Mathematics - 2021-03-06 (page 3 of 4)

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3:00 PM

@Thorgott That paper doesn't look hellish to me

Seems like the authors deftly cut down the problem

Does uniformly bounded have any nice implications about convergence? For example, if I have a uniformly bounded family, does a convergent (sub)sequence converge uniformly? Maybe adding "on compact subsets"?

I am stuck on this problem where I need to show that a uniformly bounded sequence of holomorphic functions (on compact subsets of the domain) uniformly converges to a holomorphic f on compact subsets provided that every subsequence which converges, converges to the same f.

Arzela-Ascoli, yes

@BalarkaSen If you like seeing number theory and probability check out the papers by my colleague in grad school, Redmond McNamara

He has two I think

Thanks! I'll check it out

Matthew Christopher Bartsh

@LeakyNun I don't follow.

3:05 PM

what are your allowed operations?

Matthew Christopher Bartsh

Is that to me?

Arzela-Ascoli gives me that it is a pre-compact subset, so that it is equicontinuous and the sequence acting on a point is a bounded set (for each point in the domain).

Matthew Christopher Bartsh

I didn't say anything about "1".

@LeakyNun Matthew is not too well-versed in the formalities of algebra. You will have to approach it a little bit more softly than that.

@MatthewChristopherBartsh what are we allowed to do to "2" to generate other numbers?

3:08 PM

@MatthewChristopherBartsh Leaky is trying to ask if you have any operations that your set should be "closed under". For example, a set is "closed under addition" if for any two elements a,b of the set, a+b is necessarily in the set as well.

His example was that if division is allowed and 2 is in it, then 2/2 = 1 must be in it as well.

@MatthewChristopherBartsh also I don't understand how you got 2i

Matthew Christopher Bartsh

I am not a mathematician.

I am not good at maths.

@MatthewChristopherBartsh perhaps you can explain your goal, and then we can help you.

Matthew Christopher Bartsh

One goal is to find out what else there is that is like imaginary numbers, or negative numbers, or negative imaginary numbers.

@MatthewChristopherBartsh that was a question not a criticism

I'm only trying to understand your question

3:14 PM

@MatthewChristopherBartsh so like ways to "extend" the numbers?

Matthew Christopher Bartsh

Like them in importance, interestingness, and weirdness.

You could say that anakrho.

If you want to take a step forward from the addition of i, you can also add j and k, kind of like the quaternions. If you wanted to remove i and take a step backwards, you can then go down the route of the hyperreals/surreal numbers, so you can add infinitely large and infinitely small numbers to it.

@MikeMiller ok good one

I suppose you might have the hypercomplex numbers and surrcomplex numbers. :P

Not sure how fun those are, though

Matthew Christopher Bartsh

How to write them so I can extend the list consistently?

This list:

2, -2, 1/2, -1/2, 2i, -2i, i/2, -i/2, ...

3:17 PM

The problem is it's not exactly clear how you want to extend the list.

Matthew Christopher Bartsh

Any way it can be would be a start.

Is 4 in your list?

Matthew Christopher Bartsh

No.

@MatthewChristopherBartsh so how did you get 2i?

Why is 4 not in your list?

Matthew Christopher Bartsh

3:18 PM

I just typed i after 2.

lol

But it's a fair summary.

wow today i learnt

Matthew Christopher Bartsh

What did you learn?

that i can type i after 2 to produce 2i

@MatthewChristopherBartsh why is 4 not on your list?

Was it not on your list yesterday, when you considered 2^2?

Matthew Christopher Bartsh

Because it doesn't contain '2'.

3:20 PM

It does, it is 2^2

Matthew Christopher Bartsh

That's a different list.

Okay, so why is 2^2 not allowed?

It contains 2, of course.

Matthew Christopher Bartsh

Well it might be allowed, if a there's a reason for it to be allowed.

That's the problem, we don't know any of the reasons you have for allowing what you allow.

For example, Leaky asked you why you allowed 2i.

