2.1.3 - Scales of the Macrocosm

2.1.3

Scales of the Macrocosm

"Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space."

-- Douglas Adams, The Hitchhiker's Guide to the Galaxy

PREV>> 2.1.2 - A Primer on Scientific Notation

Introduction

As you're probably aware of ... the universe is BIG. No really. It's horrifyingly tremendously gigantically HUMONGOUS! It's so big that there is just no way that we can ever fully wrap our brains around it! It wasn't always this way. The universe used to be a lot smaller ... at least we thought so anyway. The universe of antiquity didn't stretch much beyond the solar system. Now we know that this is just the sun's backyard, and the sun is just one amongst a galaxy of billions of stars, in a universe of billions of galaxies! Numbers like these are easy to underestimate. Even just one billion is something that's very difficult to get a visceral feel for. Just how big is the universe? Can we really get any handle on something like that? Maybe, maybe not, but we sure can try!

The universe is absolutely bursting with large numbers! So understanding the vastness of the universe is part of understanding the vastness of numbers themselves. With the universe, it no longer becomes possible to dismiss large numbers as simply the product of a deranged mathematical imagination. Large Numbers, much much larger than a billion or even a trillion, are REAL; just as real as the numbers two or three.

As a way to help us to comprehend the incomprehensible I propose a journey ... from our cozy familiar reality to one just as real, but far far away from the human realm; a survey of the dimensions of the heavens that will simultaneously humble and uplift! We will take a measuring tape to the cosmos, and we'll let one object serve to measure the next. In this way, through comparison, we will attempt to make sense of the very very large, in terms of the ordinary. Interested? Let's begin...

Units of Measurement

We'll be using meters in this article to measure the lengths of various objects in the cosmos. The choice of the meter is because it is a unit nearly commensurate with human experience. A human being stands on average only about 1.7 meters tall. However, the real unit of measurement that we will be using to understand the size of these objects is comparison, specifically the concept of the ratio. Saying something is millions of meters across hardly gives us any conception of that, but by comparing large objects to smaller ones, we can begin to wrap our heads around the vastness of these things.

I'll also be making use of a combination of decimal notation and E-Notation in this article. If you're unfamiliar with E-Notation you can learn about it from the article on Scientific Notation.

In any case, this article is designed so that the notation actually isn't necessary. If you honestly consider the progression, you may actually get something of a visceral sense of how large these things are. We'll begin with something ordinary and small enough for us to have an immediate understanding of. From there the sky is the limit ... literally ...

A Survey of the Cosmos

Motorcycle

1*E0 ~ 2*E0

The Manhattan Life Insurance Building is over 8 times as tall as the Newby-McMahon Building. Now imagine yourself standing by the tiny door of the Newby-McMahon. Feels pretty big already. But this is tiny compare to what's coming...

Chrysler Building

3.19*E2

Saturn V

1.1*E2

Mount Everest

8.84*E3

951 Gaspra is just a "tiny" asteroid in the asteroid belt, yet beside Mount Everest it looks like a monster! It's longest axis measures about 18,200 meters (1.82E+4) making it stand roughly 2 times as tall as Everest when stood longways! An asteroid very similar to this is said to have impacted earth in the Chixculub crater resulting in the extinction of the dinosaurs with the force of 100 trillions tons of TNT. To give this figure some perspective, the impact was equivalent to 2 million hydrogen bombs! As much as a monster as this asteroid seems at the moment, it's tiny compare to other celestial objects. It will take us a little while to get there though ...

Chicxulub Crater

1.8*E5

Woah ... this is the world's largest crater. It is purported to be the impact crater that lead to the extinction of the dinosaurs. Measuring roughly 180,000 meters across (1.8*E5), this makes it roughly 10 times the length of 951 Gaspra. YIKES! Pretty scary ... and we still are just getting started...

