Monday, March 9, 2020

259: Is Reality Really Real?

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Recently I read an amusing book by a cognitive scientist named Donald Hoffman, titled “The Case Against Reality”.    Hoffman argues that what we think we are perceiving as reality is actually an abstract mathematical model created by our neurons, with very little relationship to reality as it may actually exist.   Note that this is not one of those popular arguments that we’re living inside a computer simulation— Hoffman isn’t claiming that.   This also isn’t an argument about the limits of our perception, such as our inability to fully observe subatomic particles at a scale that would confirm or deny string theory.    He accepts as a starting point that we do actually exist and are perceiving something.    However, that ‘something’ that we seem to be perceiving is radically different from the core concepts of space, time, and general physics that we think we’re observing.

A key metaphor Hoffman points to is the idea of your computer desktop screen, where you see icons representing files and applications.   You can perform various actions on this screen, moving files between folders, starting applications, etc.   Some of them even have real consequences:   you know that if you drag a file into the trash and click the ‘empty trash’ button, the file will cease to exist on your computer.   Yet you are completely isolated from the world of electrical signals, semiconductor physics, and other real aspects of how those computer operations are actually implemented.   The ultra-simple abstract desktop serves your need for practical purposes in most cases.   Hoffman believes that our view of the universe is similar to a user’s view of a computer desktop:  we are seeing a minimal abstract model needed to conduct our lives.

It’s easy to argue, from observing more primitive animals in nature, that evolution does have a tendency to take shortcuts whenever possible.   Hoffman points out a number of funny examples, like a type of beetle that identifies females through their shiny backs, and can be fooled into trying to mate with a small bottle.   If the species could successfully perpetuate itself by using this shininess heuristic to quickly identify females with minimal energy, why would evolution bother trying to teach it to observe the world in more detail?   Hoffman calls this the FBT, or “Fitness Beats Truth” concept.   He even tries to raise it to the status of a theorem, by making various assumptions and then showing that given the choice between providing true perceptions or the minimal required to enable reproductive fitness in a particular area, the sensible minimal-cost evolutionary mechanism would always choose fitness over truth.

So, it this an unassailable proof that we are simply observing some complex computer desktop, rather than actually perceiving something close to reality?   Actually, I see a few issues with Hoffman’s argument.   The first one is that he dismisses far too casually the idea that maybe, once a certain amount of interaction with reality is needed, it’s easier for evolution to build actual reality-perceiving mechanisms than to come up with a new, complex abstraction that applies to the situation.    While a major computer chip manufacturer can do lots of work using abstract design schematics, for example, at some point they may need to debug key manufacturing issues.   When this happens they stop using purely abstract models, and look at their actual chips using powerful electron microscopes.    Isn’t it possible that evolution could reach a similar point, where there is a need for general adaptability, and the best way to implement it is to provide tools for observing reality?  

Another big argument in favor of our perceptions being close to reality is that we are able to derive very complex indirect consequences of what we observe, and show that they apply in practice.   For example, a century ago Einstein came up with the theory of relativity to help explain strange observed facts, such as the speed of light seeming to be the same for moving and nonmoving objects.   He and other scientists derived numerous consequences from the resulting equations, such as surprising time dilation effects.   Eventually these consequences became critical in developing modern technologies such as the Global Positioning System, which we use every day to accurately navigate our cars.   Could evolution have come up with such a self-consistent abstract system, originally in order to enable groups of advanced monkeys to more efficiently traverse the treetops and gather bananas?   I’m a bit skeptical.   I think for evolutionary purposes, our approximate abstract perception that the speed of light is 0 has been perfect for most of history, and our advanced observations beyond that are detecting a real level of reality that evolution wasn’t particularly caring about.

Finally, one other critical flaw is that Hoffman claims that even our core concepts such as space and time are part of this abstract model that evolution has created for us.   But evolution itself is a process that we have observed to occur in space and over time.  So if evolution has created some kind of abstract model for us, that in itself proves that space and time exist in some sense, or else the overall argument is self-contradictory due to the nonexistence of evolution.    I suppose you could rescue it by saying just enough of space and time is real to enable evolution, but that seems a little hokey to me.

So, for now, I’ll happily move on with my life in the belief that reality really does exist.    

And this has been your math mutation for today.


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Saturday, January 25, 2020

258: Memory Or Knot

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The discussion of computer memories and time in the last episode brought to mind another form of digital memory I’ve been planning to talk about at some point.   The short life span of our current computer memories is always a potential concern— as you can see in the chart linked in our show notes at mathmutation.com, nearly all current forms of data storage, such as hard drives, flash memories, or floppy disks, will likely last less than 30 years.    For things that are important, data providers and backup services are continually copying and transferring our data.   But did you know that there is a simple form of digital storage that requires no ongoing power, and can last more than 500 years?    I am, of course, talking about the Inca system of knotted strings known as the quipu.

The quipu system, which was used by the Incas of Peru before the Spanish conquest in the 1500s, was actually quite sophisticated for its time.    The knotted strings represented a place-based number system, essentially assigning a region of the string to each digit of a number they wanted to store.   Thus, to record  the number 246 in a quipu, you would put 2 knots in the first region, 4 in the second, and 6 in the third.   They were even aware of the concept of 0 in a place-based system as well, a concept that was just emerging into common use in Europe when the Spanish began conquering the Americas.   The quipu properly represented the digit 0 by having no knots in the corresponding region.   

As another clever enhancement, they had a special type of knot, a “long knot” which involved extra turns of the string, which would always be used only to represent a digit in the ones place.    This way they didn’t have to waste a string if recording a number that was only a couple of digits:  they could start a new number in the next part of the string, by switching to long knots to show they were back in the ones place.   So if you had a 6-segment string, and wanted to store the numbers 246 and 123, you could put them both on the string, without any worry about it being confused for 246,123.  You just had to make sure that you tied the sections representing the 6 and the 3 with long knots.

With this system, the Incas had an easy and efficient way to do proper accounting for business, taxes, and similar issues.    Researchers are pretty certain that this interpretation of quipus is correct, since there are some cases where periodic summary quipus are placed that each show the sum of the previous set of quipus— it would be hard for these sums to work out correctly by luck alone.   There is actually a lot more to these quipus though:  there are many intricate quipus that don’t seem to be recording numbers, and likely have other meanings.   Sadly, the Spanish invaders didn’t think of trying to preserve the quipus or their interpretation, so we don’t have any records of detailed guidance from the original creators of the quipus.    About 900 known quipus have survived to the present day.

There have, however, been some intriguing developments in the last few decades, providing progress in interpreting the non-numerical aspects of this system.  Anthropologist Gary Urton of Harvard noticed that in an area where Spanish census takers had recorded 132 local lords paying tribute, there was a known quipu with exactly 132 strands.   This led to an interpretation where clans could be identified based on the way the quipu cords were attached to the main one.    Also, anthropologist Sabine Hyland from St Andrews University discovered a remote Peruvian village where there were locals who could connect narratives passed down through the generations to a particular set of quipus, leading to further breakthroughs in their interpretation.   She found 95 core combinations of color, fiber, and knot direction, which together may be interpretable as a phonetic system, essentially like letters of the alphabet.  The research is still in progress, but it may be that the quipus were effectively the equivalent of a full written language.

So, if you are nervous about the short lifespan of your computer data, go buy a bundle of strings and start knotting them in a well-defined pattern.   Anything you could save on your hard drive could easily be saved on a sufficient number of quipu strings, and might be more likely to be accessible to your great-great-great-grandchildren.  Just remember to tell someone what they mean before Spanish invaders come knocking at your door.

And this has been your math mutation for today.


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