Matthew Christopher Bartsh

But I think there should be only one '2' in each member.

2i has one '2' in it.

3:22 PM

So is sqrt(2) in your set?

Matthew Christopher Bartsh

2^2 has two.

sqrt(2) I did consider. Not sure.

How about 1+2?

Matthew Christopher Bartsh

sqrt(2) is an important number

But is sqrt(8) important?

Arguably all numbers are important.

But that's besides the point. Is 1+2 in your set?

Matthew Christopher Bartsh

Not in set.

But it could be if there was a reason to add it.

3:27 PM

Why is it not in the set?

Matthew Christopher Bartsh

Because it is not a form of 2.

-2 is negative 2

2i is imaginary 2 (?)

Then why is 1/2 in the set?

Matthew Christopher Bartsh

1/2 is reciprocal 2

*the reciprocal of 2

1+2 is what happens when you add 1 to 2. What's wrong with that?

Matthew Christopher Bartsh

It's not a form of two.

3:30 PM

Seems like a form of 2 in the same way 1/2 is.

1 "some operation" 2.

Matthew Christopher Bartsh

3 and 1/3 and so one would be another parallel list.

*a parallel list

No point in redundancy.

If you can see at this point, you arbitrarily add new conditions to be in this set.

Matthew Christopher Bartsh

Or to put it another way. I am interested in powers of two and not in 3.

So it makes it very difficult to help.

But you are not interested in powers of 2. You didn't want 2^2.

Matthew Christopher Bartsh

4, 1/4, -4, and so on is also a parallel list.

So that would be redundant.

But yes, I am interested in 4, and 8, and all other powers of two.

I want 4, but on a different sublist/paralllel list.

3:36 PM

I recommend you figure out exactly what you want, and then ask when you know that.

Matthew Christopher Bartsh

I told you. I want the list to be longer.

Or to know that it can't be made longer.

Add 1 to it, then.

Matthew Christopher Bartsh

Why does 1 belong?

You just said you wanted it longer.

Matthew Christopher Bartsh

1 belongs in the sublist of 1, -1, i

3:38 PM

But 2-1 = 1. So I don't see why it can't be there. or 2^0 = 1.

is e^2 in the set?

how about sin(2)?

log(2)?

Matthew Christopher Bartsh

Is e^2 a number commonly mentioned?

Yes.

Matthew Christopher Bartsh

What about e^4?

Yes, e^x is very important in math

same with log(x)

and sin(x)

Without these, math would not be the same.

TREE(2), as well.

Matthew Christopher Bartsh

3:41 PM

base ten log?

What's TREE(2)?

TREE function, very important.

Matthew Christopher Bartsh

My goal is to create a system of easily-pronounced names of commonly-mentioned and/or interesting numbers especially powers or two and their reciprocals, and other variants/extensions such that the name of each number can be easily deduced from a small set easily learned rules. I've already published some of this.

What I am trying to do in this conversation with you is to find out what other things I could usefully create names for.

*powers of two

what other numbers

do you by any chance call 2, "two"?

Or maybe "deux"

Matthew Christopher Bartsh

I haven't created names for imaginary powers of two yet, but it seems like an interesting idea. I am wondering what other variants of powers of two besides negatives, reciprocals, and imaginaries might be good to make names for.

or "dos"?

Matthew Christopher Bartsh

3:54 PM

I sometimes call it 'two', and I sometimes call it 'deux'.

Usually I call it 'two'.

I sometimes call it 'ti'.

That's a name I created for 2.

How I sometimes count in binary:

si, ti, ti si, ni, ni si, ni ti, ni ti si, mi, mi si, mi ti.

Translation: one, two, two one, four, four one, four two, four two one, eight, eight one, eight two.

the difficulty seems to be less in developing a system than in getting people to adopt it. it might be better of the US were on the metric system, for example. but fat chance of doing that.

Matthew Christopher Bartsh

AKA: One, two, three, four, five, six, seven, eight, nine, ten.

