogis believe that perseverance and balanced emotion can help sharpen this process - i.e. improve your smṛitḥ, your memory. They also believe that the more good saṃskāra you have, the better a person you will be.

Patañjali's yogasūtra 1:10 Nidrā

{1.10}

अभावप्रत्ययालम्बना वृत्तिर्निद्रा 

abhāva pratyayālambanā vṛittir nidrā

अभाव प्रत्यय आलाम्बना वृत्तिः निद्रा 

The modification[of the mind] based on the absence of [any] content [of the mind] is sleep 

अभाव - absence, nullity; masc. noun.

प्रत्यय - idea, concept, content of mind; masc. noun

आलाम्बना - support, basis

वृत्तिः - modification (of the mind); masc. noun

निद्रा - sleep; fem noun

During the time that a person is in this state - of sleep, the mind is, as it were, a void. It is blank. Evidently it is dreamless sleep that is being referred to here.  Commentators stress the fact that this is not similar to the state of samādhi, where also there is no content in the mind. 

Taimini explains this sūtrā simply. He says in samādhi, all content is deliberately removed while in a waking state - where as in sleep, the brain and the mind are disconnected, so that content is not recorded or registered. It's like a car that has been put into neutral. The engine is running, but because the gears are disengaged, it will not move. As soon as we wake up, the connection is re-established (the gears are engaged) and the brain becomes the seat of mental activity once again.   

Patañjali's yogasūtra 1:9 Vikalpaḥ

{1:9}

शब्दज्ञानानुपाती वस्तुशून्यो विकल्पः 

Śabdajñānānupātī   vastuśūnyo  vikalpaḥ

शब्द ज्ञान अनुपाती वस्तु शून्यः विकल्पः 

[An image] conjured up by words without any substance is fancy/fantasy

शब्द - sound, word; masc. noun  

ज्ञान - knowledge, cognizance; neuter noun

अनुपाती - following upon

वस्तु - thing, object; neuter noun

शून्यः - empty [of], nothingness; masc. noun

विकल्पः - fancy, fantasy; masc. noun

Vikalpa refers to things our mind makes up, and has no correspondence with reality, or actual experiences.  It is not based on past experience, because then it would be in the realm of memory. It is purely a creation of the mind, following words.  When I say mermaid, centaur, gingerbread house, the vritti in your mind is vikalpa. When you read The Hobbit, the mental images that get created in your mind are vikalpa. The little people in Gulliver's travel are vikalpa. To be vikapla, a vritti has to meet two conditions - it must be something conjured by words [a description] and it does NOT exist in reality.

Please also note, that vikalpa is used in regular language to mean choice, option and indecision - and that the sense of fantasy  only arises when it is used as a technical yogic term.

Das yogasutra 1:8 von Patanjali (scroll down to previous post for English)

{1.8} 

विपर्ययो मिथ्याज्ञानमतद्रूपप्रतिष्ठम् 

viparyayo mithyājñānamatadrūpapratiṣṭhitam

[Ein] falschen Eindruck auf falsches Wissen begrundet ist [in dem unser Geist] eine Vorstellung nicht von seiner [des Objekts] eigene Form hat

विपर्ययः= मिथ्या+ज्ञानं अतत्+रूपं प्रतिष्ठम्

विपर्ययः - umgekehrt, Fehler, Gegensätzlichkeit; Maskulin Nomen.. (Hindi Lautsprecher wird dies als aus der gleichen Wurzel wie विपरीत erkennen [वि+पृ 3P]) 

मिथ्या - falsch, unwahr, unrichtig; nicht deklinierbar, verwandt mit dem Eng. Mythos

ज्ञानम् - Wissen, wissend;  Neutrum Nomen von √jñā 9P

अतत् - Nicht von dass

रूपम् - Form, Aussehen, Figur, Neutrum Nomen von √rūp 10P

प्रतिष्ठम् - Zentrum, Basis; Neutrum Nomen von prati√sthā 1P

Diese vritti wird oft von den Kommentatoren mit Sankaracaryas berühmten Beispiel erklärt "sehen Seil, denken Schlange '. Grundsätzlich gibt es Kontakt mit einem äußeren Objekt, sondern das Bild / Daten der Geist bekommt zaubert eine Antwort, die nicht die wahre Form des Objekts ist. Ein weiteres Beispiel wäre die Geschichte aus dem Ramayana, in dem Dasharatha  das Gurgeln eines Wassertopf hörte und dachte, ‘dass ist ein Elefant.’

Wichtig zu beachten, viparyaya gilt nur, wenn es einen Mangel zwischen unserer geistigen Bild und dem eigentlichen Objekt gibt. Es ist nicht mit falschen Bilder, die auf das eigentliche Objekt entsprechen betroffen. Zum Beispiel, in einem Nebel oder Dunkelheit, sehen Sie möglicherweise ein unscharfes Bild von jemand, den Sie kennen, oder ein Gebäude - aber wenn es in der Tat, dass Person / Gebäude, das ist nicht ein Fall von viparyaya.

