# Do grandmother cells fly?

How do we hold ideas in our brains? One model is that for every concept, word or object we can think about there is a cell (or more likely a small group of cells) that are that idea. Such cells have been called grandmother cells, gnostic cells, cardinal cells, as well as other names.

Most people have difficulty taking in this notion because it seems to require too large a number of cells. So lets do some arithmetic.

1. A good English dictionary contains about 500,000 words. A persons vocabulary of understood words is unlikely to be greater than this.
2. For every word there is likely to be a visual representation are well as a semantic one. Add another 500,000.
3. If we assume that a person adds about 1000 new people to the people that they recognize each year of their life, than in a 100 year lifetime they would store 100,000 people. And let us assume that they get to know a similar number of places and another 200,000 for proper names and their equivalents.
4. Let us assume that words, images, people and places only cover the majority of ideas. So double the count to cover a minority of other types of idea. That is a total so far of 2.4 million.
5. We would have to assume that each idea has a number of forms. Take Sally: there is Sally when she was a child, Sally as an adult, Sally when she bleached her hair, Sally as one person out of fourteen in her choir group, Sally as a professional at work, and so on. Let us assume that each idea has a subgroup of 100 simpler or even duplicated ideas. That gives us 240 million.
6. Further, we can say that there would be more than one cell for each idea. Let us leave room for each sense mode to have a couple of separate idea maps. And let us leave room for a couple maps each for planning, consciousness, and memory to use. That would be 16 copies  make it 20. Now we have just under 5000 million.

So how do 5 billion cells dedicated to a gnostic function compare with the number of cells available? It is 5% of the 100 billion neurons estimated to be in the brain. But all the brain is not used for cognition, consciousness and memory. Suppose that three-quarters of the neurons are concerned with homeostasis, with motor coordination, and with early sensory input – activities that would not use gnostic cells. We are still using only 20% of the neurons directly concerned with cognition, consciousness and memory. The other 80% could be available to make, break or modify the connections between ideas. I do not see any impossibility in this model.

From a computer point of view (not that conventional computer science is necessarily applicable to understanding how the brain works) there is an analogy with storage structures. If grandmother cells are equivalent to extremely sparse matrix storage, then the extreme other end of spectrum would be a very dense matrix storage. 5 billion outcomes can be stored in 33 devices (2 to the power of 32 is just under 5 billion). Maintaining sparse and dense matrices require very different types of algorithms though. The nice thing about grandmother cells is how natural they seem to feel. They seem to feel more like the concepts we know than does the outcome of a dense matrix.