The metric system is based on base ten.

That makes it seriously flawed, in my opinion.

there are groups of people who want to switch to base eight. i've also seen base twelve as a possibility. good luck to them i guess.

Fortunately for us, people already know how to communicate numbers to each other without difficulty, as evidenced by the fact that they have been doing it for centuries. Absolute crankery. Fortunately for you, there's plenty of people here with time to kill who will engage with you.

Matthew Christopher Bartsh

Gallons, quarts, and pints are 'dyadic', to use a word I learned only today.

4:02 PM

But for my part, I am done. Good luck with your Dr. Seuss names.

Matthew Christopher Bartsh

That makes them better in a way.

We humans could have developed a base 12 system using the phalanges of our index-middle-ring-baby fingers :D

Matthew Christopher Bartsh

Don't you think you should prove me wrong if I am wrong. This is a completely new idea as far as I know.

i've never seen the attraction of base 12. base 8 i kind of get. is it just that 12 has a lot of divisors?

@leslietownes yeah

4:04 PM

well that's just silly.

Matthew Christopher Bartsh

I admire Dr. Seuss and his work.

Base 12 is superior to base ten.

Coming from someone who claimed to not be good at math, I am not sure if we should trust you.

Matthew Christopher Bartsh

It's very obvious that it is superior. It has everything that base ten has and a bit more.

thomas koerner has a good book, the pleasures of counting. it's pitched at a high school audience. it has a thoughtful discussion of alternate bases and a hilarious tour of the pre-metric system of british currency.

there are exercises where interest rates are stated in shillings and tuppence and whatever, and you get to figure out the payments. it's a lot of fun if you like changing units.

Matthew Christopher Bartsh

What is harder to explain to people is why base 8 is better than base 12.

4:06 PM

not a lot of fun for anybody else.

@MatthewChristopherBartsh It doesn't rhyme

Matthew Christopher Bartsh

What doesn't rhyme?

"I admire Dr. Seuss and his work.
Base 12 is superior to base ten."

seuss also may have avoided the word 'superior.' he liked to keep the words simple.

base twelve is something the cat in the hat would bring into the house. it's appropriately anarchic. mom and dad will not be happy to see it in the house when they get home.

Matthew Christopher Bartsh

@anakhro I'm not asking anyone to trust me. Judge my ideas on their own merits.

@leslietownes I agree.

I respect those that champion base twelve.

At least they can see how flawed base ten is.

On the other hand, they don't see how great it is to have a base that is a power of two.

4:13 PM

Efforts to push people to adopt bases other than ten will go the way of the Latino Sine Flexione.

Matthew Christopher Bartsh

Bases, 2, 4, 8, 16 are clearly awesome. Maybe also bases 32, 64 or even larger.

Latino Sine Flexione.
What is that?

that's a good parallel. devotees of alternate bases and constructed languages have something similar to one another

Matthew Christopher Bartsh

I have done a lot of thinking about conlangs.

@leslietownes both get ignored reasonably by the public.

yeah, there's a mix of being ignored, and also maybe in some sense being right that if we could do it all over again we might have made different and better choices.

4:15 PM

is $P(X = r | X \sim D) = y$ appropriate notation for conditional probability? what I want to say with it is "if X has distribution D the probability of $X=r$ is y"

and persisting in the campaign despite the impossibility of it all.

i tend not to see the probability distribution specified within P( ) although that is an interesting idea. probabilistic notation is often overloaded and your way would simplify that.

Matthew Christopher Bartsh

I've never seen a conlang that I thought was worth learning.

@leslietownes thanks for the input, I guess I'll roll with it then

i like the English language, in all of its ugliness. particularly its rich trove of profanity.

Matthew Christopher Bartsh

Many names have been created for hexadecimal numbers, and some sets are perhaps worth learning. But you need to memorize all the names. That's why I came up with my naming system. My names can be deduced. They are also more concise, but that is not the main thing.

