Math w/o symbols?

May 2015
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32
Arlington, VA
Does mathematics exist without symbolism?
 

topsquark

Math Team
May 2013
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The Astral plane
I'll answer the question with another question: If we have no symbolism, then how do you communicate the number 3?

-Dan
 
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May 2015
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As numbers had arisen : by objects. What was not whole was beyond whole. Eventually, objects evolved into numbers. Today,, "the Piraha, an Amazonian tribe, lacks number words."

Also, the human brain may have archetypes, unconcious appreciation of what would become numbers. The earliest tracable numbers are thought to be notched in stone. Before that, maybe they were sheep, or whatever had value to early man. Mating sheep became more sheep before they were called "three" (or a greater number of) sheep.

The more elementary the mathematics, the more profound it may be, both likely beyond counting. Recall Alfred North Whitehead and Bertrand Russell trying unsuccessfully to explain 1+1=2 in three volumes of Principia Mathematica!
 
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SDK

Sep 2016
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Today,, "the Piraha, an Amazonian tribe, lacks number words."
What makes this desirable? They also lack satellites.
Recall Alfred North Whitehead and Bertrand Russell trying unsuccessfully to explain 1+1=2 in three volumes of Principia Mathematica!
I've heard this argument before and its compelling. Unfortunately, its also completely untrue.
 
May 2015
509
32
Arlington, VA
Our ancestors, and seemingly the Piraha, reached a period where their human brains passed from thinking prelogically to using cognitive symbols for numbers, then translating them into their environment.

How close did Whitehead's and Russell's proof come to argue that 1+1=2, as is widely reported? It is not hard to find many sources on the subject agreeing, with reasonable evidence, that Principia. attempted simple addition, specifically 1+1=2. Where is there a respected and understandable refutation of the "completely untrue " belief?

Truth can be evasive, both in mathematics and politics. Does there exist any absolute proof at all, as Whitehead and Russell missed over decades? I guess my point is that there is none.
 
May 2015
509
32
Arlington, VA
Our ancestors, and seemingly the Piraha, reached a period where their human brains passed from thinking prelogically to using cognitive symbols for numbers, then translating them into their environment.

How close did Whitehead's and Russell's proof come to argue that 1+1=2, as is widely reported? It is not hard to find many sources on the subject agreeing, with reasonable evidence, that Principia. attempted simple addition, specifically 1+1=2. Where is there a respected and understandable refutation of the "completely untrue " belief?

Truth can be evasive, both in mathematics and politics. Does there exist any absolute proof at all, as Whitehead and Russell missed over decades?
 

mathman

Forum Staff
May 2007
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Without symbols, you couldn't have a written language. Symbols for numbers are just a subset.
 
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May 2015
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I speculate that objects preceded their mental representation preceded counting preceded symbols.

At the earliest, of these there was just prelogic.

Object representation followed, begetting the ability to reckon and thus one need for symbology.

I would say that these had selected specializations in the brain, adapting parallel to language in general.
 

SDK

Sep 2016
745
498
USA
How close did Whitehead's and Russell's proof come to argue that 1+1=2, as is widely reported? It is not hard to find many sources on the subject agreeing, with reasonable evidence, that Principia. attempted simple addition, specifically 1+1=2. Where is there a respected and understandable refutation of the "completely untrue " belief?
Its very difficult for me to refute a claim which has no basis in fact. What "argument" should I use to refute it? If I tell you that Hitler was actually a time traveler and was best friends with Harriet Tubman, how would you refute it? What source would you find that even mentions Hitler, time travel, and Harriet Tubman? That doesn't make it true.

More importantly, the onus is not on me to refute your claim. It is on you to prove it. Feel free to link one of those "many sources". Keep in mind your original claim was the following:
Recall Alfred North Whitehead and Bertrand Russell trying unsuccessfully to explain 1+1=2 in three volumes of Principia Mathematica!
I'm interested to see a credible source which claims that they did not understand arithmetic or were unable to prove that 1+1 = 2.
 
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May 2015
509
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Arlington, VA
There are examples of where math exists without symbolism, psychologically and temporally. One possibility is the calculations of a savant. Also, math existing before symbols.

Even in mathematical discovery, there is a "leap of faith" between known math and the unknown, even between 1 and itself. That example too reflects what is "math without symbols."

Do I understand all of the relevant thousands of pages of Principia Mathematica? No, but sometimes one must trust authorities, and I cannot find one on either side of the argument.

Principia relies a lot on symbolism, but I believe is not by itself consistant, as with any proof. However, I guess it is the best insight into the foundation of mathematics made by man.

If I asked Whitehead and Russell why does 1+1=2, I surmise that they would start with axioms, and that even in their logic there might be some subjectivity, such as what a "number" is.