Ceres

9.5*E5

This is Ceres, the largest object in the asteroid belt. It's so large that it's gravitational field crushes it into a roughly spherical shape. It measures about 950,000 meters across (950 thousand or 9.50E+5). This makes it nearly a million meters in diameter. Compare it to the Chixculub crater! You can still make out the 951 gaspra asteroid in the image and it's tiny in comparison. Remember, that asteroid is bigger than Everest! If Ceres had a mount Everest it would only extend about 1.8% further from the center than the surface! Next time you want to understand a million try to imagine this behemoth!

And yet Ceres is just a tiny little dwarf planet! We've just begun our journey into the celestial realm. Things start to get scary big from here on out ...

The Moon

3.48*E6

The Moon is an object familiar to any child on earth. In the sky it looks pretty innocuous. Compare it to Ceres however, and it looks like a terrifying giant! The Moon has a diameter of about 3,480,000 meters (3.48 million or 3.48E+6). It's about 3.66 times the size of Ceres. It's huge! It would take roughly 325 days of constant walking around the moon wind up back where you started. More realistically, factoring in hours for rest, it would take 488 days. Now that you have some idea just how massive the moon is, it can be used as a reference point for even larger objects. In the universe however, the moon is just a microbe! It's sobering to consider that despite how much it's seems like we've gone so far ... we've only gone about 5.4 orders of magnitude from the Newby McMahon Building! And there's plenty more where that came from...

The Earth

1.27*E7

Of coarse we had to make a stop at Earth. At about 12,770,000 meters across (12.77 million or 1.27E+7) it's huge in human terms. Keep in mind, everything we consider "the world" occurs here. It houses the roughly 7 billion people of earth, and trillions of insects. On this planet all of human history has played out. It's roughly 3.66 times the size of the moon. This makes the ratio of the earth to the moon, almost exactly the same as the ratio of the moon to Ceres ... and remember, even Ceres makes 951 Gaspra look tiny, which is like mount Everest, which totally dwarfs the tallest man-made structure! Yet as crazy big as the Earth is ... it's still tiny compare to the stuff that lies ahead ...

Jupiter

1.39*E8

Jupiter is the largest planet in the solar system. Measuring at just over 139,000,000 meters across (139 million or 1.39E+8) it's a behemoth that could swallow the whole earth into its vaporous depths! It's diameter is roughly 10.88 times that of the Earth's, placing it almost exactly 1 order of magnitude above it.

Yet even Jupiter gets humbled by ...

The Sun

1.40*E9

Going up one more order of magnitude we reach the sun! The Sun is roughly 1,400,000,000 meters (1.4 billion or 1.40E+9) across, making it almost exactly 10 times the size of Jupiter. The Earth can just barely be made out in the above image. The sun really is a terrifying giant, that could literally swallow up the whole world into a literal lake of fire! Imagine, a literal hell crosses our sky every day that's more than 100 times the size of the earth!

Yet the sun is actually not such a big star after all...

Sirius A

2.40*E9

Sirius A is the brightest star from earth. At about 2,400,000,000 meters across (2.4 billion or 2.40E+9) it's about 1.711 times the size of the sun. Although it's larger than the sun, in terms of size it's basically in the same class. There are much much larger stars out there...

Arcturus

3.50*E10

Rigel or Orion Beta is roughly 103,000,000,000 meters (103 billion or 1.03E+11) across. It's roughly 3 times the size of Arcturus and 75 times the size of the sun. Next time the number hundred billion comes up, and you want to try and wrap your brain around that ... try to imagine the size of Rigel! At this point we've already traveled 10 orders of magnitude. Rigel is as many orders of magnitude from the moon as the moon is from the Newby McMahon Building. At this point it becomes virtually impossible to grasp the size of these things in familiar terms because we can't hold all of the various comparisons in our heads simultaneously. The best we can do is compare it to a familiar large object, like the sun, and understand that Rigel is still way bigger than that! What comes next however is totally terrifying ...