4:21 PM

i also like Spanish. my daughter is apparently better at it than English at school. she stumbles over English grammar but not Spanish. she doesn't speak it at home, so i have no idea.

porridgemathematics

if $A,B,C$ are groups and $A \oplus C \equiv B \oplus C$ then certainly $A \equiv B$ right?

Matthew Christopher Bartsh

@leslietownes Absolutely. I love English passionately.

porridgemathematics

just a sanity check

i expect that you will need more hypotheses for that. it makes me nervous. no counterexamples come to mind.

Yeah, I agree it makes me nervous, too.

porridgemathematics

4:22 PM

i feel like it has to be true

because, cmon, right?

i know that isnt a proof, lol

Matthew Christopher Bartsh

I like Spanish a lot, though I only speak a smattering of it. I like foreign languages, phonetics, poetry in English and other languages. I also like profanity in all languages.

here is someone handling the case of finite abelian groups. math.stackexchange.com/questions/3579745/…

here is a purported counterexample outside the world of finitely generated groups, but still abelian groups. math.stackexchange.com/questions/2519951/…

porridgemathematics

ouch

abelian groups in general are scary.

porridgemathematics

what if $C = \mathbb{Z}$?

Matthew Christopher Bartsh

4:24 PM

I seem to be the first to have created a set of new names to be used in counting out loud in binary.

Does the case for C=Z follow from the classification of finitely generated Abelian groups (for finitely generated Abelian groups)?

Matthew Christopher Bartsh

I need to go do something. Thanks for the conversation.

there's a paper "On Cancellation in Groups" by Hirshon

the result is that all finite groups can be cancelled from direct products

(groups, not necessarily abelian)

that's great

This is what keeps up Thorgott at night

4:30 PM

Thorgott has bigger fish to fry than this.

really great birding in my yard right now. three northern flickers, two western bluebirds, a black phoebe, and a house finch. all just hopping around and enjoying life.

what keeps me up at night is trying to understand Novikov additivity

does any of you know this?

I remember it being hell

also, the paper by Hirshon contains an example of Z not being cancellable as well

Tell me about it

4:33 PM

i was friends with somebody who knew it in graduate school. that's useless, but also true.

Tell me a proof with boldface at places you get stuck

Surely that says signature is additive under connected sum for $4k$-manifolds or something

It's a boundary pasting thing

He can probably prove it using Atiyah-Patodi-Singer index formula

Lol

signature is additive under gluing along boundaries

is the statement

4:35 PM

What's the signature on a manifold with boundary

I'm actually trying to read the proof in Atiyah-Singer Index of Elliptic Operators III, Section 7

I guess signature of pairing on H^n/2(M, dM)

mathoverflow.net/questions/69167/… has links to some proofs, some behind paywalls and some not. not the atiyah singer proof.

the argument doesn't use the index theorem or anything from the previous 6 sections, let alone the previous 2 papers, though

@MikeMiller yeah

this pairing is degenerate in general

but it descends to a non-degenerate pairing on the image of H^{n/2}(M,dM)->H^{n/2}(M) by Lefschetz duality

Ye I just forgot that doesn't matter

4:36 PM

it's weird that atiyah and singer are both gone now.

I don't think it's weird that people die.

Anyway I need to do some computations tell me your proof and I will check back once I've gotten something pinned down here

i realize they were both quite long-lived. it's just weird to see the world i 'grew up' in vanish. you do feel like people are going to be around forever. or at least i do.

ok, I shall recast the argument

the papers are still here, anyway

4:52 PM

@MikeMiller what's the Patodi part?

Boundary term

Oh, interesting.

5:10 PM

@leslietownes Not my experience, personally, though I hope it's obvious I don't fault anyone for having a different experience than I do

Death is a sad occurrence, to me, but not a weird or eerie one

i still hear my advisor's voice in my head sometimes. i don't even do math anymore, but i hear it. "hrm." when i could have done better.

Can't tell if that's good or bad.

it's good. i mean i'm not really hearing the voice. that might be bad.

