Yesterday was tax day here in the US. It was a brutal brutal tax day. Tax Day typically doesn’t hurt as much when you have income. Being jobless is rough. But enough about financial woes and the G-men getting their due… Let’s get to the topic.
This week’s topic is “Numbers.” Again, thanks go out to Chad and Bart for some of the questions and Some Other Guy for the rest of them.
Here come the questions:
1. Do numbers actually exist?
Not really. You cannot point to something and call it a 5. You can look at something at a dense enough resolution and see and atom, a nucleus, a proton, a neutron, a quark, etc… but you cannot point to an 8. I mean there are symbols that stand for the concept… you get what I’m saying
2. Do you think numbers are discovered or invented?
Numbers are concepts that are both discovered and invented. They are invented pending on how the particular number system works, but they are discovered by playing with previously invented numerical concepts.
3. Can numbers be considered a universal language? Why or why not?
No completely… mainly because our overarching numerical concepts are mostly associated with a base 10 counting system. If a cultural system has a different based numerical system, the language would be nigh unrecognizable.
4. Do you believe in the concept of lucky or unlucky numbers? Why or why not?
Not empirically… but there is comfort associated with some numeric presentations. Interior design really likes an odd number, for example, but 7 is not inherently lucky and 13 is not inherently unlucky.
5. How do different cultures approach the concept of counting and numerical systems? Besides base-10 (decimal), what other counting systems exist, and how do they work?
Okay, the Babylonians had a base 12 system. That looks like anything that is associated with the circle or time. 24 hours in the day, 60 seconds in a minute, 360 degrees in a circle, etc. We deal with a base 12 system all the time. Base 2 or binary is for computer systems because it is math that is determined by “on/open” and “off/closed” positions. Systems that require electricity like computers rely on the off/on, yes/no of binary… this leads to hexadecimal, or base 16. Hexadecimal is also a bit of a machine mathematics as well. One byte of information is made of 8 binary bits, so 2 there are 16 positional possibilities for the on/off system of bits… anyone who has dealt with colors in a computer has had to do things in hexadecimal. Those are the primary number systems in our modern day. Base 10 = number of fingers and thumbs on your hands, Base 12 is the number of joints on your four fingers that you can count using your thumb. Base 2 = on or off, 1 or 0, yes or no. Hexadecimal Base 16 = the binary base (2) to the third power and that multiplied by 2 for the number of on off positions for the bits in a byte of information.
6. Are there any philosophical implications of the infinite nature of numbers?
Of course. Infinity is a weird concept because it is hard for people to get their minds around infinity as being a quantity and because there are different kinds of infinities. There is an infinite amount of numbers between 0 and 1, as well as there being an infinite number of numbers themselves. So… infinity implied both density as well as expansiveness.
7. Do you think artificial intelligence will ever develop an understanding of numbers in a way similar to humans?
It will take a long while for generalized AI to be able to creatively use numbers and mathematics to solve unanswered questions. Generalized AI can already do brute force calculations better than people, but the spark of a new idea for how to use tensor sets for a novel reason will elude AI for a long while.
8. Does the human brain really understand math?
Mostly, yes, but people do not have a great ability to understand large numbers. Our ability to estimate numbers of things is really good until the number of things gets to be around 100. You can look at a pile of nails and say that it is less than 100, but people have a difficult time estimating above that. Our brains just look at the mass of things and think “that is a shit-ton of things” not “That is around 4,356 things.”
9. Can you think of any examples where numbers have been used to deceive or manipulate people?
There is a book called “How to Lie with Statistics,” which goes into all the different ways that you can use real statistics to generate bias.
10. How do numbers contribute to our perception of time, space, and reality?
Time is a consistently propagating dimension for 3 dimensional beings such as ourselves, but time would just be another orthogonal plane to higher dimension beings. We have to segment time to give ourselves an understanding of it, but time (like length, width or depth) is not really these quantized little segments. Time is another plane that we are traveling on. It has topography just like length and width can have topography. The space-time continuum is real.
11. How did civilizations represent and work with numbers before the concept of zero was invented?
Most number systems came about because of accounting. The only reason to keep ledgers is if someone is owed something. Once the imbalance was dealt with, the accounting ledger was just closed. There was no reason to show someone owing 0 eggs to someone else… there was just no longer a debt. That being said, the concept of a placeholder happened with the ancient Babylonians in their clay tablets (they would just poke the back of their stylus into the clay and make a simple round hole to indicate a placeholder or 0)… but that is not most likely the original of nothing, just the first time it was recorded and that record was not destroyed because it was made out of clay. There is a book called “Signifying Nothing” all about the propagation of the concept of zero.
12. Across cultures, certain numbers are considered lucky or unlucky. Why do you think these associations develop?
It often has to be with mathematical operations. 7 is lucky because it is the last prime number before you get to double digits, and 7 things in a row are aesthetically pleasing since there is a middle and it is easily countable. Thirteen is unlucky because 12 is divisible by 2, 3, 4, and 6. 12 is a magical number and an important number because of how it can be factored, so 13 is the first number after that magical number 12 and therefore bad. Other cultures and other significant numbers have similar cultural associations.