Betelgeuse

1.33*E12

Betelgeuse is a red super-giant. The actual size of this star isn't known with any high precision, but going with conservative figures this star is at least 1,330,000,000,000 meters across (1.33 trillion meters or 1.33E+12). That would make it about 12.8 times the size of Rigel, and 950 times the size of the sun. Although Betelgeuse is quite sizable for a star it's not the largest ...

VY Canis Majoris

1.99*E12

VY Canis Majoris is the largest known star. It's a red supergiant that measures roughly 1,988,000,000,000 (1.988 trillion or 1.99E+12) meters across. It's actually not too much bigger than Betelgeuse. As incredible as this star is, it's quite small compare to what's to come...

The Solar System

1.17*E13

This is roughly the size of the orbit of a dwarf planet known as Sedna. You can make out the orbit of pluto in the above image. As you can see this is a massive orbit. It's longest axis is about 150,000,000,000,000 meters across (150 trillion or 1.50E+14). The orbital period for Sedna is 11,400 years! Yet even this is tiny compare to Nebulas...

Cat's Eye Nebula

3.78*E15

Here we see Sedna's orbit, compare to the Cat's Eye Nebula ... a small stellar remnant Nebula. Nebula's are huge clouds of gas which serve as the birth place of stars. This particular one is pretty small for a nebula. It's only about 0.4 Light years across. This still amounts to 3,786,000,000,000,000 meters across (3.78 quadrillion or 3.78E+15). This is just CRAZY BIG ... even Betelgeuse which just a little while ago seemed like quite the behemoth is now smaller than a pixel at this scale ... but it get's even bigger than that ...

Pillars of Creation

3.78*E16

The Pillars of Creation is just a tiny part of the Eagle Nebula. It's sublime beauty has made it a popular image in the public sphere. The majesty of the pillars really comes to life when we realize that they tower at up to 4 light years high! That's roughly 37,800,000,000,000,000 meters (37.8 quadrillion or 3.78E+16). That's over 13 orders of magnitude from the height of Khalifa, the tallest man made structure. In other words, you'd have to stack 10 trillion Khalifa's to reach the height of a pillar of creation! Even the Cat's Eye Nebula is small in comparison. The orbit of Sedna is vanishingly small already! The pillars of creation are actually a stellar nursery ... a birth place of stars, hence the name. As peaceful as these vast cloudy depths may seem you have to remember that this cloud is big enough to house dozens of hellish super giants like betelgeuse that could vaporize our tiny blue planet. The universe is just scary huge ... and it's just out there following it's own law as if we don't even exist ... and it would continue to do so even if we vanished from these vast depths. Our planet is like a microscopic mote of dust drifting thorough a murky ocean of firey embers. Would it not be arrogant to think that this grand sight was created solely for us to enjoy? And Even this magnificent sight is just a tiny little twirl of gas into the greater milky way, but it will still be a while 'til we get there...

Crab Nebula

1.04*E17

The Crab Nebula is some 11 light years across. That's 104,000,000,000,000,000 meters (104 quadrillion or 1.04E+17). It's roughly in the same ballpark as the pillars of creation in terms of size, though it is roughly twice it's size. But we still haven't reached the end of nebulas ...

Carina Nebula

6.15*E17

The Carina Nebula is roughly 65 light years across. That's 615,000,000,000,000,000 meters (615 quadrillion or 6.15E+17). If you can still make out the Cat's Eye Nebula, you can see that it's now a tiny whiff of smoke now in comparison. And even THAT nebula is HUGE considering it could swallow up the whole solar system and the orbit of sedna! Already the pillars of creation are beginning to recede. At this scale even the largest stars are impossibly small to imagine. All this can be quite mesmerizing and it might be tempting to be lost in a sense of lightness and glory ... but keep in mind that most of this vast space is only a few degrees above absolute zero and is an almost perfect vacuum ... and the few rare places that wouldn't freeze us solid through and through would vaporize us in an instant in million degree infernos known as "stars". The universe is glorious, but deadly...