Sure. I had one of the most kind and supportive advisors I could ask for. That did not stop me from getting anxiety about not being productive or clever enough. So I could easily imagine those memories being stressful.

yeah some people really get mentally beaten up. thankfully it was not my experience.

Matthew Christopher Bartsh

5:18 PM

Imagine wondering whether you are a crank and not being able to find out.

An easy test in your case is to ask yourself whether you believe you actually have objective evidence that base 10 is bad and should not be used for math. If so, you can safely assume you are a crank.

i never understood my advisor fully until i saw him give a very friendly pep talk to someone who had given a talk that had gone very badly. i realized that for him, friendliness was something you applied to people who seemed like they maybe needed encouragement to a better direction. people going in the right direction got "hrm."

porridgemathematics

well what is 'objective evidence'

Matthew Christopher Bartsh

I don't believe that.

@porridgemathematics I think the colloquial definition is decent enough.

5:20 PM

@leslietownes This is a good attitude. Different students, in different moments, need different support.

Matthew Christopher Bartsh

I mean, I don't believe that base 10 should not be used for math.

@porridgemathematics Good question.

has anybody read underwood dudley's books on the subject? there's a general one called mathematical cranks, and another one specific to trisection.

porridgemathematics

anakhro yeah but, my point is that you could probably make a heuristic argument for more factorizable bases, and compute that if the world was different we would be more inefficient in these areas and less efficient in these areas, but the other areas don't matter as much etc etc, this is not crank argumentation at all

anakhro that being said, you know you aren

Matthew Christopher Bartsh

I haven't read it. What does he say?

porridgemathematics

*aren't a crank if you can see that bases are not needed for doing mathematics conceptually

5:21 PM

he was sued once for calling somebody a crank. it was dismissed in an appellate opinion by noted jurist richard posner.

porridgemathematics

the cranks ive met are stuck on the concept of bases as some necessary tool

*more efficient in these areas and less efficient in ... , whoops :)

he doesn't say much about cranks. he goes and visits people who have unorthodox ideas and reports on his findings. and the trisectors book is just a list of approximate trisections.

I think I leafed through a copy of one in undergrad. It was pleasant, but I've lost what was in there.

augustus de morgan wrote a bunch of articles about crankery, many of them are still very informative. dover published it as 'a budget of paradoxes,' two volumes in one package.

Matthew Christopher Bartsh

I can see that you can do all maths using base 10.

5:23 PM

Same with "mathematics made difficult". For that one I can recover the jokes by reading an nLab article.

porridgemathematics

or no bases at all..

bases are just coordinates, and you can always work coordinate free

Matthew Christopher Bartsh

@porridgemathematics What do you mean?

@MikeMiller oof

a lot of the cranks he corresponds with are fairly highly trained people with a lot of free time that they have poured into stuff like trisecting the angle. this objectively false and misguided crankery is distinguishable from just being unorthodox about ideas that are not likely to ever be widely shared.

de morgan's book is more about the latter topic

"As an axiom on which to base the positive numbers and the integers,
which have in the past produced much harmless amusement and are
still widely accepted as useful by most mathematicians, some such
proposition as the following is sometimes considered as being
pleasant, elegant, or at least handy:
AXIOM: Equalisers exist in the category of categories."

porridgemathematics

5:25 PM

@MatthewChristopherBartsh you can think of a 'base' as a coordinate system for a sequence space

Matthew Christopher Bartsh

My main complaint with base 10 is that repeated doubling or halving generates more and more decimal places of numbers. This is mitigated in base 12 but only so far.

@porridgemathematics if you could formulate a successful heuristic to make such a claim about efficiency, I would be thoroughly impressed.

porridgemathematics

you can probably make this precise, but im not trying to do that

Matthew Christopher Bartsh

What is a sequence space?

porridgemathematics

@anakhro you don't think such a heuristic exists?

