The soul is 1/10000 the size of the tip of a hair. This is quite big. How to understand that?

A human hair is about 100 microns thick. A cylindrical segment of the end of the hair is about 785,000 µm³. Dividing this be 10,000 we would still have 78.5 µm³ which is bigger than most bacteria.

In his purport to the Bhagavad-gītā 2.17, Prabhupada mentions that "When the upper point of a hair is divided into one hundred parts and again each of such parts is further divided into one hundred parts, each such part is the measurement of the dimension of the spirit soul."

This is a reference to the Śvetāśvatara Upaniṣad (5.9):

bālāgra-śata-bhāgasya, śatadhā kalpitasya ca

bhāgo jīvaḥ sa vijñeyaḥ, sa cānantyāya kalpate

There is another version of the same verse that was spoken by Sri Caitanya Mahāprabhu in His teachings to Śrīla Rūpa Gosvāmī:

keśāgra-śata-bhāgasya, śatāmśaḥ sādṛśātmakaḥ,

jīvaḥ sūkṣma-svarūpo ’yam, sankhyātīto hi cit-kaṇaḥ

The two verses contain the same information about the size of the soul, but the second adds one extra detail that is essential to understanding the analogy.

The first two lines, keśāgra-śata-bhāgasya śatāmśaḥ sādṛśātmakaḥ describe that when the tip of the hair (keśāgra) is divided into one hundred parts (śata-bhāgasya) and each part is again divided into one hundred parts (śatāmśaḥ), each part is similar in size to the measurement of the soul. This is the idea included by Srila Prabhupada in his purport.

The second part of the verse then adds extra details, helping us to understand the analogy:

jīvaḥ sūkṣma-svarūpo ’yam, sankhyātīto hi cit-kaṇaḥ

The words "jīvaḥ sūkṣma-svarūpo" indicate that the jīva is extremely subtle, clarifying that it is not like a gross material particle that can be measured and studied. This soul is beyond measurement (ayam sankhyātīto). The verse then concludes with "hi cit-kaṇaḥ", stating that, indeed (hi), the soul is a particle of consciousness (cit-kaṇaḥ).

We can see that the second part of the verse appears to contradict the first. The first part suggests the soul has a defined size, measuring 1/10000 of the size of the tip of a hair, while the second part suggests that the soul is not measurable at all, being very subtle, and indeed a particle of consciousness instead of a measurable object.

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As in other passages, the contradiction appears to exist only as far as we don't properly understand the passage.

Let's start with the first idea. On average, a human hair is about 100 microns thick, or 1/10 of a millimeter. If we were to take out a cylindrical segment of the end of the hair, this would represent about 785,000 µm³. Dividing this into 10,000 parts, we would still have 78.5 µm³, which is quite easy to measure and study with modern instruments. For comparison, this volume is 100x larger than an Escherichia coli bacterium, and tens of thousands of times larger than most viruses. We can see that when we interpret in this way, the analogy quickly breaks down, since the soul appears to be not just a relatively large particle that could then be found and studied, but also too large to enter most bacteria and other minute organisms.

This is, however, because this interpretation of the verse is incorrect. When we take into consideration the second part, we can clearly see that the point of the verse is not to give a precise material measurement of the soul, but to simply illustrate how elusive it is. Starting with something we can barely see (the tip of a hair), and then explaining that the soul is still smaller. Whatever is the smallest particle we can measure, the soul will be still smaller. This shows that trying to find the soul by material means is futile. The soul can be perceived only by perfect intelligence, and part of the process of understanding it passes through giving up the idea of the soul being a physical particle that can be found, measured, pushed around, etc.

In the second part of the verse, the soul is defined as extremely subtle and beyond measurement. The verse then concludes by stating that the soul is not a physical particle at all, but instead a particle of consciousness. The word used is "cit," which literally means consciousness or perception.

How to understand that?

Lord Kapila explains (on SB 3.26) that material consciousness is created at the beginning of the material creation as a reflection of the original, spiritual consciousness of the soul. This follows the example of the light of the sun entering a dark room and being reflected on a pot of water and then on the walls, which is used by Lord Kapila to explain this point, which we already studied in detail in past articles.

In this way, the soul, which is transcendental, always pure and immovable, becomes manifested inside the material creation as a reflection, just like the Lord. This reflection is then covered by the seven coverings (the false ego, mind, intelligence, senses, vital airs, gross body, and the organs of the senses). This explains the idea of the soul being a particle of consciousness (cit-kaṇaḥ). Extra confirmation is given in SB 2.9.1, where Sukadeva Goswami mentions that "there is no meaning to the relationship of the pure soul in pure consciousness with the material body. That relationship is just like a dreamer seeing his own body working."

In short, what the verse tells us is that the soul is not a material particle, and therefore it can't be found by experimental means. When the word “particle” is used to describe the soul, it should be taken figuratively, as a way to emphasize that the soul is very minute. Similarly, the 1/10000 of the tip of a hair should be understood in the sense that whatever is the smallest particle one is capable of measuring using whatever instruments one has at their disposal, the soul is still smaller. With the naked eye, the tip of a hair is the smallest particle one can see. However, if one has an electron microscope, one will see that ultimately the tip of the hair is a single atom. In both cases, the soul is still smaller and subtler, and thus always escapes the understanding of the materialist. The soul can thus be understood only through purified intelligence, and not through a microscope.

When we properly understand the passage, we can understand how Prabhupada used it to prove the transcendental and inconceivable nature of the soul.