Omega Centauri

1.63*E18

Omega Centauri is what is known as a gobular cluster. It's a huge collection of stars held together through the forces of mutual gravitation. As you can see, these can be even vaster in size than nebulas. This particular gobular cluster has a diameter of roughly 172 light years or 1,627,000,000,000,000,000 meters (1.627 quintillion or 1.63E+18). Omega Centauri literally contains millions of stars. Towards the center of it's core the stars are said to be so close together that they average only 0.1 light years apart. That's still about 1,000,000,000,000,000 (1E15) meters apart, but at this point it gets difficult to tell the difference of 2 or 3 orders of magnitude from looking at the decimal expansions. The numbers begin to blur. Still even 0.1 light years is about 10 times the major axis of the orbit of Sedna. That's still ample room to place Betelgeuse size stars away from each other. As mind-blowing as all this is we still have another 3 orders of magnitude to go to reach the size of the milky way galaxy...

Large Magellanic Cloud

1.32*E20

That "star" in the middle of the red square is no star ... that's Omega Centauri ... home to a million stars. Now compare that to the Large Magellanic Cloud ... a dwarf galaxy of a mere 30 billion stars! This monsterosity is roughly 14,000 light years across or 132,440,000,000,000,000,000 meters (132 quintillion or 1.32E+20). This "small" galaxy is a nearby neighbor of the milky way only 160,000 light years from us. And now ladies and gentlemen we reach ...

The Milky Way Galaxy

9.46*E20

Finally after going through some 20 orders of magnitude we arrive at the Milky Way Galaxy, our galactic home address. It's home to some 200 billion stars. The disc of the Milky Way has a diameter of roughly 100,000 light years across or 946,000,000,000,000,000,000 meters (946 quintillion or about 9.46E+20). The Milky Way is a sextillion meters across!

At this point however such numbers have little meaning. Even our little demonstration can't really help us fully grasp it's size because we can't remember enough of the comparisons simultaneously to bring it down to earth. Even Omega Centauri is now a tiny point of light ... but remember even that is a huge cosmic object of a million stars. Going back to Omega Centauri ... The Cat's Eye Nebula is already too small to be seen... going back to the Cat's Eye Nebula even Betelgeuse is too small to see ... going to Betelgeuse our own star is a tiny point of light and going back to the sun, Ceres is way too tiny to make out, and going back to Ceres, Khalifa the worlds tallest skyscraper is too tiny to actually see ... and if we were to actually be before that huge tower it alone would blow our minds!!! Even in this summarized form there still is too many levels to keep straight in your head simultaneously. So much for having any hope of comprehending the size of a galaxy ... and yet we aren't done ... o_0;

The Local Group

1*E23

The Milky Way is itself part of a family of gravitationally bonded galaxies which form the so called Local Group. The Local Group contains more than 54 galaxies and covers an area of about 10 million light years. That would be about 100,000,000,000,000,000,000,000 (100 sextillion or 1.00E+23) meters across.

Virgo Super Cluster

1.42*E24

The Virgo Super Cluster is a huge cluster of clusters that includes our own Local Group. It is roughly 150 million light years across. That's about 1,420,000,000,000,000,000,000,000 (1.42 septillion or 1.42E+24) meters. It contains roughly 10,000 galaxies. The biggest cluster of galaxies can be found in the Virgo Cluster, which contains some 2000 galaxies. The Virgo Supercluster believe it or not is considered to be a rather sparse supercluster! Unbelievably as INSANELY big as the Virgo Supercluster is, it is just one among millions of superclusters scattered throughout the observable universe...

The Local SuperClusters

1.89*E25

Scientist's have already cataloged several superclusters in the vicinity of the virgo supercluster. This is a sphere 2 billion light years across centered on the earth. It's 18,920,000,000,000,000,000,000,000 (18.92 septillion or 1.89E+25) meters across! Now let's move on to the observable universe...