5:26 PM

there's trisections in there too, but some of the crankier topics are really goofy stuff. someone wrote a pamphlet on the sun maybe being a gigantic ball of ice. (it acted like a lens, focusing stuff from somewhere else.) and flat earth stuff is in there.

porridgemathematics

Im not saying I can formulate it, im just stipulating one likely exists

de morgan's father in law denied the existence of negative numbers. i think he was sympathetic to crankery on at least that basis.

@porridgemathematics I don't see any evidence that suggests one exists.

porridgemathematics

@anakhro here is another way of thinking about it, do you think that it is likely base $10$ is optimal for humans ?

Matthew Christopher Bartsh

Define "exist".

porridgemathematics

5:27 PM

that we've landed on the optimal base, and that no other base would serve us better in totality

@porridgemathematics I don't think "optimal for humans" is very quantifiable as stated. Or said another way, I have not seen any evidence that suggests that changing the base would result in a radical change to the way we do mathematics.

radical/meaningful

porridgemathematics

@Matthew you do not need bases to define $\mathbb{Z}$ or $\mathbb{Q}$ or $\mathbb{R}$ t

@anakhro yeah Im not talking about mathematics, im talking about how easy it is for an average person to learn arithmetic, to compute things in their heads, etc

mathematics would hardly change

@Thorgott Grabbed a PDF to give another classical example

i think the need for hand computation has mostly vanished with the advent of technology. this has largely wiped out any considerations for how we represent numbers. most people encounter numbers mainly in buying and selling things, where usually past experience in buying and selling informs what the prices ought to be, at least approximately. i don't need to perform calculations in any base to know that $5 for an apple is too much.

unless it is a honeycrisp in peak condition, then i'd consider it

Matthew Christopher Bartsh

Using the spaces between the fingers, you would naturally count in base eight. And I think there is a tribe somewhere that does that, in base eight. So we may have narrowly missed using base 8, even given that we have ten fingers.

porridgemathematics

5:31 PM

@leslietownes fair point, maybe at this point in time the argument I'm making is weak, but at a time before the advent of technology it could be stronger, and then perhaps the positive externalities of the different base at that prior point might accelerate where we could be today

@leslietownes I disagree with this, though what it is needed for is different. One should certainly be able to do pretty trivial arithmetic when making sure you know how much you're spending at the grocery store before getting to the checkout aisle, but I don't consider that the important reason. More importantly people who are not used to computation tend not to have any number sense and fail to make sanity checks.

Matthew Christopher Bartsh

You can of course ignore the thumbs, but no tribe has done that it seems.

If their calculator gives them a nonsense answer they jot it down and move on because the calculator Knows.

@porridgemathematics if we are not talking about math, then I am not sure what we are talking about. My original statement was "have objective evidence that base 10 is bad and should not be used for math."

porridgemathematics

@anakhro im talking about minimizing inefficiencies in day to day living

which is what cranks are usually actually trying to argue for

5:32 PM

i do hope my daughter learns all of the usual algorithms but the need for performing and organizing complex calculations by hand no longer exists. so the advantages of system X over system Y are marginal at best. now. if we could go back in time maybe numeracy would have been improved, but you really can't retrofit it after centuries of this baggage.

porridgemathematics

although they conflate that with 'better for mathematics'

How many people do you know compute arithmetic in their head in "day to day living"?

Your last statement is more specific and I agree with it.

Internal to math by-hand computation gives one a sense of how things you're working with behave. But I don't think I need to convince people who are studying linear algebra that it's worth knowing how to add and multiply in their head, so I don't tend to make this point.

porridgemathematics

@anakhro I do a lot actually, its normally computations involving time and scheduling my day

and I agree with @MikeMiller 's number sense comments

@porridgemathematics so is your experience representative of the average person's?

porridgemathematics

5:35 PM

@anakhro well, we all do need to manage our time, we are implicitly doing computations to do so, anyway I apologize for misunderstanding your point

i do wish people would just think critically about statements about numbers. i don't think this is base specific. you see all kinds of wild claims that would fail under half a second of critical thinking, but once there's a number, people are conditioned to act like that's authoritative. like it's doing something that normal words don't. there's no change of base that will get us out of number mysticism.

or maybe there is. i've begun to become a devotee of base 17. let me explain this a little. it's a pamphlet. if you venmo me money you'll get the real truth.