13. What are imaginary numbers, and how did mathematicians come to develop the concept?
Imaginary numbers are a bit of a misnomer. These number are no more imaginary than other numbers, they just change something from a simpler set of math being “undefined” to having an actual definition. In the “Real Numbers” system one cannot have the square root of a negative number. The imaginary number i is the square root of -1. This allows us to actually conduct mathematical exercises on previously undefined concepts.
I’m going to go a little bit on a naming convention tangent for a bit here, because the Hellenic Greeks did us dirty with their naming conventions. Here we go, pardon me whilst I get up on my soapbox…
Mathematical systems all build on top of each other. You start with whole numbers (1, 2, 3, 4, etc…) and with the equation 3 - 4, the answer is undefined because there is no negative number in that mathematical system, so we created a set of numbers call integers (...,-3, -2, -1, 0, 1, 2, 3, …), so the previously undefined number 3 - 4 is now known to be -1. Thank you integers. Integers are stepping stones though and do not have any numbers between each other. So, a number like ¾ is undefined in the Integer system, but Pythagorus created a system of mathematics where numbers can be the ratio of 2 integers. These numbers are called “rational” due to the fact that they are “ratios.” Rational numbers can be shown as decimal numbers because they are the ratio of 2 numbers. ¾ becomes 0.75 as a decimal form.
Pythagorous thought all numbers could be broken down into a rational number, the decimal form might continue on for 40 places, but eventually it would solve out and stop being refined. So if you take the ratio of the circumference to the diameter of a circle, the value c/d, the number never stops being resolved, it is an infinite decimal place non-repeating number… which means it cannot ever be ratioed, it is “irrational.”
Now DesCartes, who thinks he is incredibly clever (he was a philosophical ass) in the 1500’s, combines the rational and irrational numbers to become the “Real Numbers” mathematical system. These are “real” numbers because even if they are unable to be resolved as a ratio, they can actually be measured in the “real” world. In the real numbers, the idea of the square root of a negative number is undefined.
Even though the concept of the square root of a negative number was determined to exist by another Hellenic math guy, the ability to do complex mathematical operations on those numbers until some Italian guy (contemporary with DesCartes) formalizes the square root of -1 to be the number “i.” Since the square root of -1 cannot be measured, this system of mathematics became the “Imaginary Numbers.”
This is a naming convention. Imaginary numbers exist just as much as other numbers exist, we have just labeled them with a naming convention that has a very specific cultural meaning. The number i was created as a placeholder denoting a set of mathematical rules, much like 0 is a placeholder that was added to denote nothing. Rational numbers don’t make sense where irrational ones don’t, and real numbers don’t exist in our world where imaginary numbers only live in our wishes, hopes, and dreams. It is a terrible naming convention because the connotation and denotation of the words have different meanings culturally than they do mathematically. The number i, exists just as much as the number 1,786.
Okay, imma get off my soapbox.
14. Did the crime drama "Numb3rs" accurately portray the role of mathematics in solving real-world problems?
No more than any other TV shows portray anyone as doing anything in the real-world. Police procedural shows suck at showing real world policing, and CSI has ruined people’s expectations of what a crime lab can actually do.
15. Our brains struggle to grasp very large numbers. How do mathematicians and scientists communicate these concepts effectively?
I am not sure they do or they can. The idea of a million of anything is truly staggering, and when you get to a billion, it really has no basis in reality.
16. What is arithmophobia, and how can it impact people's lives?
The fear of math, is a bane of most middle to high schoolers who “do not like math.”
17. Why are some people fascinated with calculating Pi to ever-increasing decimal places?
We want it to resolve, we do not like that it continues ad infinitum because we have a staggeringly hard time with concept of infinity.
18. Does numerology, the study of the connection between numbers and events, hold any scientific merit?
Nope
19. How do mathematical principles play a role in creating music and musical harmony?
Music is ultimately sound waves, and waves can be defined by mathematical formulae, and modified by mathematical functions, every filter that people use in audio editing programs is a mathematical function. So the existence of harmonics and doing any kind of waveform manipulation are easily demonstrated as math that plays a role in music.
20. Are there any fundamental mathematical concepts that might forever remain beyond human comprehension?
Yes.
To recap:
Numbers are cool things
But numbers aren’t really things
They’re like a concept
Still on the prowl for a jobby job from Jobfreesborough, TN
Soooo, if you know of a job in UX that needs filling by someone who knows in inordinate amount of mathematical history
I’m that unicorn
I am a purple goddamn unicorn
And, I can divide by zero
I will tell you if you ask
I will write it up as a formal proof if you get me a job
Taxes were hard this year
Taxes are hard every year, but especially since I am sans employment
I have been writing more though
Now I need to get the drawing daily back up and running
Remember you could get this post on my SubStack
Have a great week everyone