The Observable Universe

8.79*E26

The so called "Observable Universe" is the portion of the universe that we can actually observe because light has had enough time since the big bang to reach us. The area that we can actually see is mind-crushingly huge. The observable zone is a giant sphere centered on our planet (simply because we are the observers, not because we hold any special position). The diameter of that grand sphere is about 93 billion light years or 879,000,000,000,000,000,000,000,000 (879 septillion or 8.79E+26) meters! That's almost one octillion meters or 1.00E+27.

At the scale of the above image, the Virgo Super Cluster is smaller than a single pixel! The matter in the Observable Universe is organized into a complex web of mutual attraction, with huge voids between filaments called cosmic voids. On the largest scales the observable universe appears to be distributed in a mostly uniform manner.

This leaves an important open question however ... how big is the universe? Scientists don't actually have a fix on that yet! It is even an open possibility that the universe as a whole might be infinite. But that would be boring from a googologist's point of view, since it's more interesting to have specific examples of large finite numbers in physics. Although there isn't sufficient evidence yet to come to any definitive answer we can at least look at the speculative theories. If these theories are correct than even the observable universe is googol-scopic compare to the universe as a whole ...

The Local Friedmann Bubble

1*E1,000,000,000,000

According to a version of inflationary theory devised by Andre Linde known as Chaotic Inflation, The Universe as a whole may be GIGANTIC in a way that simply makes everything we've imagined so far just the very smallest tip of the iceberg. According to Chaotic Inflation the universe expanded very rapidly 1E-35 seconds after the big bang ... really really rapidly. The rapid expansion can be estimated by considerations of the relative smoothness of the observable universe. According to one version of these calculations the universe underwent at least 3.32 trillion doublings in 1E-35 seconds. This means the universe would have to be about 1E+1,000,000,000,000 meters across [1]! In stacked exponents this can be written as 10^10^12, and in stack notation as E12#2.

After this the universe expanded in a much more gradual rate, going from an exponential rate of size increase to a linear one, in which the rate of doubling slows down over time. Of coarse this is still speculative, but scientists are trying to find evidence to support this model.

Chaotic Inflation also predicts something else; that the fabric of space-time is expanding at different rates in different regions due to differences of energy density, resulting in fractal like structure in the fabric of space-time itself! In fact, the theory contends that the "big bang" was just one singularity which arose as an inflationary epic of just one tiny domain of a far grander scheme of space time! The figure 10^10^12 was chosen to explain the smoothness of the observed microwave background radiation. Therefore this is actually the minimum possible size of a grander inflationary universe. What was formed from the our big bang 13.7 billion years ago was only a single massive "friedmann bubble". But if there are multiple friedmann bubbles out there, each a "universe" in it's own right, then how BIG is the entire chaotically inflating multiverse?

We'll look into that momentarily, but first let's get a handle just how big even just our friedmann bubble is.

The above image is meant to convey an idea of what our universe may look like as a whole as viewed from outside space-time. Imagine the surface of the above figure as representing space itself. Galaxies, clusters, super-clusters, deep cosmic voids and filaments of matter all exist on the surface of this bubble.

If you go back to the original image of the motorcycle, and go up to the observable universe, you've only traveled roughly 27 orders of magnitude. Imagine making the trip through 27 orders of magnitude 37,000,000,000 times!!!

This is just impossible to comprehend, seeing as even imagining 37,000,000,000 cycles is difficult to really appreciate (our raw numerical sense is even worse with time than it is with space, so imagining 37,000,000,000 repetitions of something is rather fuzzy. However to help with the analogy, if you cycled through all the images 1 second each time round it would take you roughly 1190 years to cycle through it 37,000,000,000).

So is this all of creation, everything that exists? If Andre Linde is right about chaotic inflation, then even our friedmann bubble is only a tinier part of a much grander creation...