@porridgemathematics You don't need to apologize for anything. But do you think that the perceived benefits of changing to a different base would actually yield a meaningful difference given that you are limiting peoples' use of arithmetic to scheduling their day? Like if you can make everyone's computations 1 second faster (just as a random number), do you think people would honestly save more than a minute on doing arithmetic in a day?

can i pay in bitcoin instead

i only accept dogecoin and base17coin, which is my new cryptocurrency.

Well, I'm happy to give you $100 for a good book, but I'll be expressing that in base 17 when submitting the venmo transaction.

I guess you still make out with about half that.

5:39 PM

the benefits of base 17 are mainly that they free us from old ways of thinking. it is like being born into a new world.

i may have carried this too far and i will stop now.

Matthew Christopher Bartsh

A minute a day is six hours a year. Sixty hours a decade.

@leslietownes I think what you say is useful and interesting.

we are at war with the devotees of base 19. there can be only one base.

porridgemathematics

@anakhro I can't make a good argument that an average person would save much time, the best I can come up with is one that involves retrofitting the argument to a past time, and then conjecturing we would be much bigger brained today because our ancestors were sharper with number sense

i think most of number sense is just attention span. people who don't cultivate it won't have it. we could have an oracle that provides us precise answers to everything and it would not improve the world one bit.

@porridgemathematics You could try such a retrofitting, but I don't think it would be convincing. There is far too much baggage when it comes to "what could have been".

5:44 PM

i'm cynical

@Thorgott see here

Matthew Christopher Bartsh

The computer would presumably have been invented sooner, right?

porridgemathematics

@anakhro agreed, it isn't convincing

user image

porridgemathematics

@anakhro another hunch I have is that were somehow stipulating in all this that base $10$ is optimal in some sense that I cannot define, and it is likely that we are wrong, again not saying this is convincing, but it may be over a drink

here again I emphasize I mean optimal in a grander sense than 'for proving theorems'

5:45 PM

lmao

that's very similar to what de morgan had to argue against his father in law. i'm glad that i have no idea of my father in law's position on negative numbers.

porridgemathematics

which I totally agree, it would make no difference

Maybe a dozen drinks and a few lines of white powder.

that book is filled with gems

Matthew Christopher Bartsh

Being able to repeatedly double and halve with the number still ending in zero is important for visualizing a lot of things. The earth for example, and latitude and longitude.

The sky and declination and right ascension.

Base ten or twelve or seventeen or nineteen don't work as well as a base that is a power of two, for example, base sixteen.

Visualization is important not just for understanding but also for memory (memorization).

People don't get worse a English if they learn French and/or Chinese. Likewise, people would surely not get worse at base ten if they got fluent in base sixteen.

porridgemathematics

5:54 PM

actually, I'm pretty convinced with what you just said

Matthew Christopher Bartsh

*at English

porridgemathematics

so I suppose from your perspective learning multiple bases would enhance mathematical ability at least in the sense of numeracy

but I think most people believe it wouldn't matter at all in the context of theorem proving, nowadays

which makes sense, because its rare to really come across 'numbers' in a strict sense

Matthew Christopher Bartsh

I'm not a mathematician, and I'm not good at maths. However, I am numerate.

I barely know what a number is

been years since I last saw one

i was thrilled to publish a paper with numbers with decimal points in it. this was a sticking point for one of the reviewers.

5:58 PM

@leslietownes lol

Matthew Christopher Bartsh

@porridgemathematics Thanks Porridge. Does this mean I am not a crank?

given your Medium articles, you still are.

porridgemathematics

@MatthewChristopherBartsh you don't sound like one to me

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Mar '216

$Mathematics$ Mathematics

Associated with Math.SE; for both general discussion & math qu...

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