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Im not sure how this would ever be tested but is there a limit to how much the brain can 'hold' before it reaches capacity ?

I guess this could also be interpreted in terms of memory, as how well some one remember something before reaching capacity / forgetting 'old' memories to make way / space for new ones.

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    $\begingroup$ Yes. The brain has finite size. You can't keep an infinite amount of information in a finite space. $\endgroup$ – daniel Jul 12 '14 at 15:02
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Yes, there is a limit:

Despite the impressive complexity and processing power of the human brain, it is severely capacity limited [1].

Human brain has 78.82– 95.40 billion neurons [2] and about $3.6 \cdot 10^{14}$ synapses in the cortex [3]. We shouldn't worry about running out of space, because neurons connect with each other to exponentially increase brain capacity to about 2.5 million gigabytes as Paul Reber, professor of psychology at Northwestern University claims for Scientific American [4]:

Each neuron forms about 1,000 connections to other neurons, amounting to more than a trillion connections. If each neuron could only help store a single memory, running out of space would be a problem. You might have only a few gigabytes of storage space, similar to the space in an iPod or a USB flash drive. Yet neurons combine so that each one helps with many memories at a time, exponentially increasing the brain’s memory storage capacity to something closer to around 2.5 petabytes (or a million gigabytes).


References:

  1. Marois R, Ivanoff J. Capacity limits of information processing in the brain. Trends Cogn. Sci. (Regul. Ed.). 2005 Jun;9(6):296-305. doi: 10.1016/j.tics.2005.04.010. PubMed PMID: 15925809. Full text available on http://www.psy.vanderbilt.edu/faculty/marois/Publications/Marois_Ivanoff-2005.pdf
  2. Azevedo FA, Carvalho LR, Grinberg LT, Farfel JM, Ferretti RE, Leite RE, Jacob Filho W, Lent R, Herculano-Houzel S. Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain. J Comp Neurol. 2009 Apr 10 513(5):532-41. p.535 right column top sentence. Via Bionumbers http://bionumbers.hms.harvard.edu//bionumber.aspx?id=106322&ver=4
  3. Roth G, Dicke U. Evolution of the brain and intelligence. Trends Cogn Sci. 2005 May9(5):250-7. p.253 right column 1st paragraph. Via Bionumbers http://bionumbers.hms.harvard.edu//bionumber.aspx?id=106138&ver=2
  4. Paul Reber. What Is the Memory Capacity of the Human Brain? Scientific American. Apr 2010. Available from http://www.scientificamerican.com/article/what-is-the-memory-capacity/. Accessed 12.07.2014
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