Grand Chaotic Inflationary Universe

1*E(1*E64)

This gigantic figure represents one continuously connected fabric of space-time, the theoretical entirety of the Andre Linde Chaotic Inflationary Universe. In this sense it represents the whole of The Universe, as commonly conceived. However, in inflationary theory it's more commonly referred to as a multiverse, on account of the fact that different regions may operate under different laws of physics (the different colors represent different laws of physics in different inflating regions). However they are all related by the same types of parameters that govern the whole ensemble, such as the strength of gravity or the electromagnetic force, or the mass of the proton, etc. In fact, we might even think of this inflationary multiverse, as not just the product of a single big bang, but as many local regions being the product of countless local big bangs. The grand "reality" then is an evolving Universe, forever expanding and developing smaller pocket universes connected to the whole. The result is a grand fractal of universes constantly budding smaller universes.

Andre's model provides no predictions of the actual size of this "Grand Universe". Where as we can date the age and size of our local universe based on observations of the big bang, we have no similar analogy for Linde's Grand Universe. In fact Linde leaves the size an age of the Grand Universe an open question. However there is one way to at least come up with a minimal size for the Grand Universe. According to Chaotic Inflation, although regions of the Grand Universe cease to inflate, resulting in "Big Bangs" that turn into local universes, there always exists some domain in which inflation continues and thus the Grand Universe is eternally inflating. This means that Grand Universe could not have began inflating any earlier than the creation of our own universe, but it also means it continued to inflate even to this day. Taking the hypothetical expansion rate of 10^10^12 fold increase every 1E-35 seconds, and extending it for 13.7 billion years, this gives a minimum size of the Grand Universe of

1*E(1*E64) meters. Alternatively, 10^10^64 or E64#2.

Keep in mind that this is only a lower bound on the size of the Grand Universe. There is no reason, in Linde's model, why our big bang had to be the first. There could have been any number of big bangs arrayed over any period of time. We simply have no way to bound the potential size of the Grand Universe within Linde's framework. In fact, in Linde's original formulation, he not only claimed that the Grand Universe was without end once it got started, but was also without beginning. However, if the 2nd law of thermodynamics applies across the Grand Universe, than it's a contradiction for the Grand Universe to be eternal. Why? Because if it was it would have already cooled off and become completely uniform [2]. It hasn't. So no matter how large the Grand Universe is it must have begun a finite amount of time ago. Just as our Universe must have begun in a singularity, the big bang, the Grand Universe must have begun in a grand singularity I'll call the Grand Bang. Could it be that the 2nd law of thermodynamics doesn't apply to the whole? Or perhaps the Grand Universe always had and always will have an infinite store of energy so that the 2nd law of thermodynamics never exhausts it. We simply can't say!

So Basically all we can say is that if the Grand Universe is real, it's somewhere between 10^10^64 meters to infinity in size.

Just contemplating the minimum size is horrendous. The above image attempts to provide an analogy. Imagine our local friedmann bubble, was as tiny relative to a 2nd order friedmann bubble, as a motorcycle to our Friedmann bubble! The 2nd order friedmann bubble (which would result from an inflationary period of 2*E-35 seconds instead of 1E-35) would be 1*E(2*E12) meters across (1 followed by 2 trillion zeroes). Now imagine a 3rd order friedmann bubble, a 4th, 5th, 6th, 7th, 8th, etc. The Grand Universe is at least the size of a 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000th order Friedmann Bubble! That's a 1*E52 order Friedmann Bubble. If the Friedmann Bubble was virtually impossible to comprehend then this is beyond incomprehensible!

So is this all of creation?! ...

Absolutely Everything in Existence

1*E!?!?!?!?

Recall earlier that I described The Grand Universe as one continuous totally connected fabric of space-time. But there is nothing that seems to prevent the possibility that other isolated fabrics might exist. There could be an Omniverse made of such isolated bubbles of space-time with any number of such Grand Universes. But how many?! 10^10^12 or 10^10^64, who knows?! There might even be an infinite number of them! We simply don't know, and we have no way to determine how many.