Patañjali's yogasūtra 1:8 - Viparyayaḥ

{1.8} 

विपर्ययो मिथ्याज्ञानमतद्रूपप्रतिष्ठम् 

viparyayo mithyājñānamatadrūpapratiṣṭhitam

[An] erroneous impression is based on false knowledge [in which our mind has] a conception not of its [the object's] own form

विपर्ययः= मिथ्या+ज्ञानं अतत्+रूपं प्रतिष्ठम्

विपर्ययः - contrariety, reverse, mistake; masc., noun. (Hindi speakers will recognise this as arising from the same root as विपरीत [वि+पृ 3P]) 

मिथ्या - false, untrue, incorrect; indeclinable, cognate with the Eng. myth

ज्ञानम् - knowledge, knowing; neuter noun from √jñā 9P

अतत् - not of that 

रूपम् - form, appearance, figure; neuter noun from √rūp 10P

प्रतिष्ठम् - centre, base; neuter noun from prati√sthā 1P

This vritti is often explained by commentators using Śankarācārya’s famous 'seeing rope, thinking snake' example. Basically, there is contact with an external object but the image/data received by the mind conjures a response which is not the real form of the object. Another example of this would be the story from the Rāmāyaṇa in which Daśaratha mistakes the gurgling of a water pot for an elephant.

Important to note, viparyaya only applies when there is a lack of correspondence between our mental image and the actual object. It is not concerned with erroneous images that correspond to the actual object. For instance, in a fog or the dark, you might see a blurred image of someone you know, or a building - but if it is in fact that person/building, that is not a case of viparyaya.   

Patañjali's yogasūtra 1:7

So far, sūtras 1:1-6 have informed us that one of the central aims of Yoga is to still the mind, by blocking vrittis, which are  defined as modifications or activity in the mind. Over the next 5 sūtras the vrittis are explained in more detail. 

Today we look at Pramāṇa.  

{1:7} प्रत्यक्षानुमानागमाः प्रमाणानि 

Correct/right knowledge is based on direct cognition, inference [and] testimony

प्रत्यक्ष अनुमान आगम प्रमाणानि 

प्रत्यक्ष - impression derived from the senses; directly before the eyes neuter noun from prati+√akṣ

अनुमान - inference; neuter noun from anu (following)+√man=to perceive, to think

आगम - acquisition of knowledge; handed down and fixed by tradition; masculine noun from ā+√gam (lit. what comes)

प्रमाण - means of knowledge, correct notion; plural of neuter noun from pra+√man=perceive, understand, comprehend  

प्रत्यक्षानुमानागमाः is a dvandva compound comprising three elements, hence the ending is in the plural.

Pramāṇa roughly translates as knowledge related to facts, that are collected through direct or indirect contact through the senses. I.K Taimini explains: 

You see your car coming up the drive, so you know your car is approaching: direct - pratyakṣa. 

You hear it driving up and know its sound so you know that it is approaching: anumāna - as it involves some element of inference. 

Suppose you neither see nor hear it, but your mother comes and informs you your car has arrived, it is āgama, as you are depending on the testimony of a trusted person.

Patañjali's yogasūtras 1:5-6

As we go forward, it helps to note that the yogasūtras were not written  as a teaching tool. Concepts are not explained in order, starting from the simple, going to the complex. Rather they presuppose a knowledge of the entire system. Scholars believe that they were a way of preserving the expert tradition. That makes it harder for us to understand the sūtras, and the interconnecting concepts, till we have read about them all*. But having studied them for a year, I believe the effort was more than worth it. 

{1:5}
वृत्तयः पञ्चतय्यः क्लिष्टाक्लिष्टाः 

वृत्तयः पञ्चतय्यः क्लिष्टाः अल्किष्टाः 

Modifications [of the mind are] five-fold [and are] painful [or] non-painful

वृत्तयः - nominative plural of वृत्ति - activity, modification

पञ्चतय्यः - five-fold agreeing with वृत्तयः

क्लिष्टाः - tormented, injured, pained - adjective agreeing with वृत्तयः from √kliś (9P) to torment, to afflict 

अल्किष्टाः - not connected with pain or suffering

Importantly, the vrittis (activities of the mind) are classifed as kliśṭa and 

akliśṭa, because of their connection to a central yogic concept - that of 

kleśas (suffering, affliction) which are treated in Ch 2, sūtras 2-12. 

At one level this  sūtras refers to simple experiences - a beautiful sunset, freshly cut grass, road-kill, the living dead; or even neutral experiences - stirring tea, combing one's hair. Interestingly what is pleasurable for one person, may not be so for another. Not everyone loves the opera, blue cheese and wasabi. There are people who don't like dogs or are downright scared of them. The reason for these individual reactions is treated later in the sūtras. But it bears reflection at this stage.

{1:6}

प्रमाणविपर्ययविकल्पनिद्रास्मृतयः 

प्रमाण विपर्यय विकल्प निद्रा स्मृतयः

[These are] right knowledge, wrong knowledge, fancy/imagination, sleep and memory

प्रमाण - right perception (sing., neuter., nominative)

विपर्यय - misapprehension, error (sing., masc., nominative)

विकल्प - contrivance, imagination (sing., masc, nom)

निद्रा - sleep (sing., fem., nom)

स्मृतयः - स्मृति remembrance, memory from √smṛ (the plural ending is because all five states are in a compound ending with  स्मृति)

Pramāṇa and viparyaya comprise of all those activities in the mind which are formed by direct contact through one of the sense organs. Vikalpa, and smṛti are internal processes produced in the mind without any contact with the outer world. Notice that in our waking state, we can control Vikalpa (imagination), but in the dream state we have no control on it. These states, including nidrā are explained in detail in the next five sūtras.

*If you can, please read about Sāṃkyha and Yoga in  M. Hiriyanna's excellent and affordable book "Essentials of Indian Philosophy" http://www.amazon.co.uk/s/ref=nb_sb_noss?url=search-alias=aps&field-keywords=m+hiriyanna