What do you do for fun?
I investigate interesting ideas. I mean, it's not the only thing that I do for fun; I certainly enjoy dog walks, hot tubs, and family visits, but the point of today's post is to share with you a new discovery about the brain. As it turns out, it was fun.
When I say 'new discovery about the brain' I am referring to something that I discovered, or in the infinite wisdom of Plato, recollected. You see, Plato's theory of recollection is one of remembrance; he [Plato] was describing what knowledge felt like when it experienced knowledge. Do you recall the feeling of remembering something at the moment you wanted to remember it? Feels good right? How does it feel when you can't remember something, it's like being at a party, vaguely remembering the perfect joke for the situation but unable to recall it from that complex brain structure of 86 billion neurons.
Is that where the thought resides, in one of these 86 billion neurons? Is there a specific location, a coordinate that is the resting place of the tought, the individual unit of knowledge worthy or remembering? It would be a fool's errand to continue this thought because we know that is not how the brain works. Our thoughts exist in a network, emerging from the biological of our philogentic chain, captured in our DNA and then experienced by the energy consumers that we are.
Bringing the fun back into the equation, the ah ha moment was realizing that the cerebral cortex is responsible for more than half neurons (approximately 60%) and that the synapsis density is off the charts! That's where you, me and all the memories we recall are experienced.
The Sand Reckoner and the Quest for Infinity
While Plato focused on recollection, another great mind of antiquity, Archimedes, embarked on an intellectual journey to quantify the unquantifiable. His work, The Sand Reckoner, is a testament to human curiosity and the relentless pursuit of knowledge. This endeavor wasn't just about counting sand; it was about expanding the boundaries of mathematical thought and challenging the perceptions of his time.
Naming Large Numbers
Archimedes faced a fundamental challenge: the number system of his day could only express numbers up to a myriad, which is 10,000. To calculate the number of grains of sand that could fit into the universe, he needed to invent a new way to talk about extraordinarily large numbers. In doing so, he created a system that would eventually inspire the modern understanding of large numbers.
He began by defining a "first order" of numbers up to 100 million (10,000 x 10,000), which he called the "unit of the second order." From there, he constructed larger orders, culminating in the definition of a number as vast as 100 million raised to the power of 100 million. This imaginative leap was not just an exercise in mathematics but a philosophical exploration of infinity itself.
Archimedes' method resembled a positional numeral system with a base of 100 million, a concept that was revolutionary in the ancient Greek world. This new language of numbers allowed him to convey the sheer enormity of the universe in a way that was both precise and poetic.
The Law of Exponents
In the process of inventing this numerical system, Archimedes also discovered a fundamental principle in mathematics that relates to multiplying large numbers. When you multiply numbers like 1,000 by 10,000, you can think of it as adding together the number of zeros at the end. So:
- 1,000 times 10,000 equals 10,000,000.
This rule showed Archimedes that simple arithmetic operations could explain complex relationships between numbers and laid the groundwork for future mathematical discoveries.
Estimating the Size of the Universe
Archimedes didn't stop at naming large numbers; he sought to apply his newfound numerical system to estimate the size of the universe. Using the heliocentric model of Aristarchus of Samos, which posited that the Earth revolved around a stationary Sun, Archimedes ventured to calculate the number of grains of sand needed to fill this cosmic expanse.
To establish an upper bound, Archimedes made several assumptions:
- The Universe is Spherical: This assumption allowed him to use geometric principles to calculate volumes.
- Relative Sizes: He estimated the perimeter of the Earth and the sizes of celestial bodies, like the Sun and Moon, based on available observations.
- Angular Measurements: Archimedes calculated angular diameters and distances, considering the limitations of Greek observational techniques.
With these assumptions, he concluded that the universe could contain up to a staggering number of grains of sand, specifically 10 followed by 63 zeros. Each grain, in his thought experiment, was a minuscule 19 micrometers in diameter—a measurement that reveals the intricacy and ambition of his calculations.
Calculation of the Number of Grains of Sand
Archimedes' calculations were grounded in meticulous reasoning:
- Poppy Seed Measurements: He determined that 40 poppy seeds laid side by side equaled one Greek dactyl (19 mm).
- Sphere Calculations: By extrapolating from poppy seeds to sand grains, he estimated the volume of a sphere in terms of these tiny particles.
- Scaling Up: Multiplying these calculations through different scales, he arrived at the staggering figure of 10 followed by 63 zeros grains in the universe.
This exercise was more than a mere mathematical curiosity; it was a demonstration of how to handle incredibly large numbers and the challenges of working with astronomical scales.
Additional Calculations and Philosophical Insights
Archimedes also ventured into other fascinating computations, such as estimating the angular size of the Sun from Earth, considering the finite size of the eye's pupil. This work may represent one of the earliest forays into psychophysics, a field that examines the relationship between physical stimuli and perception.
He explored solar parallax, calculating the difference in distances when viewing the Sun from the Earth's center versus its surface. This was one of the first known attempts to address solar parallax, demonstrating Archimedes' visionary thinking.
A Reflection on Infinity
Archimedes' reflections on infinity and the nature of large numbers invite us to ponder the limits of human understanding. His letter to King Gelo II of Syracuse eloquently captures this spirit of exploration:
"There are some, king Gelon, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited..."
Through geometrical proofs and the invention of a novel numerical system, Archimedes challenged the notion of infinity, revealing that even the vastness of the universe could be expressed in human terms. His work serves as a reminder of the power of imagination and the boundless potential of mathematical thought.
Conclusion
Just as Archimedes expanded the boundaries of mathematics and explored the infinite, our modern understanding of the brain and its incredible network of neurons invites us to continue questioning and exploring the mysteries of existence. By daring to quantify the infinite and navigate the complex web of thoughts and memories, we honor the legacy of thinkers like Archimedes and Plato, whose quests for knowledge continue to inspire us.
So, as we ponder the grains of sand beneath our feet and the neurons firing in our minds, let's embrace the joy of discovery and the thrill of understanding, one grain and one thought at a time.
What do you do for fun?