If it's true that there are alternate space-times out there then by definition we couldn't travel to any of these other grand universes, since they are disconnected, but we couldn't rule out their possible existence either! This is what I call the "box problem". If there is a limit to what you can perceive, if in some sense you are living in a box, then you can't know what lies outside that box, and you can't rule out that reality might be bigger than your box. This is probably the main reason why you can't prove a negative. That is, why you can't prove that something does not exist. We can't know with any certainty that any particular observed collection of objects, represents all that exists.

Not only might there be an infinite number of such grand inflationary universes, but each of them may themselves be infinite. On the other hand there might be a finite number of finite grand inflationary universes. If that's so then there is some largest finite number that has been concretely realized. However we should be careful not to use such a physical constant to define a finite number, because we can't actually take it for granted that it is finite.

There are some serious problems with thinking about everything in existence. The biggest problem is that such a thing could never have a cause in the proper sense, since the cause would either have to come from outside itself, which is a contradiction since it's everything, or the cause would occur inside itself, in which case it would already have to exist rendering it's "cause" meaningless as an explanation for it's existence. The only possibility seems to be that it either always existed and is eternal or it emerged literally from nothing without cause. But here we have reached the pinnacle of speculation...

Conclusion

We have reached the limit of the scales of reality that we can legitimately claim exist. We have passed well beyond our first cosmic horizon. Existence may be infinite ... but we simply don't know. In terms of physical measurement, the largest finite distance I can legitimately glean from a professional theory is 10^10^64 meters for the hypothetical minimum dimensions of the Grand inflationary Universe. Venturing any further would be pure speculation on something that already is quite theoretical and speculative! So we've reached the end of length measurements in physics. Amazingly 10^10^64 is not the largest number in physics, but to get larger numbers we have to consider some other measurement other than length. In later articles we'll consider other ways that large numbers crop up in science.

In any case if there is anything to learn from this it's that large numbers are no more a fiction than the observable universe. Sure they are big. Sure we can't comprehend them ... but that doesn't make them unreal. The universe has to be at least 1*E27 meters across, so any number below this point is quite tangible. As we'll see in later articles, much larger numbers are also quite tangible ...

NEXT>> 2.1.4 - Scales of the Microcosm

Additional Links

For those interested, the following link will lead you to an interactive demonstration of the sizes of the cosmos similar to my demonstration here. Given it's interactive nature its even more likely to blow your mind. I highly recommend checking it out...

http://htwins.net/scale2/

Source Material

[1] http://www.stanford.edu/~alinde/1032226.pdf

[2] http://www.reasonablefaith.org/the-end-of-the-world

Additional Reading

This is a common paper that comes up when looking into large numbers in physics. In the paper Andre Linde along with co-writer Vitaly Vanchurin attempt to estimate the total number of distinguishable "Locally friedmann universes" in the Chaotic Inflationary Multiverse. They come up with the ginormous figure 10^10^10^7, which is STILL not the largest number in physics! Although often interpretted to describe the size of the multiverse, the paper doesn't make any claim about how many Locally friedmann universes, actually exist. It only estimates how many types of such universes could exist. It's like saying there are 52 types of cards, but a pile of cards could have any combination of these types, and any number of such cards. As stated in the article, Linde's framework does not allow for a definitive prediction of how large the multiverse is, only how large our universe is. Which really only moves the question of the size of everything one order higher...

http://arxiv.org/pdf/0910.1589v3.pdf

In this paper by Alan Guth, it is mentioned that in Chaotic Inflation theory that the number of pocket universes may increase as much as e^10^37 fold (roughly 10^10^37) every second! Robert Munafo has used this figure to estimate that the inflationary multiverse must contain at least 10^10^54 pocket universes at present; a figure very close to my minimum size of 10^10^64 meters. Here is the original paper...

http://arxiv.org/pdf/hep-th/0702178v1.pdf

Here is the link to Robert Munafo's entry of 10^10^54 on his "Notable properties of Specific Numbers" list:

http://mrob.com/pub/math/numbers-21.html#lp1_e054_187